(Chapters 1–5) leads us to the next and equally important question of what the engine of new methods and tools is. But researchers studying scientific methods focus on a specific method—like statistical techniques or microscopy. (Or philosophers investigate scientific methodology abstractly from a conceptual perspective, exploring principles like falsifiability of theories or the classic scientific method of hypothesis testing). Yet remarkably, there are no systematic studies, applied or theoretical, that explain how science's diverse new methods and tools—from cutting-edge telescopes to supercomputers—emerge across fields and how we can speed up their development. Here we tackle this key question from different perspectives and angles. We begin by examining the ten central methods and instruments most used to spark discoveries and the inventors behind them—our great method-makers of science. These innovators, from Ernst Ruska's electron microscope to Max von Laue's x-ray diffraction, did not just solve pressing method challenges—they reshaped the future of discovery. Each of the top ten transformative tools and methods triggered multiple nobel-prize discoveries across fields, far beyond their original domains. But what drove these researchers to shift gears from traditional scientific research within their fields to creating these new method innovations—to developing entirely new ways of doing scientific research? What compelled them to rethink the methods they used to explore the world and how can we rethink the methods we use? By tracing their career paths and the key turning points in their work, we uncover six key factors behind science's greatest tool breakthroughs. One, we find that the pioneering inventors of the top ten general tools of discovery generally ran into methodological limits and were then motivated by the need to 138 T HE ENGINE OF SCIENTIFIC DISCOVERY create a new tool by pragmaticallyovercoming a constraint to an existing tool. Working within conventional scientific fields, they encountered barriers that hindered them in studying key phenomena using available tools. So they turned the problem around and set out to fill these method gaps—with for example DNA analysis being very slow and inefficient until Kary Mullis developed a simple way to rapidly amplify DNA that ultimately transformed genetics: the PCR method. Two, these researchers each shifted their research focus from addressing scientific questions to tackling method and tool questions. They studied and worked in established fields like physics and chemistry; but transitioned from traditional science to an unconventional pursuit of extending our tools to explore the world in new ways— with for example Theodor Svedberg studying macromolecules and colloids but then turning to how to measure their properties more accurately that led to inventing the ultracentrifuge. Three, they took a very practical experimental approach, not simply theorising about the limitations but tackling specific shortcomings of our tools that held back progress—with for example Ernst Ruska refining electron lenses, step by step, until he had a working electron microscope with vastly improved resolution like nothing before. Four, these innovators commonly produced the new tool at low or modest costs and not in large research teams. Motivated, resourceful researchers can make foundational breakthroughs with little resources and simple materials—from Mullis' PCR method and Tiselius' electrophoresis to Fisher's modern statistics. Five, they were primarily interdisciplinary scientists, with eight out of ten trained in different fields. This enabled them to generate new connections by often drawing on methods and evidence from different domains—with for example Ernest Lawrence's degrees in physics and chemistry enabling him to better understand the nature of atomic interactions and design the first practical particle accelerator. Six, these inventors were not prominent scientists before designing the groundbreaking tool. Most were relatively unknown and did not make a major discovery before—with for example Mullis an unknown biotech researcher and Ruska, Tiselius and Synge PhD students at the time (Table 6.1). A remarkable insight emerges: science's most important toolmakers are not elite researchers at the peak of their careers but rather typical scientists when looking at their background. This is important: it highlights that applied and resourceful researchers—regardless of reputation and institution—can turn their attention towards tackling practical method problems that can transform science. So what specifically motivates us to develop new discovery tools and methods? Let us take a closer look at science's most transformative tools. Svedberg created the ultracentrifuge to overcome the limits of the ultramicroscope in studying particles. Tiselius then invented electrophoresis that addressed constraints of the ultracentrifuge and the struggles of biochemists to separate proteins effectively. Martin and Synge designed partition chromatography to resolve the shortcomings of earlier chromatography methods. Each of these inventions unlocked new ways of separating and studying substances. Von Laue generated x-ray diffraction that enabled going beyond traditional x-ray analysis and probing the atomic and molecular structure of materials. Ruska pioneered the electron microscope that T broke the optical barrier of light microscopes by bypassing the diffraction limit of visible light that prevented visualising tiny structures. Bloch and Purcell developed NMR spectroscopy that advanced earlier techniques, especially Rabi's molecular beam method, to uncover a powerful new way of probing atomic nuclei with unprecedented precision. Fisher invented modern statistical methods to tackle the inadequacies of earlier data analysis techniques, providing rigorous tools to design experiments and draw reliable conclusions. Townes created the maser that overcame limitations in generating and controlling electromagnetic waves and soon led to the laser—though he did not have a specific application for the tool in mind. Mullis invented the PCR method to make the process of DNA amplification and analysis much more efficient and rapid. Lawrence constructed the particle accelerator that enabled vastly expanding existing models of linear accelerators. This trend is striking across science: it is often applied researchers—not generally theorists—who hit upon and spot a tool's defects, but rather than just commonly accepting them they seek to tackle them head-on. It is generally technical bottlenecks—when methods fall short and progress hits a wall—where the birth of breakthroughs begins. The origins of science's best tools challenge a long-standing assumption—that theories play the central role in driving science—yet science's most transformative tools generally arise not from abstract theorising but from practical deficits in earlier tools. In fact, Lawrence's inspiration for example came in 1929 when reading articles in the university library at Berkeley one evening. He wrote that he 'came across an article in a German electrical engineering journal by Wideröe on the multiple acceleration of positive ions. Not being able to read German easily, I merely looked at the diagrams and photographs of Wideröe's apparatus … This new idea immediately impressed me as the real answer which I had been looking for to the technical problem of accelerating positive ions, and without looking at the article further I then and there made estimates of the general features of a linear accelerator' . That year, he published his landmark paper, The production of high speed light ions without the use of high voltages, in the journal Physical Review. At just 28, the youngest professor at Berkeley at the time, Lawrence had designed the first particle accelerator, giving an entirely new impulse to high-energy physics. We explore the inspiration of these great toolmakers deeper within the boxes (in Chapters 1, 5 and 6). Surprisingly, these stories behind the ten most influential tools in sparking discoveries in scientific history challenge the popular narrative about scientific progress. The stories reveal a deeper insight: the overlooked flaws of tools are key in driving scientific progress. Great breakthroughs commonly begin not with just a grand question but with a technical obstacle impeding investigation. What does this mean? It means we need to pay much closer attention to the gaps in our instruments rather than just the gaps in our knowledge. Because tools shape the questions and theories we can even formulate and the discoveries we can make (we explore this in greater detail later). After zooming in on science's top tools, we now zoom back out and broaden the focus. We compare the features of the top ten nobel-prize-winning methods and tools—those sparking the greatest number of later nobel-prize discoveries—with the 140 T HE ENGINE OF SCIENTIFIC DISCOVERY features of all other 523 nobel-prize discoveries across science. We find that these top ten discovery tools were all developed through direct observation and experimenting, while other nobel-prize discoveries were less likely to rely on these approaches (as we see in Figure 6.1a). Science's pioneering method-makers shared several unique and surprising traits: not only were eight out of ten interdisciplinary—each earning two or more degrees in different fields before their breakthrough; but half of them were not professors and only completed a PhD or less, and were under 35 (see Figure 6.1b for a comparison with other nobel-prize discoverers). We next take an even broader approach by examining all 149 nobel-prize-winning method discoveries—including the top 10—and compare them to all other 384 nobelprize discoveries (experimental and theoretical breakthroughs). What stands out is that these groundbreaking methods and instruments were more likely to require experimenting and lead to a new field, than other discoveries (Figure 6.1c). Exploring science's most influential toolmakers deeper, we uncover a unique pattern—one that challenges a common assumption about where innovation happens and who drives it. We find that among these ten great toolmakers, one group consists of low-profile researchers not at top universities, developing four of the ten most powerful tools. A second group is made up of academic outsiders—researchers in tech and biotech companies that are very applied research environments, inventing three of the ten tools. This is surprising since 99% of all other nobel-prize discoverers were at universities or research institutions. And a third group involves higher-profile researchers at top 50 academic institutions, creating three of the ten (Table 6.1). Stepping back and exploring all 149 nobel-prize-winning method breakthroughs we find a similar trend: almost two-thirds of these toolmakers were not based at the world's top 50 universities (Figure 6.1d). Innovation usually begins not with privilege or prestige—but with a technological gap and someone eager to try a different approach. These ten pioneering methodologists were also younger: just 34 years old on average at the time of their innovation, compared to 39 for all other nobel-prize discoverers. The most transformative tools that change the course of science can emerge before a career has even properly started—with three publishing their tool breakthrough as part of their PhD thesis. Another unique finding is that most of these ten general tools were generated at low cost, requiring less than 1000 US$ (in 2025 prices) (Table 6.1). Since major discoveries begin with new methods that provide a new perspective to a problem—not with existing methods that represent conventional research—how do we develop those new methods? Four common ways exist, as we introduced in Chapter 1 and explored more deeply in this chapter. One powerful way is creating entirely new methods not yet conceived—like chromatography for separating chemical substances. A second transformative way is extending methods in novel ways that represent a new method not ever used before—like gas chromatography that vastly upgraded chromatography. A third innovative way is combining methods in novel ways that introduces a new method not yet leveraged before—like x-ray crystallography that joins x-ray methods with crystal analysis. A fourth foundational way is 1.00 1.00 1.00 1.00 1.00 0.27 0.95 0.82 0.84 0.47 0 .2 .4 .6 .8 1 Percentage Top 10 NP methodological discoveries All other NP discoveries Methodological and scientific features Used observation Tested hypothesis Discovery is a new method/tool Used experimentation Opened new scientific field 0.80 0.50 0.40 0.60 0.40 0.50 0.50 0.54 0.70 0.38 0.45 0.50 0.33 0.50 0 .2 .4 .6 .8 1 Percentage Top 10 NP methodological discoveries All other NP discoveries Demographic, institutional and geographic features Discoverer has interdisciplinary degrees Education: Discoverer is professor Discoverer at top 50 university Discoverer lived in Europe Discoverer lived in North America Discoverer aged 18–34 Discoverer aged 35–45 Discoverer has interdisciplinary degrees Education: Discoverer is professor Discoverer at top 50 university Discoverer lived in Europe Discoverer lived in North America Discoverer aged 18–34 Discoverer aged 35–45 1.00 0.95 0.91 0.92 0.72 0.00 0.95 0.79 0.81 0.39 0 .2 .4 .6 .8 1 Percentage All NP methodological discoveries All other NP discoveries Used observation Tested hypothesis Discovery is a new method/tool Used experimentation Opened new scientific field 0.51 0.66 0.38 0.44 0.54 0.30 0.52 0.56 0.71 0.38 0.45 0.48 0.34 0.49 0 .2 .4 .6 .8 1 Percentage All NP methodological discoveries All other NP discoveries Figure 6.1 Nobel-prize-winning methods and tools compared to all other nobel-prize-winning discoveries, by features at the time of the discovery The data reflect all 533 nobel-prize discoveries: with the top 10 nobel-prize-winning methods and tools compared to all other 523 nobel-prize discoveries (Figure a and b), and with all 149 nobel-prize-winning methods and tools compared to all other 384 nobel-prize discoveries (Figure c and d). NP stands for Nobel Prize. We outline the top 10 nobel-prize-winning methods and tools in Table 6.1, with the particle detector included here instead of modern statistics as it did not win a Nobel—each of these tools has been applied to develop at least four later nobel-prize discoveries. Table 6.1 How science's ten central methods and tools were developed that triggered most nobel-prize discoveries Traits at the time of the discovery: Method or tool Year developed Inventor's name Education level Age # of people making tool University/ Top 50 ranked Field of research Field of degree(s) Won Nobel prize for the tool Cost to develop tool* Country of birth Fields using the tool How the method or tool works—and its general use P CR method 1985 Kary Mullis PhD 41 1 Cetus (biotech company)/no Chemistry Biochemistry; Chemistry Yes, 1993 Low USA Medicine, genetics, biochemistry Amplifies a small DNA sample (e.g. a drop of blood) quickly into millions of copies—and enables medical diagnostics (like detecting HIV ) and palaeontologic findings (identifying species using fossils) (Box 1.3) Maser/laser 1954 Charles Townes Professor 39 1 Columbia University/ yes Physics Physics; Modern language Yes, 1964 Medium USA Physics, computer science, astronomy, medicine Produces concentrated beams of light or microwaves—and used to probe molecular structures and deep space, and applied in DNA sequencing, fibre optics, laser surgery and computers Spectrometer, NMR∗∗ 1946 Felix Bloch, and Edward Purcell Professor 38 2 Stanford University/ yes Physics Physics; Electrical engineering Yes, 1952 Medium Switzerland /USA Chemistry, physics, biology, medicine Visualises magnetic fields around an atomic nucleus—and used to decode the structure of proteins, produce life-saving drugs and observe tissue in our body Chromatography, partition 1941 Archer Martin, and Richard Synge PhD (research was part of PhD thesis in 1941) 29 2 Wool Industries Research Association/ no Chemistry Physics, chemistry, physiology, biochemistry Yes, 1952 Low UK Chemistry, biology Separates substances in mixtures and determines their composition—and enables identifying and understanding e.g. amino acids and sugars (Box 5.2) Electron microscope 1933 Ernst Ruska Engineering degree (research was part of PhD thesis in 1934) 26 1 Technical University of Berlin/ no Physics Electrical engineering; Physical sciences Yes, 1986 Medium Germany Biology, medicine, physics Magnifies miniscule objects using the wavelength of an electron—and enables studying microorganisms, nanoparticles, electrochemical reactions, crystals and molecules (Box 1.1) Electrophoresis 1930 Arne Tiselius PhD (research was part of PhD thesis in 1930) 28 1 Uppsala University/ no Chemistry Chemistry Yes, 1948 Low Sweden Chemistry, biology Separates substances by moving charged particles in a fluid—and applied to analyse e.g. DNA and proteins, paternity tests and DNA fingerprints (Box 6.1) Particle accelerator 1929 Ernest Lawrence Professor 28 1 Berkeley, UC/yes Physics Physics; Chemistry Yes, 1939 Low (to high) USA Particle physics, nuclear medicine Propels charged particles to high speeds using electromagnetic fields—and used to study matter and proteins, develop new drugs and cancer therapies Modern statistics 1925 Ronald Fisher Bachelors 35 1 Rothamsted (agricultural research institute)/no Statistics and genetics Astronomy (w/specialisation in mathematics) No Low UK All scientific fields Used to collect and analyse large datasets and run experiments—and applied to examine almost any phenomenon, from diseases in populations to planets, societies and even science itself (Box 5.1) Centrifuge 1924 Theodor Svedberg Professor 40 1 Uppsala University/ no Chemistry Chemistry Yes, 1926 Medium Sweden Chemistry, biology, clinical medicine Spins samples at ultrahigh speeds at over 20,000 revolutions a minute—and used to separate small particles in fluids, gases and liquids, like cells and viruses (Box 6.1) X-ray diffraction 1912 Max von Laue PhD 33 1 University of Munich/no Physics Mathematics; Physics Yes, 1914 Low Germany Chemistry, physics, material science, biomedicine Scatters x-rays using crystals—and applied to uncover crystal structures, atomic structure of matter including proteins, and identify cancers (Box 1.2) Average of 10: … … 40% professors 34 1.2 30% at a top 50 university … 80% interdisciplinary 90% Low to medium 70% in Europe … … Comparison group—all other nobel-prize discoveries: … … 69% professors 39 1.4 38% at a top 50 university … 54% interdisciplinary 100% … 45% in Europe … … The 10 central methods and tools are the most used to make the 533 nobel-prize discoveries. The comparison group (the last row) reflects all other 524 nobel-prize discoveries—with modern statistics not included as it did not win a Nobel prize. While the particle detector (1911) is at the threshold of making it into the top ten, the PCR method (1985) is included as it illustrates a powerful, more recent tool discovery that also received a Nobel prize and was used in triggering 10 major discoveries. The year reflects when the tool was first created, while all have been vastly improved. *The cost to develop the tool is based on three categories: low under $1000 US, medium between $1000 and $10,000 US and high above $10,000 US, in 2025 prices. We describe the cost for seven of the ten tools in the Boxes in Chapters 1, 5 and 6. Here we illustrate the other 3: it cost Townes about $500 US to create the maser in 1954 ($5944 US in 2025 prices). Developing the first NMR spectrometer in 1946 cost Bloch $450 US ($7379 US in 2025 prices). Creating the first operational particle accelerator prototype in 1929 cost Lawrence only about $25 US ($467 US in 2025 prices), and later scaled up accelerators about $2500 US ($46,750 US in 2025 prices). ∗∗While the first spectrograph was invented in 1859, an entirely new form of spectroscopy based on magnetic resonance—namely NMR spectroscopy—has since become far more important. 144 T HE ENGINE OF SCIENTIFIC DISCOVERY adopting new methods developed in other fields—like NMR spectroscopy created in physics and then used for the first time ever in chemistry, medicine and biology. In each of these cases, we triggered major discoveries with new methods never employed before to a given question. When we make a novel methodological leap— whether merging two tools from different domains or repurposing tools in new ways—innovation often soon follows. Digging deeper we uncover two broader underlying strategies to advance new methods: tackling a bottleneck facing a tool or opportunistically experimenting with tool designs. Which strategy is more common and successful? Scanning the method innovations sparking science's over 750 major discoveries reveals a clear trend: the most common strategy is constraint-driven innovation . Most new tools arise when researchers hit a wall—a method obstacle when doing research—and then shift their focus to extend, combine and reinvent tools to overcome the obstacle. The less common strategy is exploratory innovation—where researchers invent new tools not to solve a pre-established problem but simply to probe into the unknown and possibly discover something new. Yet some breakthroughs can be based on elements of both, a strong exploratory component and a known bottleneck that requires experimenting with a new method to find out if an assumed phenomenon exists. Consider a striking example of how constraint-driven and exploratory innovation can merge: the invention of the maser by Townes in 1954. He had no specific application in mind—only to amplify beams of microwaves. He famously described the maser as 'a solution looking for a problem' . But over time, researchers began experimenting with this peculiar invention in more and more areas—from medical clinics and physics labs to telecommunications and computer industries. We use the maser's offspring, the laser, widely in different technologies in our daily lives, from barcode scanners, smartphones and laser printers to high-precision surgeries. So does it pay off to experiment with new methods without a clearly defined use? The payoff is often high—precisely because there are very few full-time researchers dedicated to inventing methods themselves, and because what begins as tinkering with a new possible tool, like the maser, can turn into an unexpected cornerstone of science and technology. This insight opens a vast space of untapped potential. Science and technology are often intertwined. Yet science can often be more submissive to new technology. So beyond internal scientific pressures to expand our toolbox, there are also external pressures—technological and societal. Who invented for example the six most influential tools that drove 17th-century science? Surprisingly, three of the tools—the barometer, vacuum pump and calculus—were created by scientists, while the other three—the microscope, telescope and statistics—were developed outside of academia for non-research purposes. But scientists recognised their potential, refining and extending them over centuries. The microscope and telescope emerged far from the lab: at the turn of the 17th century, non-scientists developed them by tinkering with and expanding eyeglasses and magnifying glasses. Descriptive statistics were born in the 1600s out of the practical need to collect and track demographic trends T and mortality in rapidly growing European states. Interestingly, the centrifuge— typically associated with lab science—was also invented outside the walls of academia in 1864 in Germany, originally used for separating liquids from paint and later cream from milk. But the device was eventually picked up on 60 years later, in 1924, when Svedberg vastly expanded it with the ultracentrifuge, enabling extraordinary findings in fields like biochemistry and molecular biology. Scientific progress, then and now, is driven by practically minded toolmakers. New methods in artificial intelligence, machine learning and big data are increasingly pioneered by tech companies for commercial use and then applied by scientists. These not only make science more efficient but also highlight an often symbiotic relationship between industry and science. Our new tools commonly as the central driver of discovery—beyond supporting factors, from additional funding to larger teams What are seen as the most important factors driving scientific discoveries? Reviewing the literature we find a consistent pattern. Most frequently, researchers highlight two key factors for how discoveries emerge: greater research funding (for salaries and sustained long-term programmes) and team collaborations and size (for sharing expertise and research tasks). These two factors compete for the top spot and are especially emphasised by economists and scientometricians (Chapters 4 and 6). Other commonly discussed factors driving breakthroughs are greater education and human capital, providing a trained and skilled workforce in the long term. At times interdisciplinary research used to integrate perspectives and tackle complex problems. And younger researchers who can be more productive and motivated (Chapter 4). Beyond these, the more elusive role ofserendipity, sudden insights and chance are at times stressed especially by psychologists, historians and philosophers of science (Chapter 2). Then come broader basic forces: societal and policy challenges—such as pandemics like COVID, climate change and clean energy research, and government priorities—can shape some research areas. And computers, internet and AI make science more efficient and automate processes, especially in data-intensive fields (Chapters 6 and 11). At a deeper level, some examine revolutionary theories —especially highlighted by theoretical physicists and philosophers (Chapter 3). Others explore the role of problem-solving. Broad institutional structures such as universities, journals and research networks also facilitate knowledge exchange, while scientific awards can help incentivise innovation (Chapter 4). Some researchers also highlight the growing role of open access publishing , speeding up the flow of knowledge. Finally, academic freedom is needed—the space for exploring new methods and insights, risky projects and accepting 'failure' and changing paths as new opportunities arise. Taken together, researchers exploring scientific progress largely focus on these broader factors and basic conditions. 146 T HE ENGINE OF SCIENTIFIC DISCOVERY These factors vary largely by discovery, by scientific field and by scientist, and alone are not enough to make discoveries. We lay out, throughout the book, how these factors and background conditions can foster the basic environment for developing methods and science. But it is new tools that are the very spark of major discoveries across the sciences. Some broad factors, like a scientist's age or a serendipitous moment, are often beyond our direct control. Since 1900, 80% of discoverers were under 45—and about 15% of discoveries involved an element of serendipity. But even those unexpected moments are typically sparked by new tools—ones that visualise and detect the unexpected (Chapter 2). Other supporting factors can be more within reach like large funding (for certain instruments and research) and a large scientific community (for doing research using instruments). These factors mainly emerged after the second world war, with the establishment of national science foundations in the 1950s. Yet by then, most of science's leading methods and tools were already invented (Table6.1). And more than half of science's major discoveries were already made by 1945, including the majority of the major non-nobel discoveries since 1900 (Figure 4.4). Since 1900, 60% of discoverers did not work at top 50 universities—institutions with generally greater funding and resources. And since 1900, 33% of discoverers were not professors and 5% did not have a PhD—and even 36% worked in low-resource contexts with average annual incomes below 10,000 US$ (Chapter 4). These facts show that discovery does not depend on elite institutions, elite scientists and elite funding. Let us first explore deeper the factor many assume is the lifeblood of scientific progress: research funding. It is easy to assume that bigger budgets can lead to bigger breakthroughs. But we can test that assumption by examining science's over 750 discovery-making studies, including publications such as the Nobel prize lectures describing these discoveries. We find a striking insight: hundreds of high-impact breakthroughs are sparked by low-cost methods and tools. These include those among the ten most used in science: statistical and mathematical methods, light microscopes, electrophoresis, chromatography, thermometers and centrifuges—and later the PCR method and other assay techniques. Most of these tools of discovery were developed with small budgets—and today we can buy them new for less than a thousand or a few hundred dollars or are even free, like most statistical methods (Table 6.1). Tools, once acquired, can also often be shared, multiplying their impact. What is remarkable is the range and depth of nobel-prize discoveries powered by these inexpensive tools: from identifying viruses and developing life-saving vaccines, to inventing transformative statistical and mathematical methods and isolating essential chemical and biological substances. The German Robert Koch for example discovered the deadly bacteria causing tuberculosis using a light microscope together with simple and cheap staining techniques, a thermometer, syringe and guinea pigs. The Canadian Frederick Banting and Scottish John Macleod uncovered insulin using a colorimeter, scalpel, syringe and extracted pancreases from dogs—with the groundbreaking findings leading to the treatment of diabetes. The Israeli Daniel Kahneman revealed how we think and make decisions under uncertainty by using innovative but simple survey methods, statistical methods and decision-making experiments and T deviated from expected utility techniques. The American Michael Kremer developed experimental development economics by adopting randomised controlled trials— created in clinical medicine—and applying the method to conduct the first RCT on an education intervention. We highlight many other low-cost but transformative discoveries—including method discoveries like partition chromatography and the PCR method—throughout the book. These resourceful nobel-prize discoverers illustrate a recurring pattern across hundreds of breakthroughs achieved with minimal resources: they leverage innovative yet simple methods like statistical techniques or light microscopes, borrow recent cutting-edge methods from other fields and repurpose or upgrade basic lab instruments. Strikingly, these inexpensive discoveries span across major fields— from microbiology and chemistry to epidemiology, genetics and cognitive science. This reveals an important insight about the discovery process: large-scale funding is not always the norm and—aside from researchers' salaries and standard overhead costs—many discoveries require no additional funding. When we look at the hundreds of fields spanning the biological, chemical, physical, cognitive and social sciences, we find that the most expensive instruments are concentrated in a few subfields, especially within branches of physics like particle physics and astronomy. They include the Hubble space telescope constructed in 1990 by NASA and the European Space Agency which enabled discovering the accelerating expansion of the universe in 1998. The massive radio telescope built at Cambridge in 1967 led to discovering pulsars later that same year. The laser interferometer (LIGO) upgraded in 2015 in the United States made it possible to detect gravitational waves that same year. The large hadron collider (particle accelerator) developed by CERN in 2008 enabled revealing the Higgs particle in 2012. The Manhattan Project—a monumental effort requiring nuclear reactors and advanced isotope separation techniques—paved the way for the first atomic bomb in 1945. Beyond physics, some exceptionally expensive projects in genetics and medicine have also invested vast funding in major cancer research and the human genome project. Highperformance supercomputers, space programmes and other particle accelerators also demand immense resources. These are among the most popular examples of the most costly instruments and initiatives in scientific history that relied on much government funding. These exceptional cases are often mentioned as proof that science can be very expensive because these instruments are very expensive—yet they only make up a small fraction of major discoveries. While people's attention is naturally captured by these extraordinary initiatives in a few fields, they overlook the over 750 major discoveries that make up the very foundation of science. The price of discovery is often lower than usually assumed. During the centuries between Newton and Einstein, we find that science's discoveries even flourished on low budgets and small scales. Scientists funded themselves or received only modest support from universities or private foundations. The key is that it is resourceful researchers—challenging conventional thinking—who often drive transformative breakthroughs. Take also the often discussed role oflarge research teams or communitiesin advancing science. More researchers working together can cumulatively build on complex 148 T HE ENGINE OF SCIENTIFIC DISCOVERY methods and findings, pooling expertise to tackle large-scale problems. Fields like biomedicine, climate science and high-energy physics are thriving examples of this collaborative spirit. As Ernest Lawrence—the inventor of the particle accelerator— said, 'No individual is alone responsible for a single stepping stone along the path of progress' since we work within a broader scientific community. Yet a share of transformative discoveries has been achieved by researchers working alone. These range from the discovery of superconductivity by Kamerlingh Onnes, the first exoplanet by Michel Mayor and Didier Queloz and x-rays by Wilhelm Röntgen, to the discovery of cells by Robert Hooke, bacteria by Antonie van Leeuwenhoek and the moons of Jupiter by Galileo. The history of these groundbreaking discoveries began with these researchers using a new tool powerful enough to penetrate the boundaries of the known—without an existing research programme among a scientific community or any existing theory. These discoveries were sparked not because of team size, funding or institutional prestige, but once researchers had these extraordinary tools at their disposal (Chapter 2 on serendipity). A significant share of breakthroughs is also triggered by individual discoverers using a tool already developed in one field within another field to open an entirely new domain without yet a research community. An influential study published in Nature found that individual researchers and small teams are most likely to generate breakthrough research, not large-scale collaborations—which attract our attention. Nobel-prize discoveries have also commonly been awarded to a single researcher. In Scientific Elite: Nobel Laureates in the United States, Zuckerman highlights that 'laureates were especially concerned to have the record clear for their more significant work, and particularly in their prize-winning research papers' . When discoveries happen in new teams and collaborations, or new interdisciplinary settings—not just established ones—it is generally precisely because new methods or tools from different researchers are turned on a problem for the first time. They bring the new lens. It is not just about who is on a team—it is generally more about what methods they use that reveal what others could not yet see. From this perspective, it is at times about forming the kinds of collaborations that make new methods possible. Whether scientists work alone or collaborate with others, science on the whole naturally progresses collectively over the long run. Scientists are rarely isolated from the broader scientific community, with 99% of all nobel-prize discoverers working at or affiliated with a university or research institution at the time of their discovery (Appendix Table 4.1). We can think of scientific progress like an Olympic race. Some compete by training in coordinated relay teams, pushing each other and improving their performance, but when the finish line nears they break away from the pack to try and take the gold (like Crick and Watson pushing their way to the front and others to the side in depicting DNA's structure). Others train in a large pack without much competition (like the thousands of scientists working together to detect the Higgs particle). Still others take a more solitary route in unknown terrain (like Onnes uncovering superconductivity)—in each case guided by cutting-edge tools. A key insight emerges from examining the over 750 biggest discoveries: we find that significant shares of discoveries are made by scientists who can be in small or large teams, T low or high funded, young or old, at lower or top ranked universities, interdisciplinary or not, guided by theory or not, or involve a serendipitous moment or not (Chapters 2, 4 and 6). But the key factor common across all discoverers is that they directly leverage a new method to be able to break new ground—by enabling us to explore the world in a new light. No major discovery has been made without first applying a novel method or tool; and major extensions to our tools, from microscopes to spectrometers, from electrophoresis to particle accelerators, have generally always led to new discoveries—this is as causal as we can get (Chapter 1). This insight leads us to a distinct conclusion: we commonly over-focus on who is doing the research, when we should pay closer attention to what they are using to do it and how they got their hands on it. Broader cognitive, economic, societal and geographic factors do not change just before we make each discovery. These supporting factors generally remain stable over time, often lying beyond our control. They serve as the soil. But the seed that sparks the discovery itself is a new tool, lying in our direct control that we actually shape, design and refine—with most created just a few years before major discoveries (Appendix Figure 1.9). There is also at times not too much more we can say about factors like money and the scientific community in fostering science, except that they do. Common responses from researchers, on what can fuel groundbreaking research, generally circle around money and collaborations but also curiosity and serendipity. These factors support but are hardly unique to science; they are found widely in business, industry and public policy. For both scientists and non-scientists, a basic salary is generally needed to pursue work; teamwork can help merge perspectives and methods; psychological traits of curiosity and drive can lead to exploring new questions; and then there are serendipitous moments that can also arise. Far from being distinct to science, these common factors apply to most human activities. Yet what truly sets science and discovery apart are scientific tools and methods—by enabling us to explore and uncover entirely new types of complex knowledge. Scientific tools like advanced particle accelerators, x-ray crystallography, space telescopes and electrophoresis are largely exclusive to science and not used in other human domains. Looking at the ten most used methods and tools in science, we generally just use statistical methods in business, industry and public policy—and even then, they generally do not employ the complex techniques involving deep scientific modelling and rigorous controlled experiments (Table 6.1). Scientific tools uniquely define how major discoveries emerge. Machine learning methods are developed by researchers with advanced academic backgrounds also at tech companies and are gaining much importance in science. Pressing global challenges—whether in the race for new vaccines, cancer treatments and responses to aging populations, or technological solutions to climate change and renewable energies—can also influence science. They can shape some of our research priorities and the demand for discovering new solutions with new techniques. The most widely followed strategy for researchers aiming to spur new advances seems straightforward: identify an open research question and search for funding support and collaborations. This model guides projects funded by science's largest institutions, such as the European Commission and the National Science 150 T HE ENGINE OF SCIENTIFIC DISCOVERY Foundation. But is it the best model for innovation? Asking original questions not yet explored, thinking outside the box, challenging long-held assumptions and filling blind spots in what we know are central aspects of science. And new tools—by their very nature—enable us to do this more than other factors. Following new evidence and data wherever it takes us is critical, especially when it contradicts what we currently know. Experimenting in new ways and taking risks, even if the outcomes are uncertain, is key to advancing science—as unexpected data can often lead to unexpected findings. And once again, it is new tools—from x-ray methods to machine learning—that empower us to do this and explore uncharted territory. Factors like funding, teamwork, researchers' age and background can support research, but without innovative tools they alone cannot lead to breakthroughs. Hundreds of major discoveries have emerged without additional funding or collaborations, but from the moment a new tool was first applied that enables the new insights—as evidenced by discoverers in the discovery-making studies and Nobel prize lectures. New tools are commonly the central factor because they directly trigger new ideas and innovations and open entirely unimagined frontiers—more so than other factors can across science. This is highlighted in the conceptual framework in Figure 6.2. There are several reasons why tools are commonly the most direct factor we can influence in sparking discoveries: • we develop most tools of discovery within a few years—and often the same year—as the breakthroughs they enable that are otherwise not possible (Chapter 1). • we need to generally invest the greatest effort and time into tools, from design and refinement to application. • we directly modify tools as we actively develop or transfer them across fields, giving scientists unparalleled control to trigger innovation. At the end of a chain of questions into what shapes and guides new advances, we get to new tools. These are not aids but the very levers of discovery. They visualise the invisible: microscopes and telescopes reveal what is too small or too distant for the naked eye. They quantify the non-quantifiable: statistics, thermometers and measurement scales measure quantities with great precision. They sense the unsensible: spectrometers, radar devices and radio telescopes detect and measure light, radio waves and signals far beyond human sensory limits. They isolate the non-isolated: centrifuges, chromatography and electrophoresis separate substances like proteins, DNA and viruses. They simulate the unsimulated: computer technology models complex systems—from neural networks to the Earth's climate—that are too vast to study directly. They automate the unautomated: machine learning methods analyse massive datasets, run experiments and generate predictions by spotting patterns at exceptional speed. They image the non-imageable: x-ray devices, MRI, ultrasound and CT scans create extraordinarily precise images inside the human body. More than just standing on the shoulders of giants, these powerful tools enable the giants of science. These remarkable tools are the direct force uncovering what we did not even know existed—they are the discovery engine. T New discoveries New methods and tools Existing research, including data, evidence and theories, conducted at universities and institutions Researchers' interdisciplinary background and greater education (most with PhD) $ (for salaries including tools) Cognitive and psychological traits (including motivation) Existing knowledge, and features and norms of science Human capital and traits of scientists Basic factors supporting broader environment, including societal challenges Problem solving, moments of insight, serendipity/chance Tools created to enable the breakthrough observation or finding(most developed within a few years of the discovery) Basic resources and funding Scientific community/ research team Younger age (with greater productivity) Figure 6.2 The foundation of discovery: new methods and tools—our most direct levers of progress—and the factors that support them Our powerful tools also trigger our major theories of science by enabling us to see and describe what was hidden before. But how exactly do our greatest scientific theories fit into this tool-driven picture?