scientific problems that need solving

January 6, 2020

The Most Important Scientific Problems Have Yet to Be Solved

If certain areas of science appear to be quite mature, others are in the process of development, and yet others remain to be born

By Santiago Ramón y Cajal

Santiago Ramón y Cajal in the 1880s.

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American

Santiago Ramón y Cajal (1852-1934) was a neuroscientist and pathologist, and Spain’s first Nobel laureate. This excerpt from his book Advice for a Young Investigator was first posted on the MIT Press Reader on January 6, 2020. An essay on his remarkable scientific drawings appeared in Scientific American in 2015.

Here is a false concept often heard from the lips of the newly graduated: “Everything of major importance in the various areas of science has already been clarified. What difference does it make if I add some minor detail or gather up what is left in some field where more diligent observers have already collected the abundant, ripe grain. Science won’t change its perspective because of my work, and my name will never emerge from obscurity.”

This is often indolence masquerading as modesty. However, it is also expressed by worthy young men reflecting on the first pangs of dismay experienced when undertaking some major project. This superficial concept of science must be eradicated by the young investigator who does not wish to fail, hopelessly overcome by the struggle developing in his mind between the utilitarian suggestions that are part and parcel of his ethical environment (which may soon convert him to an ordinary and financially successful general practitioner), and those nobler impulses of duty and loyalty urging him on to achievement and honor.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

Wanting to earn the trust placed in him by his mentors, the inexperienced observer hopes to discover a new lode at the earth’s surface, where easy exploration will build his reputation quickly. Unfortunately, with his first excursions into the literature hardly begun, he is shocked to find that the metal lies deep within the ground—surface deposits have been virtually exhausted by observers fortunate enough to arrive earlier and exercise their simple right of eminent domain.

It is nevertheless true that if we arrived on the scene too late for certain problems, we were also born too early to help solve others. Within a century we shall come, by the natural course of events, to monopolize science, plunder its major assets, and harvest its vast fields of data.

Yet we must recognize that there are times when, on the heels of a chance discovery or the development of an important new technique, magnificent scientific discoveries occur one after another as if by spontaneous generation. This happened during the Renaissance when Descartes, Pascal, Galileo, Bacon, Boyle, Newton, our own Sanchez, and others revealed clearly the errors of the ancients and spread the belief that the Greeks, far from exhausting the field of science, had scarcely taken the first steps in understanding the universe. It is a wonderful and fortunate thing for a scientist to be born during one of these great decisive moments in the history of ideas, when much of what has been done in the past is invalidated. Under these circumstances, it could not be easier to choose a fertile area of investigation.

However, let us not exaggerate the importance of such events. Instead, bear in mind that even in our own time science is often built on the ruins of theories once thought to be indestructible. It is important to realize that if certain areas of science appear to be quite mature, others are in the process of development, and yet others remain to be born. Especially in biology, where immense amounts of work have been carried out during the last century, the most essential problems remain unsolved—the origin of life, the problems of heredity and development, the structure and chemical composition of the cell, and so on.

It is fair to say that, in general, no problems have been exhausted; instead, men have been exhausted by the problems. Soil that appears impoverished to one researcher reveals its fertility to another. Fresh talent approaching the analysis of a problem without prejudice will always see new possibilities—some aspect not considered by those who believe that a subject is fully understood. Our knowledge is so fragmentary that unexpected findings appear in even the most fully explored topics. Who, a few short years ago, would have suspected that light and heat still held scientific secrets in reserve? Nevertheless, we now have  argon  in the atmosphere, the  x-rays  of Roentgen, and the  radium  of the Curies, all of which illustrate the inadequacy of our former methods, and the prematurity of our former syntheses.

The best application of the following beautiful dictum of Geoffroy Saint-Hilaire is in biology: “The infinite is always before us.” And the same applies to Carnoy’s no less graphic thought: “Science is a perpetual creative process.” Not everyone is destined to venture into the forest and by sheer determination carve out a serviceable road. However, even the most humble among us can take advantage of the path opened by genius and by traveling along it extract one or another secret from the unknown.

If the beginner is willing to accept the role of gathering details that escaped the wise discoverer, he can be assured that those searching for minutiae eventually acquire an analytical sense so discriminating, and powers of observation so keen, that they are able to solve important problems successfully.

So many apparently trivial observations have led investigators with a thorough knowledge of methods to great scientific conquests! Furthermore, we must bear in mind that because science relentlessly differentiates, the minutiae of today often become important principles tomorrow.

It is also essential to remember that our appreciation of what is important and what is minor, what is great and what is small, is based on false wisdom, on a true anthropomorphic error. Superior and inferior do not exist in nature, nor do primary and secondary relationships. The hierarchies that our minds take pleasure in assigning to natural phenomena arise from the fact that instead of considering things individually, and how they are interrelated, we view them strictly from the perspective of their usefulness or the pleasure they give us. In the chain of life all links are equally valuable because all prove equally necessary.

Things that we see from a distance or do not know how to evaluate are considered small. Even assuming the perspective of human egotism, think how many issues of profound importance to humanity lie within the protoplasm of the simplest microbe! Nothing seems more important in bacteriology than a knowledge of infectious bacteria, and nothing more secondary than the inoffensive microbes that grow abundantly in decomposing organic material. Nevertheless, if these humble fungi—whose mission is to return to the general circulation of matter those substances incorporated by the higher plants and animals—were to disappear, humans could not inhabit the planet.

The far-reaching importance of attention to detail in technical methodology is perhaps demonstrated more clearly in biology than in any other sphere. To cite but one example, recall that Koch, the great German bacteriologist, thought of adding a little alkali to a basic aniline dye, and this allowed him to stain and thus discover the tubercle bacillus—revealing the etiology of a disease that had until then remained uncontrolled by the wisdom of the most illustrious pathologists.

Even the most prominent of the great geniuses have demonstrated a lack of intellectual perspective in the appraisal of scientific insights. Today, we can find many seeds of great discoveries that were mentioned as curiosities of little importance in the writings of the ancients, and even in those of the wise men of the Renaissance. Lost in the pages of a confused theological treatise ( Christianismi restitutio ) are three apparently disdainful lines written by Servetus referring to the pulmonary circulation, which now constitute his major claim to fame. The Aragonese philosopher would be surprised indeed if he were to rise from the dead today. He would find his laborious metaphysical disquisitions totally forgotten, whereas the observation he used simply to argue for the residence of the soul in the blood is widely praised! Or again, it has been inferred from a passage of Seneca’s that the ancients knew the magnifying powers of a crystal sphere filled with water. Who would have suspected that in this phenomenon of magnification, disregarded for centuries, slumbered the embryo of two powerful analytical instruments, the microscope and telescope—and two equally great sciences, biology and astronomy!

In summary, there are no small problems. Problems that appear small are large problems that are not understood. Instead of tiny details unworthy of the intellectual, we have men whose tiny intellects cannot rise to penetrate the infinitesimal. Nature is a harmonious mechanism where all parts, including those appearing to play a secondary role, cooperate in the functional whole. In contemplating this mechanism, shallow men arbitrarily divide its parts into essential and secondary, whereas the insightful thinker is content with classifying them as understood and poorly understood, ignoring for the moment their size and immediately useful properties. No one can predict their importance in the future.

Science leads the response to COVID-19. These 25 scientists are tackling the other global challenges

Introducing the Class of 2020 Young Scientists Image:  Photo by Drew Hays on Unsplash

.chakra .wef-1c7l3mo{-webkit-transition:all 0.15s ease-out;transition:all 0.15s ease-out;cursor:pointer;-webkit-text-decoration:none;text-decoration:none;outline:none;color:inherit;}.chakra .wef-1c7l3mo:hover,.chakra .wef-1c7l3mo[data-hover]{-webkit-text-decoration:underline;text-decoration:underline;}.chakra .wef-1c7l3mo:focus,.chakra .wef-1c7l3mo[data-focus]{box-shadow:0 0 0 3px rgba(168,203,251,0.5);} Alice Hazelton

Martha chahary.

.chakra .wef-9dduvl{margin-top:16px;margin-bottom:16px;line-height:1.388;font-size:1.25rem;}@media screen and (min-width:56.5rem){.chakra .wef-9dduvl{font-size:1.125rem;}} Explore and monitor how .chakra .wef-15eoq1r{margin-top:16px;margin-bottom:16px;line-height:1.388;font-size:1.25rem;color:#F7DB5E;}@media screen and (min-width:56.5rem){.chakra .wef-15eoq1r{font-size:1.125rem;}} COVID-19 is affecting economies, industries and global issues

.chakra .wef-1nk5u5d{margin-top:16px;margin-bottom:16px;line-height:1.388;color:#2846F8;font-size:1.25rem;}@media screen and (min-width:56.5rem){.chakra .wef-1nk5u5d{font-size:1.125rem;}} Get involved with our crowdsourced digital platform to deliver impact at scale

Stay up to date:.

• Scientists have maximum visibility in the COVID-19 response, while proposing solutions to other global challenges, from climate change to cybersecurity, poverty to pandemics, and food technologies to fracking.
• The World Economic Forum created the Young Scientists Community in 2008, to engage leaders with science and the role it plays in society. The class of 2020 represents 25 researchers at the forefront of scientific discovery from 14 countries across the world.

The COVID-19 crisis has highlighted science’s vital role in society. Science will provide us with an “exit strategy” from the pandemic when a vaccine is finally developed but until then, scientists are helping to understand the origins of the virus, how it spreads, what treatment(s) are most effective and indeed if a cure is possible.

Scientists have maximum visibility right now as different groups of people turn to them looking for answers. COVID-19 aside, science proposes solutions to the myriad of other global challenges facing society, from climate change to cybersecurity, poverty to pandemics, and food technologies to fracking.

Have you read?

Here’s how ‘science diplomacy’ can help us contain covid-19, bill gates explains how the world can use science to tackle the crisis.

That’s part of the reason why the World Economic Forum created the Young Scientists Community in 2008, to engage leaders with science and the role it plays in society. Science is no longer a specialist concern. It is the driving force behind the highest-level decisions on global governance and policy-making, while also informing the individual choices people make about how they want to live and what changes they want to make.

Today we announce our Class of 2020 Young Scientists, representing 25 exceptional researchers at the forefront of scientific discovery from 14 countries across the world.

From chemical oceanography to child psychology and artificial intelligence, these brilliant young academics are joining a community whose aims are to:

• Communicate cutting-edge research and position science discourse within the context of scientific evidence.
• Develop leadership skills and a fuller understanding of global, regional and industry agendas.
• Build a diverse global community of next-generation scientific leaders, committed to engaging in collaborations related to collectively identified issues.

Responding to the COVID-19 pandemic requires global cooperation among governments, international organizations and the business community , which is at the centre of the World Economic Forum’s mission as the International Organization for Public-Private Cooperation.

Since its launch on 11 March, the Forum’s COVID Action Platform has brought together 1,667 stakeholders from 1,106 businesses and organizations to mitigate the risk and impact of the unprecedented global health emergency that is COVID-19.

The platform is created with the support of the World Health Organization and is open to all businesses and industry groups, as well as other stakeholders, aiming to integrate and inform joint action.

As an organization, the Forum has a track record of supporting efforts to contain epidemics. In 2017, at our Annual Meeting, the Coalition for Epidemic Preparedness Innovations (CEPI) was launched – bringing together experts from government, business, health, academia and civil society to accelerate the development of vaccines. CEPI is currently supporting the race to develop a vaccine against this strand of the coronavirus.

By joining Forum events, engaging in personal and professional learning modules and sharing experiences with each other, we’re looking forward to working with the Class of 2020 Young Scientists to help leaders from the public and private sector engage more meaningfully with science and in doing so, help these amazing young researchers become stronger ambassadors for science.

Here are the World Economic Forum’s Young Scientists of 2020:

From Africa:

Sarah Fawcett (University of Cape Town, South Africa, South African): Sarah researches the role of ocean chemistry and biology in climate, as well as the impacts of human activities on marine environments.

Salome Maswime (University of Cape Town, South Africa, South African): Salome seeks to understand surgical health systems and causes of maternal death during caesarean section in poorly resourced areas to improve surgical care across populations.

From the Americas:

Gao Wei ( California Institute of Technology, USA, Chinese): Gao Wei develops skin-interfaced wearable biosensors that will enable analytics through sweat rather than blood, leading to non-invasive and real-time analysis and timely medical intervention.

Francisca Garay (Pontificia Universidad Católica de Chile, Chile, Chilean): Francisca is studying what are the most basic building blocks of the universe by developing technologies to accelerate and enhance the capabilities of particle accelerators.

Diego Garcia-Huidobro (Pontificia Universidad Católica de Chile, Chile, Chilean): Diego uses human-centred design methods to develop sustainable and scalable community-level health interventions in Chile.

Jennifer Ronholm (McGill University, Canada, Canadian): Jennifer is working to strengthen the microbiome of agricultural animals to resist infections in the absence of antibiotics, with the aim of reducing the spread of antimicrobial resistance.

Stefanie Sydlik (Carnegie Mellon University, USA, American): Stefanie designs new materials that stimulate the body's healing response to enable the regeneration of natural bone as an alternative to metal implants currently used to heal bone injuries.

Fatma Zeynep Temel (Carnegie Mellon University, USA, Turkish): Fatma uses mathematical models and physical prototypes to test and explore biologically inspired designs, leading to the development of small-scale robots and sensors

Lee Sue-Hyun (Korea Advanced Institute of Science and Technology, South Korea, Korean): Sue-Hyun researches how memories are recalled and updated, and how emotional processes affect human memory, to inform therapeutic interventions for mental disorders.

Meng Ke (Tsinghua University, China, Chinese): Meng Ke seeks to understand the socio-economic causes of population ageing and declining fertility rates to suggest what public policy measures and innovations can be used to address them.

Shi Ling (Hong Kong University of Science and Technology, China, Chinese): Shi Ling researches the vulnerability of cyber-physical systems to protect safety-critical infrastructures – such as power utilities and water transportation systems – from attacks.

Sho Tsuji (University of Tokyo, Japan, Japanese): Sho Tsuji seeks to understand how an infant’s social environment affects language acquisition – a key predictor of future literacy – to inform culturally sensitive, science-based, societal interventions.

Wu Dan (Zhejiang University, China, Chinese): Wu Dan is researching technological advances in MRI techniques to improve its ability to detect tumours and stroke, as well as monitor foetal brain development.

Yi Li (Peking University, China, Chinese): Yi Li researches social-communicative impairments in children with autism in China to develop more precise screening and diagnosis, as well as innovative treatment approaches in the country.

Ying Xu (Chinese Academy of Sciences, China, Chinese): Ying Xu’s research focuses on enhancing China's low-orbit Beidou navigation satellite system, which could lead to advances in the commercial aerospace industry

From Europe:

Celeste Carruth (ETH Zurich, Switzerland, American): Celeste is developing a new 2D ion trap experiment for quantum information processing that is expected to be more reliable and cheaper to scale up than competing technologies and aims to lead to breakthrough quantum computing results.

Nicola Gasparini (Imperial College London, United Kingdom, Italian): Nicola is developing novel technologies to treat severe and incurable vision problems caused by degeneration of the retina, which affects almost 200 million people worldwide.

Joe Grove (University College London, United Kingdom, British): Joe investigates how viruses enter human cells and evade the immune system to reveal new biology and inform the design of future vaccines.

Philip Moll (Ecole Polytechnique Fédérale de Lausanne, Switzerland, German): Philip is developing new methods to make micro-scale modifications to material structures with the potential to improve quantum computing.

Mine Orlu (University College London, United Kingdom, British): Mine is designing patient-tailored pharmaceutical and healthcare technologies that contribute to healthy and independent ageing across the life course.

Michael Saliba (University of Stuttgart, Germany, German): Michael is developing inexpensive, stable and highly efficient perovskite solar cells that will enable the acceleration of sustainable energy technology.

Andy Tay (Imperial College London, United Kingdom, Singaporean): Andy is developing new technology and materials to engineer immune cells, tissues and systems, with the aim of preventing and treating cancer.

Jan Dirk Wegner (ETH Zurich, Switzerland, German): Jan develops novel artificial intelligence methods to analyse large-scale environmental data and accelerate humanity’s ability to solve ecological problems

From the Middle East:

Joseph Costantine (American University of Beirut, Lebanon, Lebanese): Joseph’s research leverages electromagnetism to design a new generation of wireless communication systems, biomedical sensors and wirelessly powered devices through radio frequency energy harvesting.

Joanna Doummar (American University of Beirut, Lebanon, Lebanese): Joanna seeks to better understand complex underground drainage systems, known as karst aquifers, to better address and solve national water quality and quantity challenges.

Don't miss any update on this topic

Create a free account and access your personalized content collection with our latest publications and analyses.

License and Republishing

World Economic Forum articles may be republished in accordance with the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Public License, and in accordance with our Terms of Use.

The views expressed in this article are those of the author alone and not the World Economic Forum.

Related topics:

The agenda .chakra .wef-n7bacu{margin-top:16px;margin-bottom:16px;line-height:1.388;font-weight:400;} weekly.

A weekly update of the most important issues driving the global agenda

.chakra .wef-1dtnjt5{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;-webkit-flex-wrap:wrap;-ms-flex-wrap:wrap;flex-wrap:wrap;} More on COVID-19 .chakra .wef-17xejub{-webkit-flex:1;-ms-flex:1;flex:1;justify-self:stretch;-webkit-align-self:stretch;-ms-flex-item-align:stretch;align-self:stretch;} .chakra .wef-nr1rr4{display:-webkit-inline-box;display:-webkit-inline-flex;display:-ms-inline-flexbox;display:inline-flex;white-space:normal;vertical-align:middle;text-transform:uppercase;font-size:0.75rem;border-radius:0.25rem;font-weight:700;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;line-height:1.2;-webkit-letter-spacing:1.25px;-moz-letter-spacing:1.25px;-ms-letter-spacing:1.25px;letter-spacing:1.25px;background:none;padding:0px;color:#B3B3B3;-webkit-box-decoration-break:clone;box-decoration-break:clone;-webkit-box-decoration-break:clone;}@media screen and (min-width:37.5rem){.chakra .wef-nr1rr4{font-size:0.875rem;}}@media screen and (min-width:56.5rem){.chakra .wef-nr1rr4{font-size:1rem;}} See all

Winding down COVAX – lessons learnt from delivering 2 billion COVID-19 vaccinations to lower-income countries

Charlotte Edmond

January 8, 2024

Here’s what to know about the new COVID-19 Pirola variant

October 11, 2023

How the cost of living crisis affects young people around the world

Douglas Broom

August 8, 2023

From smallpox to COVID: the medical inventions that have seen off infectious diseases over the past century

Andrea Willige

May 11, 2023

COVID-19 is no longer a global health emergency. Here's what it means

Simon Nicholas Williams

May 9, 2023

New research shows the significant health harms of the pandemic 

Philip Clarke, Jack Pollard and Mara Violato

April 17, 2023

• International edition
• Australia edition
• Europe edition

The 20 big questions in science

1 what is the universe made of.

Astronomers face an embarrassing conundrum: they don’t know what 95% of the universe is made of. Atoms, which form everything we see around us, only account for a measly 5%. Over the past 80 years it has become clear that the substantial remainder is comprised of two shadowy entities – dark matter and dark energy . The former, first discovered in 1933, acts as an invisible glue, binding galaxies and galaxy clusters together. Unveiled in 1998, the latter is pushing the universe’s expansion to ever greater speeds. Astronomers are closing in on the true identities of these unseen interlopers.

2 How did life begin?

Four billion years ago, something started stirring in the primordial soup. A few simple chemicals got together and made biology – the first molecules capable of replicating themselves appeared. We humans are linked by evolution to those early biological molecules. But how did the basic chemicals present on early Earth spontaneously arrange themselves into something resembling life? How did we get DNA? What did the first cells look like? More than half a century after the chemist Stanley Miller proposed his “primordial soup” theory , we still can’t agree about what happened. Some say life began in hot pools near volcanoes, others that it was kick-started by meteorites hitting the sea.

3 Are we alone in the universe?

Perhaps not. Astronomers have been scouring the universe for places where water worlds might have given rise to life, from Europa and Mars in our solar system to planets many light years away. Radio telescopes have been eavesdropping on the heavens and in 1977 a signal bearing the potential hallmarks of an alien message was heard. Astronomers are now able to scan the atmospheres of alien worlds for oxygen and water. The next few decades will be an exciting time to be an alien hunter with up to 60bn potentially habitable planets in our Milky Way alone.

4 What makes us human?

Just looking at your DNA won’t tell you – the human genome is 99% identical to a chimpanzee’s and, for that matter, 50% to a banana’s. We do, however, have bigger brains than most animals – not the biggest, but packed with three times as many neurons as a gorilla (86bn to be exact) . A lot of the things we once thought distinguishing about us – language, tool-use, recognising yourself in the mirror – are seen in other animals . Perhaps it’s our culture – and its subsequent effect on our genes (and vice versa) – that makes the difference. Scientists think that cooking and our mastery of fire may have helped us gain big brains. But it’s possible that our capacity for co-operation and skills trade is what really makes this a planet of humans and not apes.

5 What is consciousness?

We’re still not really sure. We do know that it’s to do with different brain regions networked together rather than a single part of the brain. The thinking goes that if we figure out which bits of the brain are involved and how the neural circuitry works, we’ll figure out how consciousness emerges, something that artificial intelligence and attempts to build a brain neuron by neuron may help with. The harder, more philosophical, question is why anything should be conscious in the first place. A good suggestion is that by integrating and processing lots of information, as well as focusing and blocking out rather than reacting to the sensory inputs bombarding us, we can distinguish between what’s real and what’s not and imagine multiple future scenarios that help us adapt and survive.

6 Why do we dream?

We spend around a third of our lives sleeping. Considering how much time we spend doing it, you might think we’d know everything about it. But scientists are still searching for a complete explanation of why we sleep and dream. Subscribers to Sigmund Freud’s views believed dreams were expressions of unfulfilled wishes – often sexual – while others wonder whether dreams are anything but the random firings of a sleeping brain. Animal studies and advances in brain imaging have led us to a more complex understanding that suggests dreaming could play a role in memory, learning and emotions. Rats, for example, have been shown to replay their waking experiences in dreams, apparently helping them to solve complex tasks such as navigating mazes.

7 Why is there stuff?

You really shouldn’t be here. The “stuff” you’re made of is matter, which has a counterpart called antimatter differing only in electrical charge. When they meet , both disappear in a flash of energy. Our best theories suggest that the big bang created equal amounts of the two, meaning all matter should have since encountered its antimatter counterpart, scuppering them both and leaving the universe awash with only energy. Clearly nature has a subtle bias for matter otherwise you wouldn’t exist. Researchers are sifting data from experiments like the Large Hadron Collider trying to understand why, with supersymmetry and neutrinos the two leading contenders.

8 Are there other universes?

Our universe is a very unlikely place. Alter some of its settings even slightly and life as we know it becomes impossible. In an attempt to unravel this “fine-tuning” problem, physicists are increasingly turning to the notion of other universes. If there is an infinite number of them in a “multiverse” then every combination of settings would be played out somewhere and, of course, you find yourself in the universe where you are able to exist. It may sound crazy, but evidence from cosmology and quantum physics is pointing in that direction.

9 Where do we put all the carbon?

For the past couple of hundred years, we’ve been filling the atmosphere with carbon dioxide – unleashing it by burning fossil fuels that once locked away carbon below the Earth’s surface. Now we have to put all that carbon back, or risk the consequences of a warming climate. But how do we do it? One idea is to bury it in old oil and gas fields. Another is to hide it away at the bottom of the sea. But we don’t know how long it will stay there, or what the risks might be. Meanwhile, we have to protect natural, long-lasting stores of carbon, such as forests and peat bogs, and start making energy in a way that doesn’t belch out even more.

10 How do we get more energy from the sun?

Dwindling supplies of fossil fuels mean we’re in need of a new way to power our planet. Our nearest star offers more than one possible solution. We’re already harnessing the sun’s energy to produce solar power. Another idea is to use the energy in sunlight to split water into its component parts: oxygen, and hydrogen, which could provide a clean fuel for cars of the future. Scientists are also working on an energy solution that depends on recreating the processes going on inside stars themselves – they’re building a nuclear fusion machine . The hope is that these solutions can meet our energy needs.

11 What’s so weird about prime numbers?

The fact you can shop safely on the internet is thanks to prime numbers – those digits that can only be divided by themselves and one. Public key encryption – the heartbeat of internet commerce – uses prime numbers to fashion keys capable of locking away your sensitive information from prying eyes. And yet, despite their fundamental importance to our everyday lives, the primes remain an enigma. An apparent pattern within them – the Riemann hypothesis – has tantalised some of the brightest minds in mathematics for centuries. However, as yet, no one has been able to tame their weirdness. Doing so might just break the internet.

12 How do we beat bacteria?

Antibiotics are one of the miracles of modern medicine. Sir Alexander Fleming’s Nobel prize-winning discovery led to medicines that fought some of the deadliest diseases and made surgery, transplants and chemotherapy possible. Yet this legacy is in danger – in Europe around 25,000 people die each year of multidrug-resistant bacteria . Our drug pipeline has been sputtering for decades and we’ve been making the problem worse through overprescription and misuse of antibiotics – an estimated 80% of US antibiotics goes to boosting farm animal growth. Thankfully, the advent of DNA sequencing is helping us discover antibiotics we never knew bacteria could produce. Alongside innovative, if gross-sounding, methods such as transplanting “good” bacteria from fecal matter , and the search for new bacteria deep in the oceans, we may yet keep abreast in this arms race with organisms 3bn years our senior.

13 Can computers keep getting faster?

Our tablets and smartphones are mini-computers that contain more computing power than astronauts took to the moon in 1969. But if we want to keep on increasing the amount of computing power we carry around in our pockets, how are we going to do it? There are only so many components you can cram on to a computer chip. Has the limit been reached, or is there another way to make a computer? Scientists are considering new materials, such as atomically thin carbon – graphene – as well as new systems, such as quantum computing.

14 Will we ever cure cancer?

The short answer is no. Not a single disease, but a loose group of many hundreds of diseases, cancer has been around since the dinosaurs and, being caused by haywire genes, the risk is hardwired into all of us. The longer we live, the more likely something might go wrong, in any number of ways. For cancer is a living thing – ever-evolving to survive. Yet though incredibly complicated, through genetics we’re learning more and more about what causes it, how it spreads and getting better at treating and preventing it . And know this: up to half of all cancers – 3.7m a year – are preventable; quit smoking, drink and eat moderately, stay active, and avoid prolonged exposure to the midday sun.

15 When can I have a robot butler?

Robots can already serve drinks and carry suitcases. Modern robotics can offer us a “staff” of individually specialised robots: they ready your Amazon orders for delivery, milk your cows, sort your email and ferry you between airport terminals. But a truly “intelligent” robot requires us to crack artificial intelligence. The real question is whether you’d leave a robotic butler alone in the house with your granny. And with Japan aiming to have robotic aides caring for its elderly by 2025, we’re thinking hard about it now.

16 What’s at the bottom of the ocean?

Ninety-five per cent of the ocean is unexplored. What’s down there? In 1960, Don Walsh and Jacques Piccard travelled seven miles down, to the deepest part of the ocean, in search of answers. Their voyage pushed the boundaries of human endeavour but gave them only a glimpse of life on the seafloor. It’s so difficult getting to the bottom of the ocean that for the most part we have to resort to sending unmanned vehicles as scouts. The discoveries we’ve made so far – from bizarre fish such as the barreleye, with its transparent head, to a potential treatment for Alzheimer’s made by crustaceans – are a tiny fraction of the strange world hidden below the waves.

17 What’s at the bottom of a black hole?

It’s a question we don’t yet have the tools to answer. Einstein’s general relativity says that when a black hole is created by a dying, collapsing massive star, it continues caving in until it forms an infinitely small, infinitely dense point called a singularity. But on such scales quantum physics probably has something to say too. Except that general relativity and quantum physics have never been the happiest of bedfellows – for decades they have withstood all attempts to unify them. However, a recent idea – called M-Theory – may one day explain the unseen centre of one of the universe’s most extreme creations.

18 Can we live for ever?

We live in an amazing time: we’re starting to think of “ageing” not as a fact of life, but a disease that can be treated and possibly prevented, or at least put off for a very long time. Our knowledge of what causes us to age – and what allows some animals to live longer than others – is expanding rapidly. And though we haven’t quite worked out all the details, the clues we are gathering about DNA damage, the balance of ageing, metabolism and reproductive fitness, plus the genes that regulate this, are filling out a bigger picture, potentially leading to drug treatments. But the real question is not how we’re going to live longer but how we are going to live well longer. And since many diseases, such as diabetes and cancer, are diseases of ageing, treating ageing itself could be the key.

19 How do we solve the population problem?

The number of people on our planet has doubled to more than 7 billion since the 1960s and it is expected that by 2050 there will be at least 9 billion of us. Where are we all going to live and how are we going to make enough food and fuel for our ever-growing population? Maybe we can ship everyone off to Mars or start building apartment blocks underground. We could even start feeding ourselves with lab-grown meat . These may sound like sci-fi solutions, but we might have to start taking them more seriously.

20 Is time travel possible?

Time travellers already walk among us. Thanks to Einstein’s theory of special relativity, astronauts orbiting on the International Space Station experience time ticking more slowly. At that speed the effect is minuscule, but ramp up the velocity and the effect means that one day humans might travel thousands of years into the future. Nature seems to be less fond of people going the other way and returning to the past, however some physicists have concocted an elaborate blueprint for a way to do it using wormholes and spaceships. It could even be used to hand yourself a present on Christmas Day, or answer some of the many questions that surround the universe’s great unknowns.

The Big Questions in Science: The Quest to Solve the Great Unknowns is published by Andre Deutsch. To buy a copy for £11.99 with free UK p&p, go to guardianbookshop.co.uk .

• The Observer
• Agriculture

More on this story

Have a question science could answer?

Six stubborn myths about cancer

The ups and downs of porn: sexism, relationships and sexual aggression

Life on earth 'began on Mars'

If we're all Martians now, who are the aliens?

Women and yogurt: what's the connection?

What do we really know about the effects of screen time on mental health?

Comments (…), most viewed.

Subscribe or renew today

Every print subscription comes with full digital access

Science News

Top 10 scientific mysteries for the 21st century.

Solving the toughest problems posed by nature is not just fun and games

Calabi-Yau manifolds like this one represent extra dimensions tightly curled and wound up so they can't be detected. The question of how many dimensions of space there actually are is one of the top scientific mysteries for 21st century scientists to solve.

Rogilbert/Wikimedia Commons

Share this:

By Tom Siegfried

January 28, 2015 at 9:00 am

The last few centuries have been pretty good for science. In the 17th century, Isaac Newton solved the ancient controversy over the nature of forces and motion with his three laws. In the 18th, Ben Franklin figured out a lot about electricity. In the 19th, Darwin explained the diversity of species, Maxwell revealed the physics of light, Mendeleyev defined the families of chemical elements. In the 20th we had Einstein, who figured out all sorts of stuff, including gravity. No to mention Watson and Crick, who deciphered the molecular foundation for genetics and life. What more do you want?

Well, there are still lots of mysteries left for the 21st century to solve, and it has only 86 years left in which to solve them. So it’s a good idea to put them in a list, just to avoid any danger that everybody will forget to work on them.

Actually there are many more than 10, so this list will have to be restricted to my favorites. To select from all the many possibilities, let’s make a game of it.

10. How did life originate?

It doesn’t seem like this one should be so hard, but it continues to defy solution. There’s plenty of speculation, often related to RNA’s ability to act both as catalyst and bio–hard drive to store information. And new findings turn up all the time about how life’s basic building blocks could have been generated in primordial conditions or delivered to Earth from space. I think this question will end up having something to do with game theory, as biomolecules interact in competitive ways  that could be described as strategies, and the math for calculating optimal strategies is what game theory is all about.

9. What is the identity of the dark matter?

It has been eight decades or so since astronomers began to notice that there is more gravity pulling stuff around out in space than there is visible matter able to produce such effects. Attempts to detect the supposedly exotic (as in, unknown) species of subatomic particle responsible for the extra gravity have been frustrating. Hints seen in some experiments have been ruled out by other experiments. I think there’s a missing piece to this puzzle, but it probably has nothing to do with game theory.

8. What is the nature of the dark energy that drives cosmic acceleration?

If you think dark matter is frustrating, try explaining dark energy. Something is driving space to expand at an ever increasing rate. Physicists think that they know what it is — the never-changing density of energy residing throughout all of space, referred to by Einstein as the “cosmical term” and now called the cosmological constant. But when you calculate how strong the cosmological constant should be, the answer is too big by dozens of orders of magnitude — much more than the difference between the size of the entire universe compared with a proton. So dark energy’s identity remains a mystery; if it is the cosmological constant, something else is seriously wrong with what physicists think they know. And so far game theory has been absolutely no help.

7. How to measure evidence

This one is so mysterious that many scientists don’t even know there’s a mystery. But if they paused to think, they’d realize that the standard way of inferring conclusions from experimental data — calculating “statistical significance” — makes about as much sense as punting on fourth and seven when you’re down by 15 with eight minutes to go. One small example: if you do an experiment and get a statistically significant result, and then repeat it and get a statistically significant result again, you’d think you have better evidence than doing the experiment only once. But if the significance level was a little less the second time, the combined “P value” would be less impressive after the second experiment, even though the evidence ought to be regarded as stronger. It’s a mess. Game theory would surely be able to help somehow, possibly by virtue of its relationship to thermodynamics .

6. Genes, cancer and luck

You might have read recently that most cancer is caused by bad luck, as a study published in Science supposedly concluded. (Actually, the study concluded that the disparity in prevalence of cancer of various types was largely due to luck.) A firestorm of  protest followed, essentially based on the belief that such a study must be wrong because it would “send the wrong message” to the public. Proving the illogic of that syllogism should be left as an exercise for the reader. Other responses revealed that experts do not agree on how random mutations (bad luck) compare with heredity (parent’s fault) plus lifestyle (your fault) and environmental exposure to bad things (somebody else’s fault) in causing cancer. Sorting all that out, and in the process solving cancer’s other mysteries, should be a high-priority exercise for 21st century science. And yes, there is a considerable amount of research relating game theory to cancer .

5. Are there extra dimensions of space?

I don’t know why people keep thinking this is a mystery, as I have on several occasions pointed out that there are no extra dimensions. However many there are, they are all absolutely necessary. Posed properly, this question should be how many dimensions of space are there? (For that matter, you could also ask about how many time dimensions there are, but that might overlap with No. 4.) Many physicists believe more dimensions than the ordinary three will be needed for physics to make sense of the universe. (Don’t even ask if they’re talking about bosonic or fermionic dimensions.) A key to understanding this issue is the mathematics of Calabi-Yau manifolds , which can curl up in gazillions of different ways to prevent easy detection of the additional dimensions’ existence. And that makes it really hard to figure out which of the gazillion possibilities would correspond to the universe we inhabit (unless there is some sort of fixed point theorem that would choose one, like a Nash equilibrium  in game theory). In any event, anyone attempting to solve this riddle should first read Edwin Abbott’s Flatland , in which the protagonist character, A. Square, demonstrates the existence of an extra dimension and is promptly thrown in jail.

4. The nature of time

So many mysteries, so little time in which to solve them, unless solving this one would reveal some clever tricks to play with time. Many submysteries underlie this one, corresponding to almost all of the 44 definitions of time in the dictionary (and that’s just as a noun). What’s the nature of duration and the flow of time — is it illusory or “real” in some elusive way? What about the direction of time — does it always go forward? Why? Is time travel possible, or can messages at least be sent backward in time? (Forward in time is easy — just print this blog post out and read it a year from now.) Perhaps the biggest mystery is whether all these issues about time are related or are completely separate questions. Of course, it would all be simpler if somehow time could be connected to game theory, which it might be, because game theory can be related to cellular automata , which in turn can be related to time .

3. Quantum gravity

Quantum physics and general relativity (aka Einstein’s theory of gravity) both seem to describe the universe and its components with compelling accuracy, yet they seem wholly incompatible with one another. Attempts to combine them into a coherent unified theory have been as successful as brokering compromise in the U.S. Congress. Yet there are clues. In 1930, Einstein tried to refute quantum mechanics (specifically, the Heisenberg uncertainty principle) by suggesting a clock attached to a box hanging on a scale could measure both the mass of a photon and the precise time that it escaped from the box. (Heisenberg said you couldn’t measure both at the same time). But Niels Bohr pointed out that the time on the clock would be uncertain, because as the box moved upward in the gravitational field, Einstein’s relativity required a change in time that would introduce just the amount of uncertainty in the timing that Heisenberg required. So how, you might ask, did the uncertainty principle know about this effect of general relativity? Maybe if the experts posed the question that way they would be able to figure out the quantum gravity mystery. The next best bet would be to undertake the study of quantum game theory , which hasn’t been adequately exploited yet in this regard.   

2. Does intelligent life exist elsewhere?

It’s tempting to delete the “elsewhere,” but given what passes for intelligence on Earth, it makes sense to wonder if anything like it could be blundering about on some distant world. It seems likely, given how many other worlds there are out there. But finding out for sure will probably require receiving an actual message. Projects like SETI  have been listening for some such message, so far unsuccessfully. There are two (at least) possible explanations: One, there have been no messages (perhaps the aliens are experts at game theory and calculated that contacting humans would be a bad strategy). Two, the messages are there, but nobody knows how to detect or recognize them. Perhaps enhanced scrutiny is in order on Twitter, where numerous tweets every day seem most plausibly to be the work of aliens. 

1. The meaning of quantum entanglement

All sorts of quantum mysteries remain unsatisfactorily resolved, but maybe the rest would succumb if entanglement does. Entanglement occurs in systems with widely separated parts that share a common history; a measurement of one of the parts reveals what you will find out when you measure its distant relative. Entanglement is a fact of nature, well-established by experiment. It suggests that time and space do not constrain quantum phenomena the way they do ordinary human activity. Among the latest intriguing aspects of entanglement to be studied involves black holes. It seems that black holes can be entangled , which apparently is equivalent to their being connected by a wormhole. Related work suggests that space, time and gravity are all part of a vast quantum entanglement network. Since both the evolution of networks and quantum entanglement  fit nicely into game theory, solving all sorts of mysteries might boil down to viewing the world from a game-theoretical perspective. But maybe that will still be too hard for human brains — it might take advanced artificial intelligence, which, as this paper  suggests, might be created with the help of some version of quantum game theory.  

Editor’s Note: It might not surprise readers to find out that Tom Siegfried is the author of a book about game theory . But he says the book did not include the sort of wild speculation that is suitable only in blog posts.

Follow me on Twitter: @tom_siegfried

More Stories from Science News on Quantum Physics

A maverick physicist is building a case for scrapping quantum gravity

The development of quantum dots wins the 2023 Nobel prize in chemistry

Clara Sousa-Silva seeks molecular signatures of life in alien atmospheres

Quantum computers could break the internet. Here’s how to save it

One photon is all it takes to kick off photosynthesis

Quantum computers braided ‘anyons,’ long-sought quasiparticles with memory

A sapphire Schrödinger’s cat shows that quantum effects can scale up

Google’s quantum computer reached an error-correcting milestone

From the nature index.

Subscribers, enter your e-mail address for full access to the Science News archives and digital editions.

Not a subscriber? Become one now .

When you choose to publish with PLOS, your research makes an impact. Make your work accessible to all, without restrictions, and accelerate scientific discovery with options like preprints and published peer review that make your work more Open.

• PLOS Biology
• PLOS Climate
• PLOS Complex Systems
• PLOS Computational Biology
• PLOS Digital Health
• PLOS Genetics
• PLOS Global Public Health
• PLOS Medicine
• PLOS Mental Health
• PLOS Neglected Tropical Diseases
• PLOS Pathogens
• PLOS Sustainability and Transformation
• PLOS Collections
• About This Blog
• Official PLOS Blog
• EveryONE Blog
• Speaking of Medicine
• PLOS Biologue
• Absolutely Maybe
• DNA Science
• PLOS ECR Community
• All Models Are Wrong
• About PLOS Blogs

A Guide to Using the Scientific Method in Everyday Life

The  scientific method —the process used by scientists to understand the natural world—has the merit of investigating natural phenomena in a rigorous manner. Working from hypotheses, scientists draw conclusions based on empirical data. These data are validated on large-scale numbers and take into consideration the intrinsic variability of the real world. For people unfamiliar with its intrinsic jargon and formalities, science may seem esoteric. And this is a huge problem: science invites criticism because it is not easily understood. So why is it important, then, that every person understand how science is done?

Because the scientific method is, first of all, a matter of logical reasoning and only afterwards, a procedure to be applied in a laboratory.

Individuals without training in logical reasoning are more easily victims of distorted perspectives about themselves and the world. An example is represented by the so-called “ cognitive biases ”—systematic mistakes that individuals make when they try to think rationally, and which lead to erroneous or inaccurate conclusions. People can easily  overestimate the relevance  of their own behaviors and choices. They can  lack the ability to self-estimate the quality of their performances and thoughts . Unconsciously, they could even end up selecting only the arguments  that support their hypothesis or beliefs . This is why the scientific framework should be conceived not only as a mechanism for understanding the natural world, but also as a framework for engaging in logical reasoning and discussion.

A brief history of the scientific method

The scientific method has its roots in the sixteenth and seventeenth centuries. Philosophers Francis Bacon and René Descartes are often credited with formalizing the scientific method because they contrasted the idea that research should be guided by metaphysical pre-conceived concepts of the nature of reality—a position that, at the time,  was highly supported by their colleagues . In essence, Bacon thought that  inductive reasoning based on empirical observation was critical to the formulation of hypotheses  and the  generation of new understanding : general or universal principles describing how nature works are derived only from observations of recurring phenomena and data recorded from them. The inductive method was used, for example, by the scientist Rudolf Virchow to formulate the third principle of the notorious  cell theory , according to which every cell derives from a pre-existing one. The rationale behind this conclusion is that because all observations of cell behavior show that cells are only derived from other cells, this assertion must be always true. 

Inductive reasoning, however, is not immune to mistakes and limitations. Referring back to cell theory, there may be rare occasions in which a cell does not arise from a pre-existing one, even though we haven’t observed it yet—our observations on cell behavior, although numerous, can still benefit from additional observations to either refute or support the conclusion that all cells arise from pre-existing ones. And this is where limited observations can lead to erroneous conclusions reasoned inductively. In another example, if one never has seen a swan that is not white, they might conclude that all swans are white, even when we know that black swans do exist, however rare they may be.  

The universally accepted scientific method, as it is used in science laboratories today, is grounded in  hypothetico-deductive reasoning . Research progresses via iterative empirical testing of formulated, testable hypotheses (formulated through inductive reasoning). A testable hypothesis is one that can be rejected (falsified) by empirical observations, a concept known as the  principle of falsification . Initially, ideas and conjectures are formulated. Experiments are then performed to test them. If the body of evidence fails to reject the hypothesis, the hypothesis stands. It stands however until and unless another (even singular) empirical observation falsifies it. However, just as with inductive reasoning, hypothetico-deductive reasoning is not immune to pitfalls—assumptions built into hypotheses can be shown to be false, thereby nullifying previously unrejected hypotheses. The bottom line is that science does not work to prove anything about the natural world. Instead, it builds hypotheses that explain the natural world and then attempts to find the hole in the reasoning (i.e., it works to disprove things about the natural world).

How do scientists test hypotheses?

Controlled experiments

The word “experiment” can be misleading because it implies a lack of control over the process. Therefore, it is important to understand that science uses controlled experiments in order to test hypotheses and contribute new knowledge. So what exactly is a controlled experiment, then? 

Let us take a practical example. Our starting hypothesis is the following: we have a novel drug that we think inhibits the division of cells, meaning that it prevents one cell from dividing into two cells (recall the description of cell theory above). To test this hypothesis, we could treat some cells with the drug on a plate that contains nutrients and fuel required for their survival and division (a standard cell biology assay). If the drug works as expected, the cells should stop dividing. This type of drug might be useful, for example, in treating cancers because slowing or stopping the division of cells would result in the slowing or stopping of tumor growth.

Although this experiment is relatively easy to do, the mere process of doing science means that several experimental variables (like temperature of the cells or drug, dosage, and so on) could play a major role in the experiment. This could result in a failed experiment when the drug actually does work, or it could give the appearance that the drug is working when it is not. Given that these variables cannot be eliminated, scientists always run control experiments in parallel to the real ones, so that the effects of these other variables can be determined.  Control experiments  are designed so that all variables, with the exception of the one under investigation, are kept constant. In simple terms, the conditions must be identical between the control and the actual experiment.     

Coming back to our example, when a drug is administered it is not pure. Often, it is dissolved in a solvent like water or oil. Therefore, the perfect control to the actual experiment would be to administer pure solvent (without the added drug) at the same time and with the same tools, where all other experimental variables (like temperature, as mentioned above) are the same between the two (Figure 1). Any difference in effect on cell division in the actual experiment here can be attributed to an effect of the drug because the effects of the solvent were controlled.

In order to provide evidence of the quality of a single, specific experiment, it needs to be performed multiple times in the same experimental conditions. We call these multiple experiments “replicates” of the experiment (Figure 2). The more replicates of the same experiment, the more confident the scientist can be about the conclusions of that experiment under the given conditions. However, multiple replicates under the same experimental conditions  are of no help  when scientists aim at acquiring more empirical evidence to support their hypothesis. Instead, they need  independent experiments  (Figure 3), in their own lab and in other labs across the world, to validate their results. 

Often times, especially when a given experiment has been repeated and its outcome is not fully clear, it is better  to find alternative experimental assays  to test the hypothesis. 

Applying the scientific approach to everyday life

So, what can we take from the scientific approach to apply to our everyday lives?

A few weeks ago, I had an agitated conversation with a bunch of friends concerning the following question: What is the definition of intelligence?

Defining “intelligence” is not easy. At the beginning of the conversation, everybody had a different, “personal” conception of intelligence in mind, which – tacitly – implied that the conversation could have taken several different directions. We realized rather soon that someone thought that an intelligent person is whoever is able to adapt faster to new situations; someone else thought that an intelligent person is whoever is able to deal with other people and empathize with them. Personally, I thought that an intelligent person is whoever displays high cognitive skills, especially in abstract reasoning. 

The scientific method has the merit of providing a reference system, with precise protocols and rules to follow. Remember: experiments must be reproducible, which means that an independent scientists in a different laboratory, when provided with the same equipment and protocols, should get comparable results.  Fruitful conversations as well need precise language, a kind of reference vocabulary everybody should agree upon, in order to discuss about the same “content”. This is something we often forget, something that was somehow missing at the opening of the aforementioned conversation: even among friends, we should always agree on premises, and define them in a rigorous manner, so that they are the same for everybody. When speaking about “intelligence”, we must all make sure we understand meaning and context of the vocabulary adopted in the debate (Figure 4, point 1).  This is the first step of “controlling” a conversation.

There is another downside that a discussion well-grounded in a scientific framework would avoid. The mistake is not structuring the debate so that all its elements, except for the one under investigation, are kept constant (Figure 4, point 2). This is particularly true when people aim at making comparisons between groups to support their claim. For example, they may try to define what intelligence is by comparing the  achievements in life of different individuals: “Stephen Hawking is a brilliant example of intelligence because of his great contribution to the physics of black holes”. This statement does not help to define what intelligence is, simply because it compares Stephen Hawking, a famous and exceptional physicist, to any other person, who statistically speaking, knows nothing about physics. Hawking first went to the University of Oxford, then he moved to the University of Cambridge. He was in contact with the most influential physicists on Earth. Other people were not. All of this, of course, does not disprove Hawking’s intelligence; but from a logical and methodological point of view, given the multitude of variables included in this comparison, it cannot prove it. Thus, the sentence “Stephen Hawking is a brilliant example of intelligence because of his great contribution to the physics of black holes” is not a valid argument to describe what intelligence is. If we really intend to approximate a definition of intelligence, Steven Hawking should be compared to other physicists, even better if they were Hawking’s classmates at the time of college, and colleagues afterwards during years of academic research. 

In simple terms, as scientists do in the lab, while debating we should try to compare groups of elements that display identical, or highly similar, features. As previously mentioned, all variables – except for the one under investigation – must be kept constant.

This insightful piece  presents a detailed analysis of how and why science can help to develop critical thinking.

In a nutshell

Here is how to approach a daily conversation in a rigorous, scientific manner:

• First discuss about the reference vocabulary, then discuss about the content of the discussion.  Think about a researcher who is writing down an experimental protocol that will be used by thousands of other scientists in varying continents. If the protocol is rigorously written, all scientists using it should get comparable experimental outcomes. In science this means reproducible knowledge, in daily life this means fruitful conversations in which individuals are on the same page. 
• Adopt “controlled” arguments to support your claims.  When making comparisons between groups, visualize two blank scenarios. As you start to add details to both of them, you have two options. If your aim is to hide a specific detail, the better is to design the two scenarios in a completely different manner—it is to increase the variables. But if your intention is to help the observer to isolate a specific detail, the better is to design identical scenarios, with the exception of the intended detail—it is therefore to keep most of the variables constant. This is precisely how scientists ideate adequate experiments to isolate new pieces of knowledge, and how individuals should orchestrate their thoughts in order to test them and facilitate their comprehension to others.   

Not only the scientific method should offer individuals an elitist way to investigate reality, but also an accessible tool to properly reason and discuss about it.

Edited by Jason Organ, PhD, Indiana University School of Medicine.

Simone is a molecular biologist on the verge of obtaining a doctoral title at the University of Ulm, Germany. He is Vice-Director at Culturico (https://culturico.com/), where his writings span from Literature to Sociology, from Philosophy to Science. His writings recently appeared in Psychology Today, openDemocracy, Splice Today, Merion West, Uncommon Ground and The Society Pages. Follow Simone on Twitter: @simredaelli

• Pingback: Case Studies in Ethical Thinking: Day 1 | Education & Erudition

This has to be the best article I have ever read on Scientific Thinking. I am presently writing a treatise on how Scientific thinking can be adopted to entreat all situations.And how, a 4 year old child can be taught to adopt Scientific thinking, so that, the child can look at situations that bothers her and she could try to think about that situation by formulating the right questions. She may not have the tools to find right answers? But, forming questions by using right technique ? May just make her find a way to put her mind to rest even at that level. That is why, 4 year olds are often “eerily: (!)intelligent, I have iften been intimidated and plain embarrassed to see an intelligent and well spoken 4 year old deal with celibrity ! Of course, there are a lot of variables that have to be kept in mind in order to train children in such controlled thinking environment, as the screenplay of little Sheldon shows. Thanking the author with all my heart – #ershadspeak #wearescience #weareallscientists Ershad Khandker

Simone, thank you for this article. I have the idea that I want to apply what I learned in Biology to everyday life. You addressed this issue, and have given some basic steps in using the scientific method.

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name and email for the next time I comment.

By Ana Santos-Carvalho and Carolina Lebre, edited by Andrew S. Cale Excessive use of technical jargon can be a significant barrier to…

By Ryan McRae and Briana Pobiner, edited by Andrew S. Cale In 2023, the field of human evolution benefited from a plethora…

By Elizabeth Fusco, edited by Michael Liesen Infection and pandemics have never been more relevant globally, and zombies have long been used…

How it works

For Business

Join Mind Tools

Article • 5 min read

Using the Scientific Method to Solve Problems

How the scientific method and reasoning can help simplify processes and solve problems.

By the Mind Tools Content Team

The processes of problem-solving and decision-making can be complicated and drawn out. In this article we look at how the scientific method, along with deductive and inductive reasoning can help simplify these processes.

‘It is a capital mistake to theorize before one has information. Insensibly one begins to twist facts to suit our theories, instead of theories to suit facts.’ Sherlock Holmes

The Scientific Method

The scientific method is a process used to explore observations and answer questions. Originally used by scientists looking to prove new theories, its use has spread into many other areas, including that of problem-solving and decision-making.

The scientific method is designed to eliminate the influences of bias, prejudice and personal beliefs when testing a hypothesis or theory. It has developed alongside science itself, with origins going back to the 13th century. The scientific method is generally described as a series of steps.

• observations/theory
• explanation/conclusion

The first step is to develop a theory about the particular area of interest. A theory, in the context of logic or problem-solving, is a conjecture or speculation about something that is not necessarily fact, often based on a series of observations.

Once a theory has been devised, it can be questioned and refined into more specific hypotheses that can be tested. The hypotheses are potential explanations for the theory.

The testing, and subsequent analysis, of these hypotheses will eventually lead to a conclus ion which can prove or disprove the original theory.

Applying the Scientific Method to Problem-Solving

How can the scientific method be used to solve a problem, such as the color printer is not working?

1. Use observations to develop a theory.

In order to solve the problem, it must first be clear what the problem is. Observations made about the problem should be used to develop a theory. In this particular problem the theory might be that the color printer has run out of ink. This theory is developed as the result of observing the increasingly faded output from the printer.

2. Form a hypothesis.

Note down all the possible reasons for the problem. In this situation they might include:

• The printer is set up as the default printer for all 40 people in the department and so is used more frequently than necessary.
• There has been increased usage of the printer due to non-work related printing.
• In an attempt to reduce costs, poor quality ink cartridges with limited amounts of ink in them have been purchased.
• The printer is faulty.

All these possible reasons are hypotheses.

3. Test the hypothesis.

Once as many hypotheses (or reasons) as possible have been thought of, then each one can be tested to discern if it is the cause of the problem. An appropriate test needs to be devised for each hypothesis. For example, it is fairly quick to ask everyone to check the default settings of the printer on each PC, or to check if the cartridge supplier has changed.

4. Analyze the test results.

Once all the hypotheses have been tested, the results can be analyzed. The type and depth of analysis will be dependant on each individual problem, and the tests appropriate to it. In many cases the analysis will be a very quick thought process. In others, where considerable information has been collated, a more structured approach, such as the use of graphs, tables or spreadsheets, may be required.

5. Draw a conclusion.

Based on the results of the tests, a conclusion can then be drawn about exactly what is causing the problem. The appropriate remedial action can then be taken, such as asking everyone to amend their default print settings, or changing the cartridge supplier.

Inductive and Deductive Reasoning

The scientific method involves the use of two basic types of reasoning, inductive and deductive.

Inductive reasoning makes a conclusion based on a set of empirical results. Empirical results are the product of the collection of evidence from observations. For example:

‘Every time it rains the pavement gets wet, therefore rain must be water’.

There has been no scientific determination in the hypothesis that rain is water, it is purely based on observation. The formation of a hypothesis in this manner is sometimes referred to as an educated guess. An educated guess, whilst not based on hard facts, must still be plausible, and consistent with what we already know, in order to present a reasonable argument.

Deductive reasoning can be thought of most simply in terms of ‘If A and B, then C’. For example:

• if the window is above the desk, and
• the desk is above the floor, then
• the window must be above the floor

It works by building on a series of conclusions, which results in one final answer.

Social Sciences and the Scientific Method

The scientific method can be used to address any situation or problem where a theory can be developed. Although more often associated with natural sciences, it can also be used to develop theories in social sciences (such as psychology, sociology and linguistics), using both quantitative and qualitative methods.

Quantitative information is information that can be measured, and tends to focus on numbers and frequencies. Typically quantitative information might be gathered by experiments, questionnaires or psychometric tests. Qualitative information, on the other hand, is based on information describing meaning, such as human behavior, and the reasons behind it. Qualitative information is gathered by way of interviews and case studies, which are possibly not as statistically accurate as quantitative methods, but provide a more in-depth and rich description.

The resultant information can then be used to prove, or disprove, a hypothesis. Using a mix of quantitative and qualitative information is more likely to produce a rounded result based on the factual, quantitative information enriched and backed up by actual experience and qualitative information.

In terms of problem-solving or decision-making, for example, the qualitative information is that gained by looking at the ‘how’ and ‘why’ , whereas quantitative information would come from the ‘where’, ‘what’ and ‘when’.

It may seem easy to come up with a brilliant idea, or to suspect what the cause of a problem may be. However things can get more complicated when the idea needs to be evaluated, or when there may be more than one potential cause of a problem. In these situations, the use of the scientific method, and its associated reasoning, can help the user come to a decision, or reach a solution, secure in the knowledge that all options have been considered.

Join Mind Tools and get access to exclusive content.

This resource is only available to Mind Tools members.

Already a member? Please Login here

Get 20% off your first year of Mind Tools

Our on-demand e-learning resources let you learn at your own pace, fitting seamlessly into your busy workday. Join today and save with our limited time offer!

Sign-up to our newsletter

Subscribing to the Mind Tools newsletter will keep you up-to-date with our latest updates and newest resources.

Subscribe now

Business Skills

Personal Development

Leadership and Management

Member Extras

Most Popular

Newest Releases

Pain Points Podcast - Balancing Work And Kids

Pain Points Podcast - Improving Culture

Mind Tools Store

About Mind Tools Content

Discover something new today

Pain points podcast - what is ai.

Exploring Artificial Intelligence

Pain Points Podcast - How Do I Get Organized?

It's Time to Get Yourself Sorted!

How Emotionally Intelligent Are You?

Boosting Your People Skills

Self-Assessment

What's Your Leadership Style?

Learn About the Strengths and Weaknesses of the Way You Like to Lead

Recommended for you

Handy's motivation theory.

Motivating People to Work Hard

Business Operations and Process Management

Strategy Tools

Customer Service

Business Ethics and Values

Handling Information and Data

Project Management

Knowledge Management

Self-Development and Goal Setting

Time Management

Presentation Skills

Learning Skills

Career Skills

Communication Skills

Negotiation, Persuasion and Influence

Working With Others

Difficult Conversations

Creativity Tools

Self-Management

Work-Life Balance

Stress Management and Wellbeing

Coaching and Mentoring

Change Management

Team Management

Managing Conflict

Delegation and Empowerment

Performance Management

Leadership Skills

Developing Your Team

Talent Management

Problem Solving

Decision Making

Member Podcast

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

1.2: Scientific Approach for Solving Problems

• Last updated
• Save as PDF
• Page ID 358114

Learning Objectives

• To identify the components of the scientific method

Scientists search for answers to questions and solutions to problems by using a procedure called the scientific method . This procedure consists of making observations, formulating hypotheses, and designing experiments, which in turn lead to additional observations, hypotheses, and experiments in repeated cycles (Figure \(\PageIndex{1}\)).

Observations can be qualitative or quantitative. Qualitative observations describe properties or occurrences in ways that do not rely on numbers. Examples of qualitative observations include the following: the outside air temperature is cooler during the winter season, table salt is a crystalline solid, sulfur crystals are yellow, and dissolving a penny in dilute nitric acid forms a blue solution and a brown gas. Quantitative observations are measurements, which by definition consist of both a number and a unit. Examples of quantitative observations include the following: the melting point of crystalline sulfur is 115.21 °C, and 35.9 grams of table salt—whose chemical name is sodium chloride—dissolve in 100 grams of water at 20 °C. An example of a quantitative observation was the initial observation leading to the modern theory of the dinosaurs’ extinction: iridium concentrations in sediments dating to 66 million years ago were found to be 20–160 times higher than normal. The development of this theory is a good exemplar of the scientific method in action (see Figure \(\PageIndex{2}\) below).

After deciding to learn more about an observation or a set of observations, scientists generally begin an investigation by forming a hypothesis , a tentative explanation for the observation(s). The hypothesis may not be correct, but it puts the scientist’s understanding of the system being studied into a form that can be tested. For example, the observation that we experience alternating periods of light and darkness corresponding to observed movements of the sun, moon, clouds, and shadows is consistent with either of two hypotheses:

• Earth rotates on its axis every 24 hours, alternately exposing one side to the sun, or
• The sun revolves around Earth every 24 hours.

Suitable experiments can be designed to choose between these two alternatives. For the disappearance of the dinosaurs, the hypothesis was that the impact of a large extraterrestrial object caused their extinction. Unfortunately (or perhaps fortunately), this hypothesis does not lend itself to direct testing by any obvious experiment, but scientists collected additional data that either support or refute it.

After a hypothesis has been formed, scientists conduct experiments to test its validity. Experiments are systematic observations or measurements, preferably made under controlled conditions—that is, under conditions in which a single variable changes. For example, in the dinosaur extinction scenario, iridium concentrations were measured worldwide and compared. A properly designed and executed experiment enables a scientist to determine whether the original hypothesis is valid. Experiments often demonstrate that the hypothesis is incorrect or that it must be modified. More experimental data are then collected and analyzed, at which point a scientist may begin to think that the results are sufficiently reproducible (i.e., dependable) to merit being summarized in a law , a verbal or mathematical description of a phenomenon that allows for general predictions. A law simply says what happens; it does not address the question of why.

One example of a law, the Law of Definite Proportions , which was discovered by the French scientist Joseph Proust (1754–1826), states that a chemical substance always contains the same proportions of elements by mass. Thus sodium chloride (table salt) always contains the same proportion by mass of sodium to chlorine, in this case 39.34% sodium and 60.66% chlorine by mass, and sucrose (table sugar) is always 42.11% carbon, 6.48% hydrogen, and 51.41% oxygen by mass. Some solid compounds do not strictly obey the law of definite proportions. The law of definite proportions should seem obvious—we would expect the composition of sodium chloride to be consistent—but the head of the US Patent Office did not accept it as a fact until the early 20th century.

Whereas a law states only what happens, a theory attempts to explain why nature behaves as it does. Laws are unlikely to change greatly over time unless a major experimental error is discovered. In contrast, a theory, by definition, is incomplete and imperfect, evolving with time to explain new facts as they are discovered. The theory developed to explain the extinction of the dinosaurs, for example, is that Earth occasionally encounters small- to medium-sized asteroids, and these encounters may have unfortunate implications for the continued existence of most species. This theory is by no means proven, but it is consistent with the bulk of evidence amassed to date. Figure \(\PageIndex{2}\) summarizes the application of the scientific method in this case.

Example \(\PageIndex{1}\)

Classify each statement as a law, a theory, an experiment, a hypothesis, a qualitative observation, or a quantitative observation.

• Ice always floats on liquid water.
• Birds evolved from dinosaurs.
• Hot air is less dense than cold air, probably because the components of hot air are moving more rapidly.
• When 10 g of ice were added to 100 mL of water at 25 °C, the temperature of the water decreased to 15.5 °C after the ice melted.
• The ingredients of Ivory soap were analyzed to see whether it really is 99.44% pure, as advertised.

Given : components of the scientific method

Asked for : statement classification

Strategy: Refer to the definitions in this section to determine which category best describes each statement.

• This is a general statement of a relationship between the properties of liquid and solid water, so it is a law.
• This is a possible explanation for the origin of birds, so it is a hypothesis.
• This is a statement that tries to explain the relationship between the temperature and the density of air based on fundamental principles, so it is a theory.
• The temperature is measured before and after a change is made in a system, so these are quantitative observations.
• This is an analysis designed to test a hypothesis (in this case, the manufacturer’s claim of purity), so it is an experiment.

Exercise \(\PageIndex{1}\)

• Measured amounts of acid were added to a Rolaids tablet to see whether it really “consumes 47 times its weight in excess stomach acid.”
• Heat always flows from hot objects to cooler ones, not in the opposite direction.
• The universe was formed by a massive explosion that propelled matter into a vacuum.
• Michael Jordan is the greatest pure shooter ever to play professional basketball.
• Limestone is relatively insoluble in water but dissolves readily in dilute acid with the evolution of a gas.
• Gas mixtures that contain more than 4% hydrogen in air are potentially explosive.

qualitative observation

quantitative observation

Because scientists can enter the cycle shown in Figure \(\PageIndex{1}\) at any point, the actual application of the scientific method to different topics can take many different forms. For example, a scientist may start with a hypothesis formed by reading about work done by others in the field, rather than by making direct observations.

It is important to remember that scientists have a tendency to formulate hypotheses in familiar terms simply because it is difficult to propose something that has never been encountered or imagined before. As a result, scientists sometimes discount or overlook unexpected findings that disagree with the basic assumptions behind the hypothesis or theory being tested. Fortunately, truly important findings are immediately subject to independent verification by scientists in other laboratories, so science is a self-correcting discipline. When the Alvarezes originally suggested that an extraterrestrial impact caused the extinction of the dinosaurs, the response was almost universal skepticism and scorn. In only 20 years, however, the persuasive nature of the evidence overcame the skepticism of many scientists, and their initial hypothesis has now evolved into a theory that has revolutionized paleontology and geology.

Chemists expand their knowledge by making observations, carrying out experiments, and testing hypotheses to develop laws to summarize their results and theories to explain them. In doing so, they are using the scientific method.

The World’s Biggest Problems Are Interconnected. Here’s How We Can Solve Them This Decade

T wo decades ago, people around the world rang in the new millennium with a growing sense of optimism. The threat posed by the Cold War was fading slowly in the rearview mirror. Leading thinkers like Francis Fukuyama touted the benefits of globalization , saying it would bring democracy and prosperity to the developing world. The nascent Internet economy promised to bring us closer together.

The following 20 years took some of the air out of the assumption of steady progress, but when future historians assess the 21st century, the year 2020 is likely to serve as the point at which the optimism bubble burst. The COVID-19 pandemic has exposed a complex web of interlocking problems that have morphed into full-blown crises. The coronavirus laid bare the dangers of endemic poverty not only in the developing world but also in rich countries like the U.S., where millions lack health care and are one paycheck away from living on the street. Around the world, racial and ethnic minorities have demanded justice after centuries of structural discrimination. Woven through it all, the earth’s climate is increasingly unstable, posing an existential threat to human society as we know it. In the next decade, societies will be forced to either confront this snarl of challenges, or be overwhelmed by them. Our response will define the future for decades to come.

The recognition that these challenges are fundamentally linked isn’t new. Activists and academics have for many years pointed to the cascading effects of various social ills. Whether it’s the way racism contributes to poor health outcomes or gender discrimination harms economic growth , the examples are seemingly endless. But this understanding has made its way into the conversation about solutions too.

Notably, for the past five years, the U.N. has touted 17 interrelated sustainable development goals, objectives for building a more viable world, and called for a push to achieve them by 2030. The goals, which cover environmental, social and economic progress, are nonbinding but have become key benchmarks for commitments at a national and corporate level. Countries from China to the Maldives, as well as companies like Amazon , Microsoft and PwC, have committed to rolling out policies over the next decade that will set them on a path to eliminate their carbon footprints.

The understanding that these problems require holistic solutions has only grown amid the pandemic and its fallout. President Joe Biden has referred to four urgent crises—the pandemic, the economic crisis, racial injustice and climate change—and promised a push to tackle them all together. The European Union’s program to propel the bloc out of the COVID-19 crisis targets climate change, while incorporating equity concerns. As stock markets soared last year, institutions with trillions of dollars in assets demanded that their investments deliver not only a good return for their wallets but also a good return for society.

All these developments and many more have created new opportunities for bold ideas . These new ways of thinking will come from government leaders, to be sure, but also from activists, entrepreneurs and academics. Here, our eight inaugural members of the 2030 committee offer their own specific solutions—and in them, perhaps, the seeds of 21st century optimism.

This appears in the February 1, 2021 issue of TIME.

More Must-Reads From TIME

• Jane Fonda Champions Climate Action for Every Generation
• Biden’s Campaign Is In Trouble. Will the Turnaround Plan Work?
• Why We're Spending So Much Money Now
• The Financial Influencers Women Actually Want to Listen To
• Breaker Sunny Choi Is Heading to Paris
• Why TV Can’t Stop Making Silly Shows About Lady Journalists
• The Case for Wearing Shoes in the House
• Want Weekly Recs on What to Watch, Read, and More? Sign Up for Worth Your Time

Write to Justin Worland at [email protected]

You May Also Like

Filed under:

The 7 biggest problems facing science, according to 270 scientists

Share this story.

• Share this on Facebook
• Share this on Twitter
• Share this on Reddit
• Share All sharing options

Share All sharing options for: The 7 biggest problems facing science, according to 270 scientists

"Science, I had come to learn, is as political, competitive, and fierce a career as you can find, full of the temptation to find easy paths." — Paul Kalanithi, neurosurgeon and writer (1977–2015)

Science is in big trouble. Or so we’re told.

In the past several years, many scientists have become afflicted with a serious case of doubt — doubt in the very institution of science.

Explore the biggest challenges facing science, and how we can fix them:

• Academia has a huge money problem
• Too many studies are poorly designed
• Replicating results is crucial — and rare
• Peer review is broken
• Too much science is locked behind paywalls
• Science is poorly communicated
• Life as a young academic is incredibly stressful

Conclusion:

• Science is not doomed

As reporters covering medicine, psychology, climate change, and other areas of research, we wanted to understand this epidemic of doubt. So we sent scientists a survey asking this simple question: If you could change one thing about how science works today, what would it be and why?

We heard back from 270 scientists all over the world, including graduate students, senior professors, laboratory heads, and Fields Medalists . They told us that, in a variety of ways, their careers are being hijacked by perverse incentives. The result is bad science.

The scientific process, in its ideal form, is elegant: Ask a question, set up an objective test, and get an answer. Repeat. Science is rarely practiced to that ideal. But Copernicus believed in that ideal. So did the rocket scientists behind the moon landing.

But nowadays, our respondents told us, the process is riddled with conflict. Scientists say they’re forced to prioritize self-preservation over pursuing the best questions and uncovering meaningful truths.

"I feel torn between asking questions that I know will lead to statistical significance and asking questions that matter," says Kathryn Bradshaw, a 27-year-old graduate student of counseling at the University of North Dakota.

Today, scientists' success often isn't measured by the quality of their questions or the rigor of their methods. It's instead measured by how much grant money they win, the number of studies they publish, and how they spin their findings to appeal to the public.

Scientists often learn more from studies that fail. But failed studies can mean career death. So instead, they’re incentivized to generate positive results they can publish. And the phrase "publish or perish" hangs over nearly every decision. It’s a nagging whisper, like a Jedi’s path to the dark side.

"Over time the most successful people will be those who can best exploit the system," Paul Smaldino, a cognitive science professor at University of California Merced, says.

To Smaldino, the selection pressures in science have favored less-than-ideal research: "As long as things like publication quantity, and publishing flashy results in fancy journals are incentivized, and people who can do that are rewarded … they’ll be successful, and pass on their successful methods to others."

Many scientists have had enough.  They want to break this cycle of perverse incentives and rewards. They are going through a period of introspection, hopeful that the end result will yield stronger scientific institutions . In our survey and interviews, they offered a wide variety of ideas for improving the scientific process and bringing it closer to its ideal form.

Before we jump in, some caveats to keep in mind: Our survey was not a scientific poll. For one, the respondents disproportionately hailed from the biomedical and social sciences and English-speaking communities.

Many of the responses did, however, vividly illustrate the challenges and perverse incentives that scientists across fields face. And they are a valuable starting point for a deeper look at dysfunction in science today.

The place to begin is right where the perverse incentives first start to creep in: the money.

(1) Academia has a huge money problem

To do most any kind of research, scientists need money: to run studies, to subsidize lab equipment, to pay their assistants and even their own salaries. Our respondents told us that getting — and sustaining — that funding is a perennial obstacle.

Their gripe isn’t just with the quantity, which, in many fields, is shrinking. It’s the way money is handed out that puts pressure on labs to publish a lot of papers, breeds conflicts of interest, and encourages scientists to overhype their work.

In the United States, academic researchers in the sciences generally cannot rely on university funding alone to pay for their salaries, assistants, and lab costs. Instead, they have to seek outside grants. "In many cases the expectations were and often still are that faculty should cover at least 75 percent of the salary on grants," writes John Chatham, a professor of medicine studying cardiovascular disease at University of Alabama at Birmingham.

Grants also usually expire after three or so years, which pushes scientists away from long-term projects. Yet as John Pooley, a neurobiology postdoc at the University of Bristol, points out, the biggest discoveries usually take decades to uncover and are unlikely to occur under short-term funding schemes.

Outside grants are also in increasingly short supply. In the US, the largest source of funding is the federal government, and that pool of money has been plateauing for years, while young scientists enter the workforce at a faster rate than older scientists retire.

Take the National Institutes of Health, a major funding source. Its budget rose at a fast clip through the 1990s, stalled in the 2000s, and then dipped with sequestration budget cuts in 2013. All the while, rising costs for conducting science meant that each NIH dollar purchased less and less. Last year, Congress approved the biggest NIH spending hike in a decade . But it won’t erase the shortfall.

The consequences are striking: In 2000, more than 30 percent of NIH grant applications got approved. Today, it’s closer to 17 percent. "It's because of what's happened in the last 12 years that young scientists in particular are feeling such a squeeze," NIH Director Francis Collins said at the Milken Global Conference in May.

Truly novel research takes longer to produce, and it doesn’t always pay off. A National Bureau of Economic Research working paper found that, on the whole, truly unconventional papers tend to be less consistently cited in the literature. So scientists and funders increasingly shy away from them, preferring short-turnaround, safer papers. But everyone suffers from that: the NBER report found that novel papers also occasionally lead to big hits that inspire high-impact, follow-up studies.

"I think because you have to publish to keep your job and keep funding agencies happy, there are a lot of (mediocre) scientific papers out there ... with not much new science presented," writes Kaitlyn Suski, a chemistry and atmospheric science postdoc at Colorado State University.

Another worry: When independent, government, or university funding sources dry up, scientists may feel compelled to turn to industry or interest groups eager to generate studies to support their agendas.

Finally, all of this grant writing is a huge time suck, taking resources away from the actual scientific work. Tyler Josephson, an engineering graduate student at the University of Delaware, writes that many professors he knows spend 50 percent of their time writing grant proposals. "Imagine," he asks, "what they could do with more time to devote to teaching and research?"

It’s easy to see how these problems in funding kick off a vicious cycle. To be more competitive for grants, scientists have to have published work. To have published work, they need positive (i.e.,  statistically significant ) results. That puts pressure on scientists to pick "safe" topics that will yield a publishable conclusion — or, worse, may bias their research toward significant results.

"When funding and pay structures are stacked against academic scientists," writes Alison Bernstein, a neuroscience postdoc at Emory University, "these problems are all exacerbated."

Fixes for science's funding woes

Right now there are arguably too many researchers chasing too few grants. Or, as a 2014 piece in the Proceedings of the National Academy of Sciences put it: "The current system is in perpetual disequilibrium, because it will inevitably generate an ever-increasing supply of scientists vying for a finite set of research resources and employment opportunities."

"As it stands, too much of the research funding is going to too few of the researchers," writes Gordon Pennycook, a PhD candidate in cognitive psychology at the University of Waterloo. "This creates a culture that rewards fast, sexy (and probably wrong) results."

One straightforward way to ameliorate these problems would be for governments to simply increase the amount of money available for science. (Or, more controversially, decrease the number of PhDs, but we’ll get to that later.) If Congress boosted funding for the NIH and National Science Foundation, that would take some of the competitive pressure off researchers.

But that only goes so far. Funding will always be finite, and researchers will never get blank checks to fund the risky science projects of their dreams. So other reforms will also prove necessary.

One suggestion: Bring more stability and predictability into the funding process. "The NIH and NSF budgets are subject to changing congressional whims that make it impossible for agencies (and researchers) to make long term plans and commitments," M. Paul Murphy, a neurobiology professor at the University of Kentucky, writes. "The obvious solution is to simply make [scientific funding] a stable program, with an annual rate of increase tied in some manner to inflation."

Another idea would be to change how grants are awarded: Foundations and agencies could fund specific people and labs for a period of time rather than individual project proposals. (The Howard Hughes Medical Institute already does this.) A system like this would give scientists greater freedom to take risks with their work.

Alternatively, researchers in the journal mBio recently called for a lottery-style system. Proposals would be measured on their merits, but then a computer would randomly choose which get funded.

"Although we recognize that some scientists will cringe at the thought of allocating funds by lottery," the authors of the mBio piece write, "the available evidence suggests that the system is already in essence a lottery without the benefits of being random." Pure randomness would at least reduce some of the perverse incentives at play in jockeying for money.

There are also some ideas out there to minimize conflicts of interest from industry funding. Recently, in PLOS Medicine , Stanford epidemiologist John Ioannidis suggested that pharmaceutical companies ought to pool the money they use to fund drug research, to be allocated to scientists who then have no exchange with industry during study design and execution. This way, scientists could still get funding for work crucial for drug approvals — but without the pressures that can skew results.

These solutions are by no means complete, and they may not make sense for every scientific discipline. The daily incentives facing biomedical scientists to bring new drugs to market are different from the incentives facing geologists trying to map out new rock layers. But based on our survey, funding appears to be at the root of many of the problems facing scientists, and it’s one that deserves more careful discussion.

(2) Too many studies are poorly designed. Blame bad incentives.

Scientists are ultimately judged by the research they publish. And the pressure to publish pushes scientists to come up with splashy results, of the sort that get them into prestigious journals. "Exciting, novel results are more publishable than other kinds," says Brian Nosek , who co-founded the Center for Open Science at the University of Virginia.

The problem here is that truly groundbreaking findings simply don’t occur very often, which means scientists face pressure to game their studies so they turn out to be a little more "revolutionary." (Caveat: Many of the respondents who focused on this particular issue hailed from the biomedical and social sciences.)

Some of this bias can creep into decisions that are made early on: choosing whether or not to randomize participants, including a control group for comparison, or controlling for certain confounding factors but not others. (Read more on study design particulars  here .)

Many of our survey respondents noted that perverse incentives can also push scientists to cut corners in how they analyze their data.

"I have incredible amounts of stress that maybe once I finish analyzing the data, it will not look significant enough for me to defend," writes Jess Kautz, a PhD student at the University of Arizona. "And if I get back mediocre results, there's going to be incredible pressure to present it as a good result so they can get me out the door. At this moment, with all this in my mind, it is making me wonder whether I could give an intellectually honest assessment of my own work."

Increasingly, meta-researchers (who conduct research on research) are realizing that scientists often do find little ways to hype up their own results — and they’re not always doing it consciously. Among the most famous examples is a technique called "p-hacking," in which researchers test their data against many hypotheses and only report those that have statistically significant results.

In a recent study , which tracked the misuse of p-values in biomedical journals, meta-researchers found "an epidemic" of statistical significance: 96 percent of the papers that included a p-value in their abstracts boasted statistically significant results.

That seems awfully suspicious. It suggests the biomedical community has been chasing statistical significance, potentially giving dubious results the appearance of validity through techniques like p-hacking — or simply suppressing important results that don't look significant enough. Fewer studies share effect sizes (which arguably gives a better indication of how meaningful a result might be) or discuss measures of uncertainty.

"The current system has done too much to reward results," says Joseph Hilgard, a postdoctoral research fellow at the Annenberg Public Policy Center. "This causes a conflict of interest: The scientist is in charge of evaluating the hypothesis, but the scientist also desperately wants the hypothesis to be true."

The consequences are staggering. An estimated $200 billion — or the equivalent of 85 percent of global spending on research — is routinely wasted on poorly designed and redundant studies, according to meta-researchers who have analyzed inefficiencies in research. We know that as much as 30 percent of the most influential original medical research papers later turn out to be wrong or exaggerated.

Fixes for poor study design

Our respondents suggested that the two key ways to encourage stronger study design — and discourage positive results chasing — would involve rethinking the rewards system and building more transparency into the research process.

"I would make rewards based on the rigor of the research methods, rather than the outcome of the research," writes Simine Vazire, a journal editor and a social psychology professor at UC Davis. "Grants, publications, jobs, awards, and even media coverage should be based more on how good the study design and methods were, rather than whether the result was significant or surprising."

Likewise, Cambridge mathematician Tim Gowers argues that researchers should get recognition for advancing science broadly through informal idea sharing — rather than only getting credit for what they publish.

"We’ve gotten used to working away in private and then producing a sort of polished document in the form of a journal article," Gowers said. "This tends to hide a lot of the thought process that went into making the discoveries. I'd like attitudes to change so people focus less on the race to be first to prove a particular theorem, or in science to make a particular discovery, and more on other ways of contributing to the furthering of the subject."

When it comes to published results, meanwhile, many of our respondents wanted to see more journals put a greater emphasis on rigorous methods and processes rather than splashy results.

"I think the one thing that would have the biggest impact is removing publication bias: judging papers by the quality of questions, quality of method, and soundness of analyses, but not on the results themselves," writes Michael Inzlicht , a University of Toronto psychology and neuroscience professor.

Some journals are already embracing this sort of research. PLOS One , for example, makes a point of accepting negative studies (in which a scientist conducts a careful experiment and finds nothing) for publication, as does the aptly named Journal of Negative Results in Biomedicine .

More transparency would also help, writes Daniel Simons, a professor of psychology at the University of Illinois. Here’s one example: ClinicalTrials.gov , a site run by the NIH, allows researchers to register their study design and methods ahead of time and then publicly record their progress. That makes it more difficult for scientists to hide experiments that didn’t produce the results they wanted. (The site now holds information for more than 180,000 studies in 180 countries.)

Similarly, the AllTrials campaign is pushing for every clinical trial (past, present, and future) around the world to be registered, with the full methods and results reported. Some drug companies and universities have created portals that allow researchers to access raw data from their trials.

The key is for this sort of transparency to become the norm rather than a laudable outlier.

(3) Replicating results is crucial. But scientists rarely do it.

Replication is another foundational concept in science. Researchers take an older study that they want to test and then try to reproduce it to see if the findings hold up.

Testing, validating, retesting — it's all part of a slow and grinding process to arrive at some semblance of scientific truth. But this doesn't happen as often as it should, our respondents said. Scientists face few incentives to engage in the slog of replication. And even when they attempt to replicate a study, they often find they can’t do so . Increasingly it’s being called a "crisis of irreproducibility."

The stats bear this out: A 2015 study looked at 83 highly cited studies that claimed to feature effective psychiatric treatments. Only 16 had ever been successfully replicated. Another 16 were contradicted by follow-up attempts, and 11 were found to have substantially smaller effects the second time around. Meanwhile, nearly half of the studies (40) had never been subject to replication at all.

More recently, a landmark study published in the journal Science demonstrated that only a fraction of recent findings in top psychology journals could be replicated. This is happening in other fields too, says Ivan Oransky, one of the founders of the blog Retraction Watch , which tracks scientific retractions.

As for the underlying causes, our survey respondents pointed to a couple of problems. First, scientists have very few incentives to even try replication. Jon-Patrick Allem, a social scientist at the Keck School of Medicine of USC, noted that funding agencies prefer to support projects that find new information instead of confirming old results.

Journals are also reluctant to publish replication studies unless "they contradict earlier findings or conclusions," Allem writes. The result is to discourage scientists from checking each other's work. "Novel information trumps stronger evidence, which sets the parameters for working scientists."

The second problem is that many studies can be difficult to replicate. Sometimes their methods are too opaque. Sometimes the original studies had too few participants to produce a replicable answer. And sometimes, as we saw in the previous section, the study is simply poorly designed or outright wrong.

Again, this goes back to incentives: When researchers have to publish frequently and chase positive results, there’s less time to conduct high-quality studies with well-articulated methods.

Fixes for underreplication

Scientists need more carrots to entice them to pursue replication in the first place. As it stands, researchers are encouraged to publish new and positive results and to allow negative results to linger in their laptops or file drawers.

This has plagued science with a problem called "publication bias" — not all studies that are conducted actually get published in journals, and the ones that do tend to have positive and dramatic conclusions.

If institutions started to reward tenure positions or make hires based on the quality of a researcher’s body of work, instead of quantity, this might encourage more replication and discourage positive results chasing.

"The key that needs to change is performance review," writes Christopher Wynder, a former assistant professor at McMaster University. "It affects reproducibility because there is little value in confirming another lab's results and trying to publish the findings."

The next step would be to make replication of studies easier. This could include more robust sharing of methods in published research papers. "It would be great to have stronger norms about being more detailed with the methods," says University of Virginia’s Brian Nosek.

He also suggested more regularly adding supplements at the end of papers that get into the procedural nitty-gritty, to help anyone wanting to repeat an experiment.  "If I can rapidly get up to speed, I have a much better chance of approximating the results," he said.

Nosek has detailed other potential fixes that might help with replication — all part of his work at the Center for Open Science .

A greater degree of transparency and data sharing would enable replications, said Stanford’s John Ioannidis. Too often, anyone trying to replicate a study must chase down the original investigators for details about how the experiment was conducted.

"It is better to do this in an organized fashion with buy-in from all leading investigators in a scientific discipline," he explained, "rather than have to try to find the investigator in each case and ask him or her in detective-work fashion about details, data, and methods that are otherwise unavailable."

Researchers could also make use of new tools , such as open source software that tracks every version of a data set, so that they can share their data more easily and have transparency built into their workflow.

Some of our respondents suggested that scientists engage in replication prior to publication. "Before you put an exploratory idea out in the literature and have people take the time to read it, you owe it to the field to try to replicate your own findings," says John Sakaluk, a social psychologist at the University of Victoria.

For example, he has argued, psychologists could conduct small experiments with a handful of participants to form ideas and generate hypotheses. But they would then need to conduct bigger experiments, with more participants, to replicate and confirm those hypotheses before releasing them into the world. "In doing so,"  Sakaluk says, "the rest of us can have more confidence that this is something we might want to [incorporate] into our own research."

(4) Peer review is broken

Peer review is meant to weed out junk science before it reaches publication. Yet over and over again in our survey, respondents told us this process fails. It was one of the parts of the scientific machinery to elicit the most rage among the researchers we heard from.

Normally, peer review works like this: A researcher submits an article for publication in a journal. If the journal accepts the article for review, it's sent off to peers in the same field for constructive criticism and eventual publication — or rejection. (The level of anonymity varies; some journals have double-blind reviews, while others have moved to triple-blind review, where the authors, editors, and reviewers don’t know who one another are.)

It sounds like a reasonable system. But numerous studies and systematic reviews have shown that peer review doesn’t reliably prevent poor-quality science from being published.

The process frequently fails to detect fraud or other problems with manuscripts, which isn't all that surprising when you consider researchers aren't paid or otherwise rewarded for the time they spend reviewing manuscripts. They do it out of a sense of duty — to contribute to their area of research and help advance science.

But this means it's not always easy to find the best people to peer-review manuscripts in their field, that harried researchers delay doing the work (leading to publication delays of up to two years), and that when they finally do sit down to peer-review an article they might be rushed and miss errors in studies.

"The issue is that most referees simply don't review papers carefully enough, which results in the publishing of incorrect papers, papers with gaps, and simply unreadable papers," says Joel Fish, an assistant professor of mathematics at the University of Massachusetts Boston. "This ends up being a large problem for younger researchers to enter the field, since that means they have to ask around to figure out which papers are solid and which are not."

That's not to mention the problem of peer review bullying. Since the default in the process is that editors and peer reviewers know who the authors are (but authors don’t know who the reviews are), biases against researchers or institutions can creep in, opening the opportunity for rude, rushed, and otherwise unhelpful comments. (Just check out the popular #SixWordPeerReview hashtag on Twitter).

These issues were not lost on our survey respondents, who said peer review amounts to a broken system, which punishes scientists and diminishes the quality of publications. They want to not only overhaul the peer review process but also change how it's conceptualized.

Fixes for peer review

On the question of editorial bias and transparency, our respondents were surprisingly divided. Several suggested that all journals should move toward double-blinded peer review, whereby reviewers can't see the names or affiliations of the person they're reviewing and publication authors don't know who reviewed them. The main goal here was to reduce bias.

"We know that scientists make biased decisions based on unconscious stereotyping," writes Pacific Northwest National Lab postdoc Timothy Duignan. "So rather than judging a paper by the gender, ethnicity, country, or institutional status of an author — which I believe happens a lot at the moment — it should be judged by its quality independent of those things."

Yet others thought that more transparency, rather than less, was the answer: "While we correctly advocate for the highest level of transparency in publishing, we still have most reviews that are blinded, and I cannot know who is reviewing me," writes Lamberto Manzoli, a professor of epidemiology and public health at the University of Chieti, in Italy. "Too many times we see very low quality reviews, and we cannot understand whether it is a problem of scarce knowledge or conflict of interest."

Perhaps there is a middle ground. For example,  e Life , a new  open access journal that is rapidly rising in impact factor, runs a collaborative peer review process. Editors and peer reviewers work together on each submission to create a consolidated list of comments about a paper. The author can then reply to what the group saw as the most important issues, rather than facing the biases and whims of individual reviewers. (Oddly, this process is faster — eLife takes less time to accept papers than Nature or Cell.)

Still, those are mostly incremental fixes. Other respondents argued that we might need to radically rethink the entire process of peer review from the ground up.

"The current peer review process embraces a concept that a paper is final," says Nosek. "The review process is [a form of] certification, and that a paper is done." But science doesn't work that way. Science is an evolving process, and truth is provisional. So, Nosek said, science must "move away from the embrace of definitiveness of publication."

Some respondents wanted to think of peer review as more of a continuous process, in which studies are repeatedly and transparently updated and republished as new feedback changes them — much like Wikipedia entries. This would require some sort of expert crowdsourcing.

"The scientific publishing field — particularly in the biological sciences — acts like there is no internet," says Lakshmi Jayashankar, a senior scientific reviewer with the federal government. "The paper peer review takes forever, and this hurts the scientists who are trying to put their results quickly into the public domain."

One possible model already exists in mathematics and physics, where there is a long tradition of "pre-printing" articles. Studies are posted on an open website called  arXiv.org , often before being peer-reviewed and published in journals. There, the articles are sorted and commented on by a community of moderators, providing another chance to filter problems before they make it to peer review.

"Posting preprints would allow scientific crowdsourcing to increase the number of errors that are caught, since traditional peer-reviewers cannot be expected to be experts in every sub-discipline," writes Scott Hartman, a paleobiology PhD student at the University of Wisconsin.

And even after an article is published, researchers think the peer review process shouldn't stop. They want to see more "post-publication" peer review on the web, so that academics can critique and comment on articles after they've been published. Sites like PubPeer and F1000Research have already popped up to facilitate that kind of post-publication feedback.

"We do this a couple of times a year at conferences," writes Becky Clarkson, a geriatric medicine researcher at the University of Pittsburgh. "We could do this every day on the internet."

The bottom line is that traditional peer review has never worked as well as we imagine it to — and it’s ripe for serious disruption.

(5) Too much science is locked behind paywalls

After a study has been funded, conducted, and peer-reviewed, there's still the question of getting it out so that others can read and understand its results.

Over and over, our respondents expressed dissatisfaction with how scientific research gets disseminated. Too much is locked away in paywalled journals, difficult and costly to access, they said. Some respondents also criticized the publication process itself for being too slow, bogging down the pace of research.

On the access question, a number of scientists argued that academic research should be free for all to read. They chafed against the current model, in which for-profit publishers put journals behind pricey paywalls.

A single article in Science will set you back $30; a year-long subscription to Cell will cost $279. Elsevier publishes 2,000 journals that can cost up to $10,000 or $20,000 a year for a subscription.

Many US institutions pay those journal fees for their employees, but not all scientists (or other curious readers) are so lucky. In a recent issue of Science , journalist John Bohannon described the plight of a PhD candidate at a top university in Iran. He calculated that the student would have to spend $1,000 a week just to read the papers he needed.

As Michael Eisen, a biologist at UC Berkeley and co-founder of the Public Library of Science (or PLOS ) , put it , scientific journals are trying to hold on to the profits of the print era in the age of the internet.  Subscription prices have continued to climb, as a handful of big publishers (like Elsevier) have bought up more and more journals, creating mini knowledge fiefdoms.

"Large, publicly owned publishing companies make huge profits off of scientists by publishing our science and then selling it back to the university libraries at a massive profit (which primarily benefits stockholders)," Corina Logan, an animal behavior researcher at the University of Cambridge, noted. "It is not in the best interest of the society, the scientists, the public, or the research." (In 2014, Elsevier reported a profit margin of nearly 40 percent and revenues close to $3 billion.)

"It seems wrong to me that taxpayers pay for research at government labs and universities but do not usually have access to the results of these studies, since they are behind paywalls of peer-reviewed journals," added Melinda Simon, a postdoc microfluidics researcher at Lawrence Livermore National Lab.

Fixes for closed science

Many of our respondents urged their peers to publish in open access journals (along the lines of PeerJ or PLOS Biology ). But there’s an inherent tension here. Career advancement can often depend on publishing in the most prestigious journals, like Science or Nature , which still have paywalls.

There's also the question of how best to finance a wholesale transition to open access. After all, journals can never be entirely free. Someone has to pay for the editorial staff, maintaining the website, and so on. Right now, open access journals typically charge fees to those submitting papers, putting the burden on scientists who are already struggling for funding.

One radical step would be to abolish for-profit publishers altogether and move toward a nonprofit model. "For journals I could imagine that scientific associations run those themselves," suggested Johannes Breuer, a postdoctoral researcher in media psychology at the University of Cologne. "If they go for online only, the costs for web hosting, copy-editing, and advertising (if needed) can be easily paid out of membership fees."

As a model, Cambridge’s Tim Gowers has launched an online mathematics journal called Discrete Analysis . The nonprofit venture is owned and published by a team of scholars, it has no publisher middlemen, and access will be completely free for all.

Until wholesale reform happens, however, many scientists are going a much simpler route: illegally pirating papers.

Bohannon reported that millions of researchers around the world now use Sci-Hub , a site set up by Alexandra Elbakyan, a Russia-based neuroscientist, that illegally hosts more than 50 million academic papers. "As a devout pirate," Elbakyan told us, "I think that copyright should be abolished."

One respondent had an even more radical suggestion: that we abolish the existing peer-reviewed journal system altogether and simply publish everything online as soon as it’s done.

"Research should be made available online immediately, and be judged by peers online rather than having to go through the whole formatting, submitting, reviewing, rewriting, reformatting, resubmitting, etc etc etc that can takes years," writes Bruno Dagnino, formerly of the Netherlands Institute for Neuroscience. "One format, one platform. Judge by the whole community, with no delays."

A few scientists have been taking steps in this direction. Rachel Harding, a genetic researcher at the University of Toronto, has set up a website called Lab Scribbles , where she publishes her lab notes on the structure of huntingtin proteins in real time, posting data as well as summaries of her breakthroughs and failures. The idea is to help share information with other researchers working on similar issues, so that labs can avoid needless overlap and learn from each other's mistakes.

Not everyone might agree with approaches this radical; critics worry that too much sharing might encourage scientific free riding. Still, the common theme in our survey was transparency. Science is currently too opaque, research too difficult to share. That needs to change.

(6) Science is poorly communicated to the public

"If I could change one thing about science, I would change the way it is communicated to the public by scientists, by journalists, and by celebrities," writes Clare Malone, a postdoctoral researcher in a cancer genetics lab at Brigham and Women's Hospital.

She wasn't alone. Quite a few respondents in our survey expressed frustration at how science gets relayed to the public. They were distressed by the fact that so many laypeople hold on to completely unscientific ideas or have a crude view of how science works.

They have a point. Science journalism is often full of exaggerated, conflicting, or outright misleading claims. If you ever want to see a perfect example of this, check out "Kill or Cure," a site where Paul Battley meticulously documents all the times the Daily Mail reported that various items — from antacids to yogurt — either cause cancer, prevent cancer, or sometimes do both.

Sometimes bad stories are peddled by university press shops. In 2015, the University of Maryland issued a press release claiming that a single brand of chocolate milk could improve concussion recovery. It was an absurd case of science hype.

Indeed, one review in BMJ found that one-third of university press releases contained either exaggerated claims of causation (when the study itself only suggested correlation), unwarranted implications about animal studies for people, or unfounded health advice.

But not everyone blamed the media and publicists alone. Other respondents pointed out that scientists themselves often oversell their work, even if it's preliminary, because funding is competitive and everyone wants to portray their work as big and important and game-changing.

"You have this toxic dynamic where journalists and scientists enable each other in a way that massively inflates the certainty and generality of how scientific findings are communicated and the promises that are made to the public," writes Daniel Molden, an associate professor of psychology at Northwestern University. "When these findings prove to be less certain and the promises are not realized, this just further erodes the respect that scientists get and further fuels scientists desire for appreciation."

Fixes for better science communication

Opinions differed on how to improve this sorry state of affairs — some pointed to the media, some to press offices, others to scientists themselves.

Plenty of our respondents wished that more science journalists would move away from hyping single studies. Instead, they said, reporters ought to put new research findings in context, and pay more attention to the rigor of a study's methodology than to the splashiness of the end results.

"On a given subject, there are often dozens of studies that examine the issue," writes Brian Stacy of the US Department of Agriculture. "It is very rare for a single study to conclusively resolve an important research question, but many times the results of a study are reported as if they do."

But it’s not just reporters who will need to shape up. The "toxic dynamic" of journalists, academic press offices, and scientists enabling one another to hype research can be tough to change, and many of our respondents pointed out that there were no easy fixes — though recognition was an important first step.

Some suggested the creation of credible referees that could rigorously distill the strengths and weaknesses of research. (Some variations of this are starting to pop up: The Genetic Expert News Service solicits outside experts to weigh in on big new studies in genetics and biotechnology.) Other respondents suggested that making research free to all might help tamp down media misrepresentations.

Still other respondents noted that scientists themselves should spend more time learning how to communicate with the public — a skill that tends to be under-rewarded in the current system.

"Being able to explain your work to a non-scientific audience is just as important as publishing in a peer-reviewed journal, in my opinion, but currently the incentive structure has no place for engaging the public," writes Crystal Steltenpohl, a graduate assistant at DePaul University.

Reducing the perverse incentives around scientific research itself could also help reduce overhype.  "If we reward research based on how noteworthy the results are, this will create pressure to exaggerate the results (through exploiting flexibility in data analysis, misrepresenting results, or outright fraud)," writes UC Davis's Simine Vazire. "We should reward research based on how rigorous the methods and design are."

Or perhaps we should focus on improving science literacy. Jeremy Johnson, a project coordinator at the Broad Institute, argued that bolstering science education could help ameliorate a lot of these problems. "Science literacy should be a top priority for our educational policy," he said, "not an elective."

(7) Life as a young academic is incredibly stressful

When we asked researchers what they’d fix about science, many talked about the scientific process itself, about study design or peer review. These responses often came from tenured scientists who loved their jobs but wanted to make the broader scientific project even better.

But on the flip side, we heard from a number of researchers — many of them graduate students or postdocs — who were genuinely passionate about research but found the day-to-day experience of being a scientist grueling and unrewarding. Their comments deserve a section of their own.

Today, many tenured scientists and research labs depend on small armies of graduate students and postdoctoral researchers to perform their experiments and conduct data analysis.

These grad students and postdocs are often the primary authors on many studies. In a number of fields, such as the biomedical sciences, a postdoc position is a prerequisite before a researcher can get a faculty-level position at a university.

This entire system sits at the heart of modern-day science. (A new card game called Lab Wars pokes fun at these dynamics.)

But these low-level research jobs can be a grind. Postdocs typically work long hours and are relatively low-paid for their level of education — salaries are frequently pegged to stipends set by NIH National Research Service Award grants, which start at $43,692 and rise to $47,268 in year three.

Postdocs tend to be hired on for one to three years at a time, and in many institutions they are considered contractors, limiting their workplace protections. We heard repeatedly about extremely long hours and limited family leave benefits.

"Oftentimes this is problematic for individuals in their late 20s and early to mid-30s who have PhDs and who may be starting families while also balancing a demanding job that pays poorly," wrote one postdoc, who asked for anonymity.

This lack of flexibility tends to disproportionately affect women — especially women planning to have families — which helps contribute to gender inequalities in research. ( A 2012 paper found that female job applicants in academia are judged more harshly and are offered less money than males.) "There is very little support for female scientists and early-career scientists," noted another postdoc.

"There is very little long-term financial security in today's climate, very little assurance where the next paycheck will come from," wrote William Kenkel, a postdoctoral researcher in neuroendocrinology at Indiana University. "Since receiving my PhD in 2012, I left Chicago and moved to Boston for a post-doc, then in 2015 I left Boston for a second post-doc in Indiana. In a year or two, I will move again for a faculty job, and that's if I'm lucky. Imagine trying to build a life like that."

This strain can also adversely affect the research that young scientists do. "Contracts are too short term," noted another researcher. "It discourages rigorous research as it is difficult to obtain enough results for a paper (and hence progress) in two to three years. The constant stress drives otherwise talented and intelligent people out of science also."

Because universities produce so many PhDs but have way fewer faculty jobs available, many of these postdoc researchers have limited career prospects. Some of them end up staying stuck in postdoc positions for five or 10 years or more.

"In the biomedical sciences," wrote the first postdoc quoted above, "each available faculty position receives applications from hundreds or thousands of applicants, putting immense pressure on postdocs to publish frequently and in high impact journals to be competitive enough to attain those positions."

Many young researchers pointed out that PhD programs do fairly little to train people for careers outside of academia. "Too many [PhD] students are graduating for a limited number of professor positions with minimal training for careers outside of academic research," noted Don Gibson, a PhD candidate studying plant genetics at UC Davis.

Laura Weingartner, a graduate researcher in evolutionary ecology at Indiana University, agreed: "Few universities (specifically the faculty advisors) know how to train students for anything other than academia, which leaves many students hopeless when, inevitably, there are no jobs in academia for them."

Add it up and it's not surprising that we heard plenty of comments about anxiety and depression among both graduate students and postdocs. "There is a high level of depression among PhD students," writes Gibson. "Long hours, limited career prospects, and low wages contribute to this emotion."

A 2015 study at the University of California Berkeley found that 47 percent of PhD students surveyed could be considered depressed. The reasons for this are complex and can't be solved overnight. Pursuing academic research is already an arduous, anxiety-ridden task that's bound to take a toll on mental health.

But as Jennifer Walker explored recently at Quartz, many PhD students also feel isolated and unsupported, exacerbating those issues.

Fixes to keep young scientists in science

We heard plenty of concrete suggestions. Graduate schools could offer more generous family leave policies and child care for graduate students. They could also increase the number of female applicants they accept in order to balance out the gender disparity.

But some respondents also noted that workplace issues for grad students and postdocs were inseparable from some of the fundamental issues facing science that we discussed earlier. The fact that university faculty and research labs face immense pressure to publish — but have limited funding — makes it highly attractive to rely on low-paid postdocs.

"There is little incentive for universities to create jobs for their graduates or to cap the number of PhDs that are produced," writes Weingartner. "Young researchers are highly trained but relatively inexpensive sources of labor for faculty."

Some respondents also pointed to the mismatch between the number of PhDs produced each year and the number of academic jobs available.

A recent feature by Julie Gould in Nature explored a number of ideas for revamping the PhD system. One idea is to split the PhD into two programs: one for vocational careers and one for academic careers. The former would better train and equip graduates to find jobs outside academia.

This is hardly an exhaustive list. The core point underlying all these suggestions, however, was that universities and research labs need to do a better job of supporting the next generation of researchers. Indeed, that's arguably just as important as addressing problems with the scientific process itself. Young scientists, after all, are by definition the future of science.

Weingartner concluded with a sentiment we saw all too frequently: "Many creative, hard-working, and/or underrepresented scientists are edged out of science because of these issues. Not every student or university will have all of these unfortunate experiences, but they’re pretty common. There are a lot of young, disillusioned scientists out there now who are expecting to leave research."

Science needs to correct its greatest weaknesses

Science is not doomed.

For better or worse, it still works. Look no further than the novel vaccines to prevent Ebola, the discovery of gravitational waves , or new treatments for stubborn diseases. And it’s getting better in many ways. See the work of meta -researchers who study and evaluate research — a field that has gained prominence over the past 20 years.

More from this feature

We asked hundreds of scientists what they’d change about science. Here are 33 of our favorite responses.

But science is conducted by fallible humans, and it hasn’t been human-proofed to protect against all our foibles. The scientific revolution began just 500 years ago. Only over the past 100 has science become professionalized. There is still room to figure out how best to remove biases and align incentives.

To that end, here are some broad suggestions:

One: Science has to acknowledge and address its money problem. Science is enormously valuable and deserves ample funding. But the way incentives are set up can distort research.

Right now, small studies with bold results that can be quickly turned around and published in journals are disproportionately rewarded. By contrast, there are fewer incentives to conduct research that tackles important questions with robustly designed studies over long periods of time. Solving this won’t be easy, but it is at the root of many of the issues discussed above.

Two: Science needs to celebrate and reward failure. Accepting that we can learn more from dead ends in research and studies that failed would alleviate the "publish or perish" cycle. It would make scientists more confident in designing robust tests and not just convenient ones, in sharing their data and explaining their failed tests to peers, and in using those null results to form the basis of a career (instead of chasing those all-too-rare breakthroughs).

Three: Science has to be more transparent. Scientists need to publish the methods and findings more fully, and share their raw data in ways that are easily accessible and digestible for those who may want to reanalyze or replicate their findings.

There will always be waste and mediocre research, but as Stanford’s Ioannidis explains in a recent paper , a lack of transparency creates excess waste and diminishes the usefulness of too much research.

Again and again, we also heard from researchers, particularly in social sciences, who felt that their cognitive biases in their own work, influenced by pressures to publish and advance their careers, caused science to go off the rails. If more human-proofing and de-biasing were built into the process — through stronger peer review, cleaner and more consistent funding, and more transparency and data sharing — some of these biases could be mitigated.

These fixes will take time, grinding along incrementally — much like the scientific process itself. But the gains humans have made so far using even imperfect scientific methods would have been unimaginable 500 years ago. The gains from improving the process could prove just as staggering, if not more so.

Correction: An earlier version of this story misstated Noah Grand's title. At the time of the survey he was a lecturer in sociology at UCLA, not a professor.

Will you help keep Vox free for all?

At Vox, we believe that clarity is power, and that power shouldn’t only be available to those who can afford to pay. That’s why we keep our work free. Millions rely on Vox’s clear, high-quality journalism to understand the forces shaping today’s world. Support our mission and help keep Vox free for all by making a financial contribution to Vox today.

We accept credit card, Apple Pay, and Google Pay. You can also contribute via

The total solar eclipse is returning to the United States — better than before

Why did geologists reject the “anthropocene” epoch it’s not rock science., 17 astounding scientific mysteries that researchers can’t yet solve, sign up for the newsletter today, explained, thanks for signing up.

Check your inbox for a welcome email.

Oops. Something went wrong. Please enter a valid email and try again.

Advertisement

'Third Millennium Thinking': How to use scientific tools to solve everyday problems

Copy the code below to embed the wbur audio player on your site.

<iframe width="100%" height="124" scrolling="no" frameborder="no" src="https://player.wbur.org/hereandnow/2024/03/26/third-millenium-thinking-book"></iframe>

• Emiko Tamagawa

Life is full of decisions. “ Third Millennium Thinking: Creating Sense in a World of Knowledge ” outlines methods of making choices rationally using scientific methods.

Nobel Prize-winning physicist Saul Perlmutter , philosophy professor John Campbell , and social psychologist Robert MacCoun turned their course at the University of California Berkeley on using scientific tools to approach everyday problems into a book.

Perlmutter says it's easy to fall into mental traps or fool ourselves when making a choice. But when people assess all the variables that could influence them and the potential outcomes, they approach questions more thoughtfully, he says.

“There is so much of what is the scientific approach to the world that is never taught anywhere,” Perlmutter says. “It seemed like this was a time for us to be trying to figure out how can we teach this in ways that don't require having to become a scientist in order to do it.”

Book excerpt: 'Third Millennium Thinking: Creating Sense in a World of Nonsense'

By Saul Perlmutter, John Campbell and Robert MacCoun

INTRODUCTION

In just the past few decades, those of us who live in the internet-​connected world have obtained access to a nearly unfathomable amount of information. We can click a link and instantly gain insight into whatever we’re curious about, whether it’s treatment options for a particular health condition, how to build a solar generator, or the political history of Malta. On the other hand, sometimes there is so much information we don’t know how to sort or evaluate it. The social science database ProQuest, for example, boasts of “a growing content collection that now encompasses . . . 6 billion digital pages and spans six centuries.” And that’s just old-​school, print information! The Internet Archive’s Wayback Machine, an archive of websites and other digital artifacts dating back to 1996, hosts almost a trillion pages of digital content, tens of millions of books and audios, and nearly a million software programs.

More and more often, it can be hard to determine what to focus on, let alone how to distinguish what’s revelatory and enlightening, in and among all the highly technical, specialized, contradictory, incomplete, out‑of‑date, biased, or deliberately untrue information we can now access. Was that drug study funded by a pharmaceutical company? Did an AI system invent all those supposedly authentic product reviews? What do those statistics leave out? What does that article even mean ? It is also increasingly tricky to identify whom to trust for expert guidance in interpreting this information. There are all sorts of people out there who claim expertise — and perhaps your favorite experts aren’t my favorite experts. Experts disagree, or have ulterior motives, or perhaps don’t understand the world or “real life” beyond their own narrow perspective. How do we find an expert we can safely trust?

To make a sound decision, take a meaningful action, or solve a problem — whether as individuals, in groups, or as a society — we need first to understand reality. But when reality is not easy to discern, and we’re not sure which experts to trust to clarify the matter, we adopt other strategies for navigating the clutter. We “go with our gut”; decide what we “believe” and look for evidence to reaffirm whatever that is; adopt positions based on our affiliations with people we know; even find reassurance in belittling the people who disagree with us. We choose to consult experts who tell us what we like to hear; or bond in shared mistrust of people providing or communicating the information that confuses us, whether they are scientists, scholars, journalists, community leaders, policymakers, or other experts. These coping strategies may help us get by in our personal or professional lives; they may provide a consoling sense of identity or belonging. But they do not actually help us see clearly or make good decisions. And resorting to them can have dangerous social and political consequences.

How can we navigate better — as individuals, and as a society — in this age of informational overwhelm? How do we ward off confusion, avoid mental traps, and sift sense out of nonsense? How do we make decisions and solve problems collaboratively with people who interpret information differently or have different values than we do?

The three of us — a physicist (Saul), a philosopher ( John), and a psychologist (Rob) — have been working closely together for nearly a decade on a project to help our students learn to think about big problems and make effective decisions in this “too much information” age. We began our collaboration in 2011, in response to what was already a worrying trend toward no‑think, politics-​driven decision-​making. An issue like raising the national debt ceiling, for example, was being debated that summer as if it were a religious schism, rather than a simple, practical, probably even testable question of what economic approach would work best to improve the country’s economic well-being. Most of the arguments both yea and nay betrayed equal disregard for, or ignorance of, the most basic principles of scientific thought. We began to wonder whether it might be possible to first articulate and then teach the principles that would lead to clearer thinking, more rational arguments, and a more fruitful collaborative decision-​making process.

The result was a team-​taught, multidisciplinary Big Ideas course at UC Berkeley, intended to teach students the whole gamut of ideas, tools, and approaches that natural and social scientists use to understand the world. We also designed the course to show how useful these approaches can be for everybody in day‑to‑day life, whether working individually or collaboratively, in making reasoned decisions and solving the full range of problems that face us. To our great satisfaction, the course has been both popular and successful, and has since been replicated and adapted by other teachers at a growing number of other universities.1 Our students appear to rethink their worlds and emerge energized with new ways to approach both personal decision-​making and our society’s problems. They are better able to investigate their questions, evaluate information and expertise, and work together as members of a group or a society. Inspired by their enthusiasm, we began to think about new ways to share these tools — and this new way of thinking and working together — beyond the classroom, with students and citizens of all ages.

We have become ever more concerned that our society is losing its way, causing suffering — and missing great opportunities — simply because we don’t have the tools that could help us make sense of the extraordinary amount of complex, often contradictory information now available to us. Practical problem-​solving can come to a standstill when we cannot ascertain the facts of the problems, or, when those problems require communal or political solutions, even agree with others on what those facts are. We humans, who can figure out rocket science and fly to the moon, can’t always figure out how to navigate uncertainty and conflicting points of view to make a simple reasonable decision when we need to.

Part of the problem is that science itself is often a major source of the highly technical, opaque, inconsistent, and contradictory information that has overwhelmed, perplexed, and even angered people. Trust in science has eroded in the recent past.2 The achievements of science cannot live up to all the utopian expectations those successes have generated. Some scientific achievements have also come with negative social, political, or environmental side effects. For these and other reasons, science has become one of the totems of polarization in political discussions. In short, as science became harder to understand, was connected to undesirable side effects, and subjected to politically partisan critiques, many people lost their trust in scientists and in “science” itself.3

But science also has a phenomenal record of providing insight into — if not answers to — the most confounding questions humans have thought to ask. It has helped us to solve puzzles, address problems, and make better lives over millennia. It is a culture of inquiry rooted in the dawn of humankind, with centuries of practice in evaluating conflicting information in a baffling world, and in distinguishing what we know from what we don’t. Along the way, scientists have learned from both successes and mistakes, breakthroughs and blunders, to refine the tools with which to address new questions and solve new problems.

Over the past few years, we have all become aware of the shocking degree of polarization in our society, and the surprising interaction between this polarization and our society’s often-​problematic relationship to science and scientific expertise. If we are to have any hope of finding the practical common plans and common understandings that can move our society ahead together, we need to learn to accept the possibility of errors in our own thinking, and our need for opposing views that help us see where we are going wrong. And we need to understand the source of the disenchantment with and backlash against scientific progress that arose during the end of the Second Millennium and seek to repair it.

No one book and no single approach can heal the rifts. Not all of our polarized disagreements will vanish. But we have to start somewhere. And we believe that one of our more promising starting points is with the culture of science — if we begin to borrow its tools, ideas, and processes, and make a Third Millennium shift in our own thinking.

Adapted from "Third Millenium Thinking" by Saul Perlmutter, John Campbell, and Robert MacCoun. Copyright © 2024 by Saul Perlmutter, John Campbell, and Robert MacCoun. Used with permission of Little, Brown Spark, an imprint of Little, Brown and Company. New York, NY. All rights reserved.

Emiko Tamagawa  produced and edited this interview for broadcast with  Todd Mundt .  Grace Griffin  adapted it for the web.

This article was originally published on March 26, 2024.

This segment aired on March 26, 2024.

Scott Tong Co-Host, Here & Now Scott Tong joined Here & Now as a co-host in July 2021 after spending 16 years at Marketplace as Shanghai bureau chief and senior correspondent.

Emiko Tamagawa Senior Producer, Here & Now Emiko Tamagawa produces arts and culture segments for Here & Now.

More from Here & Now

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Mechanics (Essentials) - Class 11th

Course: mechanics (essentials) - class 11th   >   unit 2.

• Introduction to physics
• What is physics?

The scientific method

• Models and Approximations in Physics

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation..

• Observation: the toaster won't toast.

2. Ask a question.

• Question: Why won't my toaster toast?

3. Propose a hypothesis.

• Hypothesis: Maybe the outlet is broken.

4. Make predictions.

• Prediction: If I plug the toaster into a different outlet, then it will toast the bread.

5. Test the predictions.

• Test of prediction: Plug the toaster into a different outlet and try again.
• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• Iteration time!
• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

Want to join the conversation?

The Math You Need, When You Need It

math tutorials for students majoring in the earth sciences

Scientific Notation - Practice Problems

Solving earth science problems with scientific notation, × div[id^='image-'] {position:static}div[id^='image-'] div.hover{position:static} introductory problems.

These problems cover the fundamentals of writing scientific notation and using it to understand relative size of values and scientific prefixes.

Problem 1: The distance to the moon is 238,900 miles. Write this value in scientific notation.

Problem 2: One mile is 1609.34 meters. What is the distance to the moon in meters using scientific notation?

`1609.34 m/(mi) xx 238","900 mi` = 384,400,000 m

Notice in the above unit conversion the 'mi' units cancel each other out because 'mi' is in the denominator for the first term and the numerator for the second term

Problem 4: The atomic radius of a magnesium atom is approximately 1.6 angstroms, which is equal to 1.6 x 10 -10 meters (m). How do you write this length in standard form?

 0.00000000016 m  

Fissure A = 40,0000 m Fissure B = 5,0000 m

This shows fissure A is larger (by almost 10 times!). The shortcut to answer a question like this is to look at the exponent. If both coefficients are between 1-10, then the value with the larger exponent is the larger number.

Problem 6: The amount of carbon in the atmosphere is 750 petagrams (pg). One petagram equals 1 x 10 15 grams (g). Write out the amount of carbon in the atmosphere in (i) scientific notation and (ii) standard decimal format.

The exponent is a positive number, so the decimal will move to the right in the next step.

750,000,000,000,000,000 g

Advanced Problems

Scientific notation is used in solving these earth and space science problems and they are provided to you as an example. Be forewarned that these problems move beyond this module and require some facility with unit conversions, rearranging equations, and algebraic rules for multiplying and dividing exponents. If you can solve these, you've mastered scientific notation!

Problem 7: Calculate the volume of water (in cubic meters and in liters) falling on a 10,000 km 2 watershed from 5 cm of rainfall.

`10,000  km^2 = 1 xx 10^4  km^2`

5 cm of rainfall = `5 xx 10^0 cm`

Let's start with meters as the common unit and convert to liters later. There are 1 x 10 3 m in a km and area is km x km (km 2 ), therefore you need to convert from km to m twice:

`1 xx 10^3 m/(km) * 1 xx 10^3 m/(km) = 1 xx 10^6 m^2/(km)^2` `1 xx 10 m^2/(km)^2 * 1 xx 10^4 km^2 = 1 xx 10^10 m^2` for the area of the watershed.

For the amount of rainfall, you should convert from centimeters to meters:

`5 cm * (1 m)/(100 cm)= 5 xx 10^-2 m`

`V = A * d`

When multiplying terms with exponents, you can multiply the coefficients and add the exponents:

`V = 1 xx 10^10 m^2 * 5.08 xx 10^(-2) m = 5.08 xx 10^8 m^3`

Given that there are 1 x 10 3 liters in a cubic meter we can make the following conversion:

`1 xx 10^3 L * 5.08 xx 10^8 m^3 = 5.08 xx 10^11 L`

Step 5. Check your units and your answer - do they make sense?           

`V = 4/3 pi r^3`

Using this equation, plug in the radius (r) of the dust grains.

`V = 4/3 pi (2 xx10^(-6))^3m^3`

Notice the (-6) exponent is cubed. When you take an exponent to an exponent, you need to multiply the two terms

`V = 4/3 pi (8 xx10^(-18)m^3)`

Then, multiple the cubed radius times pi and 4/3

`V = 3.35 xx 10^(-17) m^3`

`m = 3.35 xx 10^(-17) m^3 * 3300 (kg)/m^3`

Notice in the equation above that the m 3 terms cancel each other out and you are left with kg

`m = 1.1 xx 10^(-13) kg`

`V = 4/3 pi (2.325 xx10^(15) m)^3`

`V = 5.26 xx10^(46) m^3`

Number of dust grains = `5.26 xx10^(46) m^3 xx 0.001` grains/m 3

Number of dust grains = `5.26xx10^43 "grains"`

Total mass = `1.1xx10^(-13) (kg)/("grains") * 5.26xx10^43 "grains"`

Notice in the equation above the 'grains' terms cancel each other out and you are left with kg

Total mass = `5.79xx10^30 kg`

If you feel comfortable with this topic, you can go on to the assessment . Or you can go back to the Scientific Notation explanation page .

« Previous Page       Next Page »

The Most Important Scientific Problems Have Yet to Be Solved

Here is a false concept often heard from the lips of the newly graduated: “Everything of major importance in the various areas of science has already been clarified. What difference does it make if I add some minor detail or gather up what is left in some field where more diligent observers have already collected the abundant, ripe grain. Science won’t change its perspective because of my work, and my name will never emerge from obscurity.”

This is often indolence masquerading as modesty. However, it is also expressed by worthy young men reflecting on the first pangs of dismay experienced when undertaking some major project. This superficial concept of science must be eradicated by the young investigator who does not wish to fail, hopelessly overcome by the struggle developing in his mind between the utilitarian suggestions that are part and parcel of his ethical environment (which may soon convert him to an ordinary and financially successful general practitioner), and those nobler impulses of duty and loyalty urging him on to achievement and honor.

Wanting to earn the trust placed in him by his mentors, the inexperienced observer hopes to discover a new lode at the earth’s surface, where easy exploration will build his reputation quickly. Unfortunately, with his first excursions into the literature hardly begun, he is shocked to find that the metal lies deep within the ground — surface deposits have been virtually exhausted by observers fortunate enough to arrive earlier and exercise their simple right of eminent domain.

It is nevertheless true that if we arrived on the scene too late for certain problems, we were also born too early to help solve others. Within a century we shall come, by the natural course of events, to monopolize science, plunder its major assets, and harvest its vast fields of data.

It is a wonderful and fortunate thing for a scientist to be born during one of these great decisive moments in the history of ideas, when much of what has been done in the past is invalidated.

Yet we must recognize that there are times when, on the heels of a chance discovery or the development of an important new technique, magnificent scientific discoveries occur one after another as if by spontaneous generation. This happened during the Renaissance when Descartes, Pascal, Galileo, Bacon, Boyle, Newton, our own Sanchez, and others revealed clearly the errors of the ancients and spread the belief that the Greeks, far from exhausting the field of science, had scarcely taken the first steps in understanding the universe. It is a wonderful and fortunate thing for a scientist to be born during one of these great decisive moments in the history of ideas, when much of what has been done in the past is invalidated. Under these circumstances, it could not be easier to choose a fertile area of investigation.

However, let us not exaggerate the importance of such events. Instead, bear in mind that even in our own time science is often built on the ruins of theories once thought to be indestructible. It is important to realize that if certain areas of science appear to be quite mature, others are in the process of development, and yet others remain to be born. Especially in biology, where immense amounts of work have been carried out during the last century, the most essential problems remain unsolved — the origin of life, the problems of heredity and development, the structure and chemical composition of the cell, and so on.

It is fair to say that, in general, no problems have been exhausted; instead, men have been exhausted by the problems. Soil that appears impoverished to one researcher reveals its fertility to another. Fresh talent approaching the analysis of a problem without prejudice will always see new possibilities — some aspect not considered by those who believe that a subject is fully understood. Our knowledge is so fragmentary that unexpected findings appear in even the most fully explored topics. Who, a few short years ago, would have suspected that light and heat still held scientific secrets in reserve? Nevertheless, we now have argon in the atmosphere, the x-rays of Roentgen, and the radium of the Curies, all of which illustrate the inadequacy of our former methods, and the prematurity of our former syntheses.

It is fair to say that, in general, no problems have been exhausted; instead, men have been exhausted by the problems.

The best application of the following beautiful dictum of Geoffroy Saint-Hilaire is in biology: “The infinite is always before us.” And the same applies to Carnoy’s no less graphic thought: “Science is a perpetual creative process.” Not everyone is destined to venture into the forest and by sheer determination carve out a serviceable road. However, even the most humble among us can take advantage of the path opened by genius and by traveling along it extract one or another secret from the unknown. If the beginner is willing to accept the role of gathering details that escaped the wise discoverer, he can be assured that those searching for minutiae eventually acquire an analytical sense so discriminating, and powers of observation so keen, that they are able to solve important problems successfully.

So many apparently trivial observations have led investigators with a thorough knowledge of methods to great scientific conquests! Furthermore, we must bear in mind that because science relentlessly differentiates, the minutiae of today often become important principles tomorrow.

It is also essential to remember that our appreciation of what is important and what is minor, what is great and what is small, is based on false wisdom, on a true anthropomorphic error. Superior and inferior do not exist in nature, nor do primary and secondary relationships. The hierarchies that our minds take pleasure in assigning to natural phenomena arise from the fact that instead of considering things individually, and how they are interrelated, we view them strictly from the perspective of their usefulness or the pleasure they give us. In the chain of life all links are equally valuable because all prove equally necessary.

Things that we see from a distance or do not know how to evaluate are considered small. Even assuming the perspective of human egotism, think how many issues of profound importance to humanity lie within the protoplasm of the simplest microbe! Nothing seems more important in bacteriology than a knowledge of infectious bacteria, and nothing more secondary than the inoffensive microbes that grow abundantly in decomposing organic material. Nevertheless, if these humble fungi — whose mission is to return to the general circulation of matter those substances incorporated by the higher plants and animals — were to disappear, humans could not inhabit the planet.

The far-reaching importance of attention to detail in technical methodology is perhaps demonstrated more clearly in biology than in any other sphere. To cite but one example, recall that Koch, the great German bacteriologist, thought of adding a little alkali to a basic aniline dye, and this allowed him to stain and thus discover the tubercle bacillus — revealing the etiology of a disease that had until then remained uncontrolled by the wisdom of the most illustrious pathologists.

Problems that appear small are large problems that are not understood.

Even the most prominent of the great geniuses have demonstrated a lack of intellectual perspective in the appraisal of scientific insights. Today, we can find many seeds of great discoveries that were mentioned as curiosities of little importance in the writings of the ancients, and even in those of the wise men of the Renaissance. Lost in the pages of a confused theological treatise ( Christianismi restitutio ) are three apparently disdainful lines written by Servetus referring to the pulmonary circulation, which now constitute his major claim to fame. The Aragonese philosopher would be surprised indeed if he were to rise from the dead today. He would find his laborious metaphysical disquisitions totally forgotten, whereas the observation he used simply to argue for the residence of the soul in the blood is widely praised! Or again, it has been inferred from a passage of Seneca’s that the ancients knew the magnifying powers of a crystal sphere filled with water. Who would have suspected that in this phenomenon of magnification, disregarded for centuries, slumbered the embryo of two powerful analytical instruments, the microscope and telescope — and two equally great sciences, biology and astronomy!

In summary, there are no small problems. Problems that appear small are large problems that are not understood. Instead of tiny details unworthy of the intellectual, we have men whose tiny intellects cannot rise to penetrate the infinitesimal. Nature is a harmonious mechanism where all parts, including those appearing to play a secondary role, cooperate in the functional whole. In contemplating this mechanism, shallow men arbitrarily divide its parts into essential and secondary, whereas the insightful thinker is content with classifying them as understood and poorly understood, ignoring for the moment their size and immediately useful properties. No one can predict their importance in the future.

Santiago Ramón y Cajal (1852 – 1934) was a neuroscientist and pathologist, and Spain’s first Nobel laureate. This article is excerpted from his book “ Advice for a Young Investigator .”

• Shopping Cart

Advanced Search

• Browse Our Shelves
• Best Sellers
• Digital Audiobooks
• Featured Titles
• New This Week
• Staff Recommended
• Suggestions for Kids
• Fiction Suggestions
• Nonfiction Suggestions
• Reading Lists
• Upcoming Events
• Ticketed Events
• Science Book Talks
• Past Events
• Video Archive
• Online Gift Codes
• University Clothing
• Goods & Gifts from Harvard Book Store
• Hours & Directions
• Newsletter Archive
• Frequent Buyer Program
• Signed First Edition Club
• Signed New Voices in Fiction Club
• Harvard Square Book Circle
• Off-Site Book Sales
• Corporate & Special Sales
• Print on Demand

• All Our Shelves
• Academic New Arrivals
• New Hardcover - Biography
• New Hardcover - Fiction
• New Hardcover - Nonfiction
• New Titles - Paperback
• African American Studies
• Anthologies
• Anthropology / Archaeology
• Architecture
• Asia & The Pacific
• Astronomy / Geology
• Boston / Cambridge / New England
• Business & Management
• Career Guides
• Child Care / Childbirth / Adoption
• Children's Board Books
• Children's Picture Books
• Children's Activity Books
• Children's Beginning Readers
• Children's Middle Grade
• Children's Gift Books
• Children's Nonfiction
• Children's/Teen Graphic Novels
• Teen Nonfiction
• Young Adult
• Classical Studies
• Cognitive Science / Linguistics
• College Guides
• Cultural & Critical Theory
• Education - Higher Ed
• Environment / Sustainablity
• European History
• Exam Preps / Outlines
• Games & Hobbies
• Gender Studies / Gay & Lesbian
• Gift / Seasonal Books
• Globalization
• Graphic Novels
• Hardcover Classics
• Health / Fitness / Med Ref
• Islamic Studies
• Large Print
• Latin America / Caribbean
• Law & Legal Issues
• Literary Crit & Biography
• Local Economy
• Mathematics
• Media Studies
• Middle East
• Myths / Tales / Legends
• Native American
• Paperback Favorites
• Performing Arts / Acting
• Personal Finance
• Personal Growth
• Photography
• Physics / Chemistry
• Poetry Criticism
• Ref / English Lang Dict & Thes
• Ref / Foreign Lang Dict / Phrase
• Reference - General
• Religion - Christianity
• Religion - Comparative
• Religion - Eastern
• Romance & Erotica
• Science Fiction
• Short Introductions
• Technology, Culture & Media
• Theology / Religious Studies
• Travel Atlases & Maps
• Travel Lit / Adventure
• Urban Studies
• Wines And Spirits
• Women's Studies
• World History
• Writing Style And Publishing

Solving Everyday Problems with the Scientific Method: Thinking Like a Scientist (Second Edition)

This book describes how one can use The Scientific Method to solve everyday problems including medical ailments, health issues, money management, traveling, shopping, cooking, household chores, etc. It illustrates how to exploit the information collected from our five senses, how to solve problems when no information is available for the present problem situation, how to increase our chances of success by redefining a problem, and how to extrapolate our capabilities by seeing a relationship among heretofore unrelated concepts. One should formulate a hypothesis as early as possible in order to have a sense of direction regarding which path to follow. Occasionally, by making wild conjectures, creative solutions can transpire. However, hypotheses need to be well-tested. Through this way, The Scientific Method can help readers solve problems in both familiar and unfamiliar situations. Containing real-life examples of how various problems are solved — for instance, how some observant patients cure their own illnesses when medical experts have failed — this book will train readers to observe what others may have missed and conceive what others may not have contemplated. With practice, they will be able to solve more problems than they could previously imagine. In this second edition, the authors have added some more theories which they hope can help in solving everyday problems. At the same time, they have updated the book by including quite a few examples which they think are interesting. Readership: General public interested in self-help books; undergraduates majoring in education and behavioral psychology; graduates and researchers with research interests in problem solving, creativity and scientific research methodology.

There are no customer reviews for this item yet.

Classic Totes

Tote bags and pouches in a variety of styles, sizes, and designs , plus mugs, bookmarks, and more!

Shipping & Pickup

We ship anywhere in the U.S. and orders of $75+ ship free via media mail!

Noteworthy Signed Books: Join the Club!

Join our Signed First Edition Club (or give a gift subscription) for a signed book of great literary merit, delivered to you monthly.

Harvard Square's Independent Bookstore

© 2024 Harvard Book Store All rights reserved

Contact Harvard Book Store 1256 Massachusetts Avenue Cambridge, MA 02138

Tel (617) 661-1515 Toll Free (800) 542-READ Email [email protected]

View our current hours »

Join our bookselling team »

We plan to remain closed to the public for two weeks, through Saturday, March 28 While our doors are closed, we plan to staff our phones, email, and harvard.com web order services from 10am to 6pm daily.

Store Hours Monday - Saturday: 9am - 11pm Sunday: 10am - 10pm

Holiday Hours 12/24: 9am - 7pm 12/25: closed 12/31: 9am - 9pm 1/1: 12pm - 11pm All other hours as usual.

Map Find Harvard Book Store »

Online Customer Service Shipping » Online Returns » Privacy Policy »

Harvard University harvard.edu »

• Clubs & Services

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• 20 March 2024
• Correction 21 March 2024

Mathematician who tamed randomness wins Abel Prize

• Davide Castelvecchi

You can also search for this author in PubMed   Google Scholar

You have full access to this article via your institution.

Michel Talagrand studies stochastic processes, mathematical models of phenomena that are governed by randomness. Credit: Peter Bagde/Typos1/Abel Prize 2024

A mathematician who developed formulas to make random processes more predictable and helped to solve an iconic model of complex phenomena has won the 2024 Abel Prize, one of the field’s most coveted awards. Michel Talagrand received the prize for his “contributions to probability theory and functional analysis, with outstanding applications in mathematical physics and statistics”, the Norwegian Academy of Science and Letters in Oslo announced on 20 March.

Assaf Naor, a mathematician at Princeton University in New Jersey, says it is difficult to overestimate the impact of Talagrand’s work. “There are papers posted maybe on a daily basis where the punchline is ‘now we use Talagrand’s inequalities’,” he says.

Talagrand’s reaction on hearing the news was incredulity. “There was a total blank in my mind for at least four seconds,” he says. “If I had been told an alien ship had landed in front of the White House, I would not have been more surprised.”

The Abel Prize was modelled after the Nobel Prizes — which do not include mathematics — and was first awarded in 2003. The recipient wins a sum of 7.5 million Norwegian kroner (US$700,000).

‘Like a piece of art’

Talagrand specializes in the theory of probability and stochastic processes, which are mathematical models of phenomena governed by randomness. A typical example is a river’s water level, which is highly variable and is affected by many independent factors, including rain, wind and temperature, Talagrand says. His proudest achievement was his inequalities 1 , a set of formulas that poses limits to the swings in stochastic processes. His formulas express how the contributions of many factors often cancel each other out — making the overall result less variable, not more.

“It’s like a piece of art,” says Abel-committee chair Helge Holden, a mathematician at the Norwegian University of Science and Technology in Trondheim. “The magic here is to find a good estimate, not just a rough estimate.”

Abel Prize: pioneer of ‘smooth’ physics wins top maths award

Thanks to Talagrand’s techniques, “many things that seem complicated and random turn out to be not so random”, says Naor. His estimates are extremely powerful, for example for studying problems such as optimizing the route of a delivery truck. Finding a perfect solution would require an exorbitant amount of computation, so computer scientists can instead calculate the lengths of a limited number of random candidate routes and then take the average — and Talagrand’s inequalities ensure that the result is close to optimal.

Talagrand also completed the solution to a problem posed by theoretical physicist Giorgio Parisi — work that ultimately helped Parisi to earn a Nobel Prize in Physics in 2021. In 1979, Parisi, now at the University of Rome, proposed a complete solution for the structure of a spin glass — an abstracted model of a material in which the magnetization of each atom tends to flip up or down depending on those of its neighbours.

Parisi’s arguments were rooted in his powerful intuition in physics, and followed steps that “mathematicians would consider as sorcery”, Talagrand says, such as taking n copies of a system — with n being a negative number. Many researchers doubted that Parisi’s proof could be made mathematically rigorous. But in the early 2000s, the problem was completely solved in two separate works, one by Talagrand 2 and an earlier one by Francesco Guerra 3 , a mathematical physicist who is also at the University of Rome.

Finding motivation

Talagrand’s journey to becoming a top researcher was unconventional. Born in Béziers, France, in 1952, he lost vision in his right eye at age five because of a genetic predisposition to detachment of the retina. Although while growing up in Lyon he was a voracious reader of popular science magazines, he struggled at school, particularly with the complex rules of French spelling. “I never really made peace with orthography,” he told an interviewer in 2019 .

His turning point came at age 15, when he received emergency treatment for another retinal detachment, this time in his left eye. He had to miss almost an entire year of school. The terrifying experience of nearly losing his sight — and his father’s efforts to keep his mind busy while his eyes were bandaged — gave Talagrand a renewed focus. He became a highly motivated student after his recovery, and began to excel in national maths competitions.

Just 5 women have won a top maths prize in the past 90 years

Still, Talagrand did not follow the typical path of gifted French students, which includes two years of preparatory school followed by a national admission competition for highly selective grandes écoles such as the École Normale Supérieure in Paris. Instead, he studied at the University of Lyon, France, and then went on to work as a full-time researcher at the national research agency CNRS, first in Lyon and later in Paris, where he spent more than a decade in an entry-level job. Apart from a brief stint in Canada, followed by a trip to the United States where he met his wife, he worked at the CNRS until his retirement.

Talagrand loves to challenge other mathematicians to solve problems that he has come up with — offering cash to those who do — and he keeps a list of those problems on his website. Some have been solved, leading to publications in major maths journals . The prizes come with some conditions: “I will award the prizes below as long as I am not too senile to understand the proofs I receive. If I can’t understand them, I will not pay.”

Nature 627 , 714-715 (2024)

doi: https://doi.org/10.1038/d41586-024-00839-6

Updates & Corrections

Correction 21 March 2024 : An earlier version of this article stated that Giorgio Parisi won the Nobel Prize in Physics in 2001. He in fact won in 2021.

Talagrand, M. Publ. Math. IHES 81 , 73–205, (1995).

Article   Google Scholar  

Talagrand, M. Ann. Math. 163 , 221–263 (2006).

Guerra, F. Commun. Math. Phys. 233 , 1–12 (2003).

Download references

Reprints and permissions

Related Articles

Fermat's last theorem earns Andrew Wiles the Abel Prize

'Beautiful mind' John Nash adds Abel Prize to his Nobel

• Mathematics and computing

A global timekeeping problem postponed by global warming

Article 27 MAR 24

Climate change has slowed Earth’s rotation — and could affect how we keep time

News 27 MAR 24

High-threshold and low-overhead fault-tolerant quantum memory

Expression of Interest – Marie Skłodowska-Curie Actions – Postdoctoral Fellowships 2024 (MSCA-PF)

Academic institutions in Brittany are looking for excellent postdoctoral researchers willing to apply for a Marie S. Curie Postdoctoral Fellowship.

France (FR)

Plateforme projets européens (2PE) -Bretagne

Tenure-track Assistant Professor in Ecological and Evolutionary Modeling

Tenure-track Assistant Professor in Ecosystem Ecology linked to IceLab’s Center for modeling adaptive mechanisms in living systems under stress

Umeå, Sweden

Umeå University

Faculty Positions in Westlake University

Founded in 2018, Westlake University is a new type of non-profit research-oriented university in Hangzhou, China, supported by public a...

Hangzhou, Zhejiang, China

Westlake University

Postdoctoral Fellowships-Metabolic control of cell growth and senescence

Postdoctoral positions in the team Cell growth control by nutrients at Inst. Necker, Université Paris Cité, Inserm, Paris, France.

Paris, Ile-de-France (FR)

Inserm DR IDF Paris Centre Nord

Zhejiang Provincial Hospital of Chinese Medicine on Open Recruitment of Medical Talents and Postdocs

Director of Clinical Department, Professor, Researcher, Post-doctor

The First Affiliated Hospital of Zhejiang Chinese Medical University

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

March 12, 2024

The Simplest Math Problem Could Be Unsolvable

The Collatz conjecture has plagued mathematicians for decades—so much so that professors warn their students away from it

By Manon Bischoff

Mathematicians have been hoping for a flash of insight to solve the Collatz conjecture.

James Brey/Getty Images

At first glance, the problem seems ridiculously simple. And yet experts have been searching for a solution in vain for decades. According to mathematician Jeffrey Lagarias, number theorist Shizuo Kakutani told him that during the cold war, “for about a month everybody at Yale [University] worked on it, with no result. A similar phenomenon happened when I mentioned it at the University of Chicago. A joke was made that this problem was part of a conspiracy to slow down mathematical research in the U.S.”

The Collatz conjecture—the vexing puzzle Kakutani described—is one of those supposedly simple problems that people tend to get lost in. For this reason, experienced professors often warn their ambitious students not to get bogged down in it and lose sight of their actual research.

The conjecture itself can be formulated so simply that even primary school students understand it. Take a natural number. If it is odd, multiply it by 3 and add 1; if it is even, divide it by 2. Proceed in the same way with the result x : if x is odd, you calculate 3 x + 1; otherwise calculate x / 2. Repeat these instructions as many times as possible, and, according to the conjecture, you will always end up with the number 1.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

For example: If you start with 5, you have to calculate 5 x 3 + 1, which results in 16. Because 16 is an even number, you have to halve it, which gives you 8. Then 8 / 2 = 4, which, when divided by 2, is 2—and 2 / 2 = 1. The process of iterative calculation brings you to the end after five steps.

Of course, you can also continue calculating with 1, which gives you 4, then 2 and then 1 again. The calculation rule leads you into an inescapable loop. Therefore 1 is seen as the end point of the procedure.

Following iterative calculations, you can begin with any of the numbers above and will ultimately reach 1.

Credit: Keenan Pepper/Public domain via Wikimedia Commons

It’s really fun to go through the iterative calculation rule for different numbers and look at the resulting sequences. If you start with 6: 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1. Or 42: 42 → 21 → 64 → 32 → 16 → 8 → 4 → 2 → 1. No matter which number you start with, you always seem to end up with 1. There are some numbers, such as 27, where it takes quite a long time (27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → 161 → 484 → 242 → 121 → 364 → 182 → 91 → 274 → ...), but so far the result has always been 1. (Admittedly, you have to be patient with the starting number 27, which requires 111 steps.)

But strangely there is still no mathematical proof that the Collatz conjecture is true. And that absence has mystified mathematicians for years.

The origin of the Collatz conjecture is uncertain, which is why this hypothesis is known by many different names. Experts speak of the Syracuse problem, the Ulam problem, the 3 n + 1 conjecture, the Hasse algorithm or the Kakutani problem.

German mathematician Lothar Collatz became interested in iterative functions during his mathematics studies and investigated them. In the early 1930s he also published specialist articles on the subject , but the explicit calculation rule for the problem named after him was not among them. In the 1950s and 1960s the Collatz conjecture finally gained notoriety when mathematicians Helmut Hasse and Shizuo Kakutani, among others, disseminated it to various universities, including Syracuse University.

Like a siren song, this seemingly simple conjecture captivated the experts. For decades they have been looking for proof that after repeating the Collatz procedure a finite number of times, you end up with 1. The reason for this persistence is not just the simplicity of the problem: the Collatz conjecture is related to other important questions in mathematics. For example, such iterative functions appear in dynamic systems, such as models that describe the orbits of planets. The conjecture is also related to the Riemann conjecture, one of the oldest problems in number theory.

Empirical Evidence for the Collatz Conjecture

In 2019 and 2020 researchers checked all numbers below 2 68 , or about 3 x 10 20 numbers in the sequence, in a collaborative computer science project . All numbers in that set fulfill the Collatz conjecture as initial values. But that doesn’t mean that there isn’t an outlier somewhere. There could be a starting value that, after repeated Collatz procedures, yields ever larger values that eventually rise to infinity. This scenario seems unlikely, however, if the problem is examined statistically.

An odd number n is increased to 3 n + 1 after the first step of the iteration, but the result is inevitably even and is therefore halved in the following step. In half of all cases, the halving produces an odd number, which must therefore be increased to 3 n + 1 again, whereupon an even result is obtained again. If the result of the second step is even again, however, you have to divide the new number by 2 twice in every fourth case. In every eighth case, you must divide it by 2 three times, and so on.

In order to evaluate the long-term behavior of this sequence of numbers , Lagarias calculated the geometric mean from these considerations in 1985 and obtained the following result: ( 3 / 2 ) 1/2 x ( 3 ⁄ 4 ) 1/4 x ( 3 ⁄ 8 ) 1/8 · ... = 3 ⁄ 4 . This shows that the sequence elements shrink by an average factor of 3 ⁄ 4 at each step of the iterative calculation rule. It is therefore extremely unlikely that there is a starting value that grows to infinity as a result of the procedure.

There could be a starting value, however, that ends in a loop that is not 4 → 2 → 1. That loop could include significantly more numbers, such that 1 would never be reached.

Such “nontrivial” loops can be found, for example, if you also allow negative integers for the Collatz conjecture: in this case, the iterative calculation rule can end not only at –2 → –1 → –2 → ... but also at –5 → –14 → –7 → –20 → –10 → –5 → ... or –17 → –50 → ... → –17 →.... If we restrict ourselves to natural numbers, no nontrivial loops are known to date—which does not mean that they do not exist. Experts have now been able to show that such a loop in the Collatz problem, however, would have to consist of at least 186 billion numbers .

The length of the Collatz sequences for all numbers from 1 to 9,999 varies greatly.

Credit: Cirne/Public domain via Wikimedia Commons

Even if that sounds unlikely, it doesn’t have to be. In mathematics there are many examples where certain laws only break down after many iterations are considered. For instance,the prime number theorem overestimates the number of primes for only about 10 316 numbers. After that point, the prime number set underestimates the actual number of primes.

Something similar could occur with the Collatz conjecture: perhaps there is a huge number hidden deep in the number line that breaks the pattern observed so far.

A Proof for Almost All Numbers

Mathematicians have been searching for a conclusive proof for decades. The greatest progress was made in 2019 by Fields Medalist Terence Tao of the University of California, Los Angeles, when he proved that almost all starting values of natural numbers eventually end up at a value close to 1.

“Almost all” has a precise mathematical meaning: if you randomly select a natural number as a starting value, it has a 100 percent probability of ending up at 1. ( A zero-probability event, however, is not necessarily an impossible one .) That’s “about as close as one can get to the Collatz conjecture without actually solving it,” Tao said in a talk he gave in 2020 . Unfortunately, Tao’s method cannot generalize to all figures because it is based on statistical considerations.

All other approaches have led to a dead end as well. Perhaps that means the Collatz conjecture is wrong. “Maybe we should be spending more energy looking for counterexamples than we’re currently spending,” said mathematician Alex Kontorovich of Rutgers University in a video on the Veritasium YouTube channel .

Perhaps the Collatz conjecture will be determined true or false in the coming years. But there is another possibility: perhaps it truly is a problem that cannot be proven with available mathematical tools. In fact, in 1987 the late mathematician John Horton Conway investigated a generalization of the Collatz conjecture and found that iterative functions have properties that are unprovable. Perhaps this also applies to the Collatz conjecture. As simple as it may seem, it could be doomed to remain unsolved forever.

This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission.

• Rules First
• Organizational Problems
• Wrong Paths
• Math Problems
• Metacognition
• What Does It Take?
• Satisfaction
• Re-examination
• 1st Hand Accounts

Scientific Problem Solving

By example, exercise, and reflection.

• SPS Home  > 

Follow Polygon online:

• Follow Polygon on Facebook
• Follow Polygon on Youtube
• Follow Polygon on Instagram

Site search

• What to Watch
• What to Play
• PlayStation
• All Entertainment
• Dragon’s Dogma 2
• FF7 Rebirth
• Zelda: Tears of the Kingdom
• Baldur’s Gate 3
• Buyer’s Guides
• Galaxy Brains
• All Podcasts

Filed under:

• Entertainment

The 3-body problem is real, and it’s really unsolvable

Oh god don’t make me explain math

Share this story

• Share this on Facebook
• Share this on Reddit
• Share All sharing options

Share All sharing options for: The 3-body problem is real, and it’s really unsolvable

Everybody seems to be talking about 3 Body Problem , the new Netflix series based on Cixin Liu’s Remembrance of Earth’s Past book trilogy . Fewer people are talking about the two series’ namesake: The unsolvable physics problem of the same name.

This makes sense, because it’s confusing . In physics, the three-body problem attempts to find a way to predict the movements of three objects whose gravity interacts with each of the others — like three stars that are close together in space. Sounds simple enough, right? Yet I myself recently pulled up the Wikipedia article on the three-body problem and closed the tab in the same manner that a person might stagger away from a bright light. Apparently the Earth, sun, and moon are a three-body system? Are you telling me we don’t know how the moon moves ? Scientists have published multiple solutions for the three-body problem? Are you telling me Cixin Liu’s books are out of date?

All I’d wanted to know was why the problem was considered unsolvable, and now memories of my one semester of high school physics were swimming before my eyes like so many glowing doom numbers. However, despite my pains, I have readied several ways that we non-physicists can be confident that the three-body problem is, in fact, unsolvable.

Reason 1: This is a special definition of ‘unsolvable’

The three-body problem is extra confusing, because scientists are seemingly constantly finding new solutions to the three-body problem! They just don’t mean a one-solution-for-all solution. Such a formula does exist for a two-body system, and apparently Isaac Newton figured it out in 1687 . But systems with more than two bodies are, according to physicists, too chaotic (i.e., not in the sense of a child’s messy bedroom, but in the sense of “chaos theory”) to be corralled by a single solution.

When physicists say they have a new solution to the three-body problem, they mean that they’ve found a specific solution for three-body systems that have certain theoretical parameters. Don’t ask me to explain those parameters, because they’re all things like “the three masses are collinear at each instant” or “a zero angular momentum solution with three equal masses moving around a figure-eight shape.” But basically: By narrowing the focus of the problem to certain arrangements of three-body systems, physicists have been able to derive formulas that predict the movements of some of them, like in our solar system. The mass of the Earth and the sun create a “ restricted three-body problem ,” where a less-big body (in this case, the moon) moves under the influence of two massive ones (the Earth and the sun).

What physicists mean when they say the three-body problem has no solution is simply that there isn’t a one-formula-fits-all solution to every way that the gravity of three objects might cause those objects to move — which is exactly what Three-Body Problem bases its whole premise on.

Reason 2: 3 Body Problem picked an unsolved three-body system on purpose

Henri Poincaré’s research into a general solution to the three-body problem formed the basis of what would become known as chaos theory (you might know it from its co-starring role in Jurassic Park ). And 3 Body Problem itself isn’t about any old three-body system. It’s specifically about an extremely chaotic three-body system, the exact kind of arrangement of bodies that Poincaré was focused on when he showed that the problem is “unsolvable.”

[ Ed. note: The rest of this section includes some spoilers for 3 Body Problem .]

In both Liu’s books and Netflix’s 3 Body Problem , humanity faces an invasion by aliens (called Trisolarans in the English translation of the books, and San-Ti in the TV series) whose home solar system features three suns in a chaotic three-body relationship. It is a world where, unlike ours, the heavens are fundamentally unpredictable. Periods of icy cold give way to searing heat that give way to swings in gravity that turn into temporary reprieves that can never be trusted. The unpredictable nature of the San-Ti environment is the source of every detail of their physicality, their philosophy, and their desire to claim Earth for their own.

In other words, 3 Body Problem ’s three-body problem is unsolvable because Liu wanted to write a story with an unsolvable three-body system, so he chose one of the three-body systems for which we have not discovered a solution, and might never.

Reason 3: Scientists are still working on the three-body problem

Perhaps the best reason I can give you to believe that the three-body problem is real, and is really unsolvable, is that some scientists published a whole set of new solutions for specific three-body systems very recently .

If physicists are still working on the three-body problem, we can safely assume that it has not been solved. Scientists, after all, are the real experts. And I am definitely not.

The next level of puzzles.

Take a break from your day by playing a puzzle or two! We’ve got SpellTower, Typeshift, crosswords, and more.

Sign up for the newsletter Patch Notes

A weekly roundup of the best things from Polygon

Just one more thing!

Please check your email to find a confirmation email, and follow the steps to confirm your humanity.

Oops. Something went wrong. Please enter a valid email and try again.

Loading comments...

Glam up your Warhammer 40K minis with everyday products from the beauty aisle

Don’t have the time to read (or watch) Shōgun? Get the audiobooks for just $10

Cloud’s unreliable narration only makes Final Fantasy 7 Rebirth’s ending more confusing

Imaginary, Lisa Frankenstein, Netflix’s The Beautiful Game, and every new movie to watch at home this weekend

• Dragon’s Dogma 2 guides, walkthroughs, and explainers

Should you give the grimoires to Myrddin or Trysha in Dragon’s Dogma 2?

All maister skills in Dragon’s Dogma 2 and how to get them

UT Institute for Geophysics

Understanding the Earth and other planets to solve key problems that affect us all. The world needs geophysicists!

March 29, 2024

UTIG Seminar Series: Chuanming Liu, UT Austin

Friday, april 5, 2024 at 10:30am ct.

Location : Bureau of Economic Geology Main Conference Room, BEG 1.202 J.J. Pickle Research Campus 10100 Burnet Road

Online : Find the meeting link in the calendar buttons below or request a link from [email protected] . You must be logged in to a Zoom account ( why do I need to sign in? ).

Speaker : Chuanming Liu , Distinguished Postdoctoral Fellow, UT Jackson School of Geosciences, Postdoctoral Fellow, University of Texas Institute for Geophysics

Host : Thorsten Becker

Title : Crustal and Upper Mantle Seismic Anisotropy Across Alaska and the Juan de Fuca Plate from Surface Wave Observations

Abstract : As one of the world’s most tectonically active convergent regions, Alaska and the Aleutian subduction zone have experienced a wide range of past and present-day tectonic processes. Within the continent, tectonic features deep within the lithosphere are invisible at the surface but can be revealed through observations of seismic anisotropy. In the case of the oceanic plate and subduction zone, seismic anisotropy can help us understand the physical properties of plate and directions of mantle flow. In this talk, I will discuss the depth variation of seismic anisotropy and its implications for deep crustal deformation in the Alaskan continent and explore the depth-dependent azimuthal anisotropy features beneath the Aleutian subduction zone and the Juan de Fuca plate.

University of Texas Institute for Geophysics

J.J. Pickle Research Campus, Building 196 10100 Burnet Road (R2200) Austin, TX 78758-4445

Phone: 512-471-6156 Fax: 512-471-2370

Driving Directions

General: [email protected]

Website & Media: [email protected]

Commitment to a Respectful Workplace

Research Facilities

HELPFUL LINKS

Directory (EID)

Job Listings

UTIG Newsletter

OUR PARTNERS

Bureau of Economic Geology

Department of Earth and Planetary Sciences

Center for Planetary Systems Habitability