through five key stages: • Method constraint: generally, we run into a practical problem we cannot solve when using a current method or tool to study a phenomenon. T • Method scanning: next, we need to scan our own field and related disciplines for a method or tool that can tackle that constraint (and if none exist, we go to the next stage). • Method conceptualising: at this point, we require conceiving a new method or tool designed to solve the constraint, expanding our cognitive or sensory scope. • Method development: we need to then test, retest and scale up prototypes of the new method or tool, enabling us to explore the world in fundamentally new ways. • New methods-driven discoveries and fields: finally, we require applying the new method or tool to trigger new findings and advances. Take for example the extraordinary discovery of detecting gravitational waves in 2015. No tool was yet sensitive enough to reveal them. Researchers set out to develop an expanded massive laser interferometer, the LIGO detector. Uncovering the discovery that same year came down to an incredible methodological feat: they designed detectors thousands of kilometres apart that operate together with almost unimaginable precision—measuring a change in distance between the detectors' mirrors 1/10,000th the width of a proton (Figure 6.4). The high-precision instrument gave us a new window to the universe. Just two years later, the discovery earned a Nobel prize—one of the fastest recognitions in Nobel history. Understanding new tools as the key causal driver of breakthroughs offers a new way to understand scientific progress. Drawing from the general analysis of science's over 750 major discoveries, the evidence lays the foundation for this general theory of discovery. While we described the practical features of this new method-to-discovery view earlier (in the section on the role of theories), here we distil its deeper features. • The theory outlines how new methods and tools are a necessary condition for major discoveries, and commonly the central driver—they are the common thread driving our biggest breakthroughs across science and history. While supporting factors—like education, institutions and psychological features—foster breakthroughs, they vary by discovery. Without a new method or tool to detect or measure, no amount of funding, collaboration, training or luck will enable a new breakthrough, and theories need them to be meaningfully developed or tested. We spark significant shares of discoveries without these other factors—factors that are more context dependent and not always necessary (Chapters 4 and 6). • It is an explanatory and predictive theory of scientific progress that holds across time and fields. It explains the causal mechanism of how we accelerate science— the pace of generating new methods is key to forecasting future breakthroughs they make possible. • It explains how new methods are powerful in disrupting research because we can apply methods widely to topics beyond their initial scope. Unlike theories or findings often bounded by context, methods are more transferable and stable when we import them into unexpected domains—such as transformational statistical, computational or experimental methods. They better defy disciplinary silos, empowering us to break free from a field's inherent assumptions and provide an entirely new lens. method development laser interferometer-LIGO detector, improved (2015) particle accelerator, Bevatron (1954) x-ray crystallography (1913) new methods-driven discoveries and fields discovery of existence of gravitational waves (2015) discovery of antiproton (1955) field of molecular biology (1938) Science our body of knowledge of the world that is the result of all methods and tools and the discoveries and fields they unlock 01 Time (between new tool and new discovery/field) method conceptualising between the detectors' mirrors 1/10,000th the width of a proton devising an instrument that accelerates protons to sufficient energy identifying a method that can detect the structure of biological molecules like DNA method scanning no method existed no method existed novel method existed in physics method constraint not able to identify miniscule changes in distances to detect gravitational waves not able to accelerate protons to sufficient energy not able to establish the structure ofDNA designing detectors able to establish a change in distance Figure 6.4 The five method-driven steps we take to trigger new discoveries and fields T • It may arguably be, through the new method-to-discovery logic, the closest we can get to aunified theory of scienceor scientific progress. While disciplines differ widely in content and culture, they are consistently powered by the same engine: new methods. If a universal theory or principle exists that cuts across physics, biology, chemistry, psychology and beyond, it does not reside in what we study— but in how we study the world in new ways (Chapters 1 and 9). Surprisingly, examining science's major discoveries we find that we cannot spark them by just observing, experimenting or theorising using an existing method, but method innovation is essential (Chapter 1). For the increased power of a tool generates new conditions for what we can observe, experiment and theorise—with greater complexity, precision, quantity, temperature, energy and pressure. New major tools commonly produce large positive externalities far beyond the original discoverer or research team: they spill over to other scientists in the same and other fields. At times, new tools are repurposed to generate a wave of discoveries across disciplines that their inventors never imagined (Chapters 1–5). Take the simple PCR method: it accelerated the sequencing of the human genome, transformed forensic science and enables rapid medical diagnostics like HIV, tracing ancient DNA in palaeontology and tracking ecological evidence of biodiversity through soil and water. Strikingly, none of these applications were foreseen by its creator, Kary Mullis. And yet paradoxically, researchers do not often capitalise on these spillover effects, because research is focused on experimental results and theoretical insights—not tool inventions. But our methods are what connect our experiments to discoveries, our data to theory. This tools-first view flips the traditional narrative of discovery: it shifts the core source of scientific change from scientific advances to method advances that enable them. It is inventing new tools that has been the missing link in explaining new breakthroughs. This new tools-driven discovery principle represents a general rule for triggering breakthroughs. It is a general logic of discovery in which scientific progress is broadly driven by method innovations—not narrow methodological rules that, applied correctly, would spark breakthroughs (Chapter 2). This tool-first principle of discovery moves us beyond leading explanations in understanding discovery: historians like Kuhn emphasise paradigm shifts in theoretical frameworks as the central parameter driving science, scientometricians and network scientists point to team dynamics, careers, research productivity and networks, economists stress funding and incentives and sociologists like Merton focus on social dynamics. Each plays a role in some but not other advances. No explanation has yet established the common mechanism sparking science's major discoveries and highlighted the direct, key role of new methods and tools (Chapter 1). So why do historians and philosophers emphasise the importance of theories as the central metric of scientific progress? Why do scientometricians highlight scientists' citations, economists stress public investment, psychologists turn to creativity and serendipity, and so on? The answer lies in the nature of their own methods and training, with each field's research gravitating towards a particular metric that shapes the questions they ask and the kinds of answers they can see. Researchers are trained to see with certain lenses—but not others. That is why stepping back and adopting a 166 T HE ENGINE OF SCIENTIFIC DISCOVERY more comprehensive perspective is so important. Here, the integrated approach we adopt enables us to overcome shortcomings of relying on one method or factor, to uncover the broader insights of how breakthroughs actually emerge (Chapters 1–6). Ultimately, a theory that aims to explain scientific progress must place new tools at the centre of focus. Scientific table of methods: mapping and fusing methods and tools of discovery How does the new method-to-discovery model make us think or rethink about how science is structured? Mendeleev transformed chemistry not by discovering a new element, but by developing a new structure: the periodic table. He arranged the elements—by weight and chemical resemblance—so his students could better understand their properties. This remarkable new structure led to predicting and uncovering unknown elements. Similarly, science is organised to make it more accessible. Science textbooks categorise fields into neatly bounded disciplines—physics, chemistry, biology, psychology, history—and present the scientific method as 'the collection of data through observation and experiment, and the formulation and testing of hypotheses' (Chapter 3). This traditional architecture is widely adopted across science. But is it a natural categorisation of science? It is simply one among other ways to structure science. In fact, it can constrain us by overlooking two key features of how science actually works and progresses: first, the sophisticated methods and tools that do heavy lifting behind science's advances; and second, science's often interdisciplinary nature. We need to restructure the scaffolding of science. So what if we restructure science not just around its subject matter or its abstract ideals, but also around the practical methodological structure that drives science and unlocks discovery? Here we tackle this question. To begin, what are the most cognitively demanding methods and tools in science? At one end of the spectrum, we find complex modelling and simulation methods — techniques that demand elaborate formalisation, iterative refinement and greater abstraction. Whether modelling climate systems, biological processes or economic behaviour, these methods force us to make critical decisions that shape our findings: what should we simplify, exclude and mathematically represent?Mathematical methods like calculus and algebra demand much theoretical reasoning, often far removed from everyday intuition—think of Newton's laws expressed using calculus. Statistical inference methods, too, are cognitively intense and involve navigating multiple layers of complexity. Moving from raw data to robust conclusions and predictions demands using methods like frequentist hypothesis testing, Bayesian inference and regression analysis—all requiring reasoning about uncertainty, probability and margin of error in the results. These methods continuously evolve, with ongoing debates over p-values, effect sizes and, more broadly, the replication crisis driving their refinement. In turn, quasi-experimental methods are used when controlled T experiments and randomisation are not feasible. In fields like epidemiology and economics, researchers can at times rely on natural experiments or instrumental variable methods to approximate causal effects from real-world data. By contrast, controlled experimental methods—like randomised controlled trials—are built on clearer foundations but remain cognitively heavy, requiring careful technical judgment in isolating causal effects and managing bias. Sampling methods are central in data-driven science and occupy a unique methodological middle ground. Take well-designed longitudinal studies that follow the same individuals over time—these demand meticulous planning to minimise problems of representativeness, attrition and weighting the sample. Dealing with small populations or big data makes study designs more complex and increases cognitive load. We then move to experimental tools—such as centrifuges, PCR and chromatography devices—that uncover data not directly accessible to our senses. Their output often later feeds into statistical analysis, even if operating the tools can at times become routine with practice. At the other end of the spectrum lieindirect observational or measurement tools, like x-ray crystallography and spectrometers. These instruments enable us to infer structures not directly observable like atoms and molecules—such as DNA's double helix. In lab settings, their use can become streamlined and routine through standardised protocols. At the simplest conceptual level are direct observational or measurement tools—light microscopes, telescopes, thermometers—that extend our sensory reach in intuitive ways resembling human senses. They do not demand deep abstraction but amplify our senses, making them generally cognitively simple. This continuum highlights a rich hierarchy of cognitive demands: from many methods—like complex experimental methods driven by elaborate statistics—demanding several years to master and complex decisions in each study, to some tools that require much less effort and minimal training to use—like light microscopes and thermometers. Many education systems reflect this gradient, introducing observational tools early and progressing towards more complex methods. So why do serendipitous discoveries tend to arise from new tools, not from new methods? This classification here sheds light on this fascinating pattern. Physical instruments like microscopes and x-ray methods can suddenly reveal what no one knew existed, often differing fundamentally from mathematical and statistical methods, often leveraged to understand, quantify and predict phenomena after we uncover that they exist. Unlike a sudden serendipitous observation, breakthroughs grounded in statistics and mathematics often emerge from slower, more deliberate cognitive effort (as we uncovered in Chapter 2). To better guide how we catalyse innovation across science, we develop here a taxonomy of science's methods and tools—a kind ofperiodic table of methods. Surprisingly, no framework yet exists that systematically maps methods and tools across science— from telescopes to t-tests. By mapping the method landscape, the taxonomy reveals gaps and possibilities—helping guide where underused or unused techniques can be applied to catalyse discovery in unexpected domains. This science-wide classification can also offer researchers, educators and innovators a structured way to think 168 T HE ENGINE OF SCIENTIFIC DISCOVERY and rethink about the range of scientific methods and how we can link, adapt and recombine them in innovative ways to generate new kinds of knowledge. We can classify—and compare—each method and tool by: • Type and purpose: we differentiate between physical instruments (like microscopes) and analytical methods (like randomised controlled trials). We also categorise them by their function (observational, experimental, statistical) and their sub-categories (like direct or indirect observational tools). • Interdisciplinary scope: we categorise how transferable methods are across domains—from field-specific impact (like radio telescopes) to interdisciplinary impact (like microscopes and PCR) and even (nearly) universal impact (like statistical and AI methods). • Cognitive demand: we distinguish across the range of methods, with some techniques requiring increasing analytical effort, constant refinement and much judgment (like complex statistical modelling) while some tools are increasingly standardised and intuitive across researchers (like light microscopes) (Table 6.2). Key insights emerge from this classification of science's toolbox. One, the taxonomy can help accelerate discovery by guiding us to scan for powerful tools from other fields—tools that have surprisingly not yet been adopted in neighbouring domains. Understanding how specific tools have unlocked breakthroughs in one field helps us pinpoint what kinds of tools are underused or entirely missing in other fields— revealing unexplored territories where our current methods fall short. The solution to a problem in one discipline often already exists in another—as we highlighted in Chapter 1. Two, the taxonomy reveals which methods are most versatile and high-impact across fields, helping institutions and funders allocate resources and set research priorities more strategically towards the most adaptable, scalable and effective methods. Three, it can help overcome an overreliance on one or a few familiar methods—biasing research directions when other powerful tools are often available. Four, the taxonomy can open a new meta-research agenda—one that tracks method diffusion in and across fields (or failure to diffuse) and identifies bottlenecks in innovation and what factors enable or stifle the spread of transformative tools. It opens new avenues for interdisciplinary work and training, where researchers are methodologically multilingual and can move across domains fluidly. While not all methods are transferable, many are far more flexible than we assume. In short, as Mendeleev's periodic table revealed hidden relationships among chemical elements, a taxonomy of scientific methods can help reveal powerful methods: uncover underused methods outside disciplinary borders, expose gaps in the method landscape, spotlight new combinations of tools and realise opportunities to reinvent new techniques—ones that can unlock the next big advances. Science's best innovators and discoverers have stumbled across these approaches—for a particular breakthrough—but now we can intentionally pursue them head-on: within a systematic methodological framework and strategically extending our methods of discovery. Think of how medicine and public health have generally far outpaced T able 6.2 Scientific table of methods: a taxonomy of science's methods and tools—by type, purpose, interdisciplinary scope and cognitive demand purpose: Observation (or measurement) Experimental design Statistics and mathematics Hybrid method combinations a single observation (or few) is possible multiple observations (data driven) type: direct observational tools indirect observational tools experimental tools (in-/direct) experiment al sampling methods controlled experiment al methods quasiexperiment al methods statistical inference and analysis methods modelling and simulation / mathematical methods tool-tool combinations method-tool combinations methodmethod combinations used in many fields light microscopes x-ray devices spectrometers lasers machine learning methods calculus, algebra (theoretical modelling)** light microscopes + spectrometers imaging (x-ray, spectrometers) + machine learning methods MRI + statistical and computational methods interdisciplinary scope thermometers electron microscopes centrifuges chromatography randomised controlled trials (placebos, doubleblinding) frequentist testing Bayesian inference mathematical modelling (differential equations, game theory methods, network models) electron microscopes + lasers randomised controlled trials + meta-analysis electrophoresis PCR* CRISPR geneediting longitudinal studies structured surveys natural experiments regression discontinuity systematic metaanalysis computational simulation (agent-based models, Monte Carlo simulation) x-ray devices + chromatography chromatography + AI-methods PCR + Bayesian inference particle accelerators stratified sampling qualitative methods instrumental variable methods, difference-indifferences methods CRISPR geneediting + simulations difference-indifferences methods + network modelling used in one or few fields spectroscopes + telescopes telescope data + quasi-experi mental methodstelescopes particle detectors radio telescopes tools methods (analytical techniques)(physical instruments) at times less cognitive demand at times more This taxonomy is developed here based on the methods and tools used to spark science's over 750 major discoveries—featured throughout the book—and includes how broadly they are used across fields. Some tools and methods—like lasers and machine learning—can fall into different categories, with lasers for example applied as both an observational tool (laser interferometry in physics) and an experimental tool (surgical lasers in medicine). Experimental methods—like controlled trials—produce data that flow into statistical analysis, linking experimental design with statistical inference. *Some tools are often described as methods or techniques, such as PCR and CRISPR, and vice versa—though these are not methods in the abstract sense like statistical inference. ∗∗Some mathematical methods are used without relying directly on data but indirectly on previously collected data and findings. Methods can also be further classified by features like scalability, automation, reusability, precision, data type and known limitations. 170 T HE ENGINE OF SCIENTIFIC DISCOVERY neighbouring fields in pioneering rigorous, scalable methods: from randomised controlled trials (RCTs) to meta-analyses and natural experiments. The RCT method is so powerful that adopting it later to economics received a Nobel prize. Yet many fields still rarely take advantage of the remarkable RCT method. Imagine its underexploited capacity in the science of science, evaluating the effects of changes in researchers' methods, universities or fields on their impact—or in environmental science, assessing pollution-reduction or forestation programmes across countries. Many opportunities hide in plain sight. Ultimately, a scientific table of discovery methods is a map of explored and unexplored method options that can help identify and predict untapped combinations of tools and where the next breakthroughs can come from. It captures several key features: • Like elements in the periodic table, scientific methods and instruments can be thought of as foundational units. • Just as we combine elements from the periodic table to create entirely new compounds, we can fuse a vast array of tools across our method landscape to create new compound methods that trigger breakthroughs. • Just as there is no fixed number of chemical compounds we can form from over 100 known elements, there is no set limit to the number of powerful composite methods we can invent from science's developed methods and tools. • We can bind, mix and match two elements or methods, or three, four or more. Techniques like randomisation, blinding and/or placebos for example can be fused together to form stronger controlled experiments; their outputs then feed into statistical analysis; these in turn can be aggregated through meta-analysis—each methodological element linking together, like Lego pieces, towards greater scientific rigour. The key insight can be powerful: each fusion is a potential catalyst for discovery. Many combinations are remarkably straightforward: most methods and tools generate data (imaging tools, PCR, surveys) that can be linked to those that process and analyse data (statistical inference, machine learning) and to those that model behaviour and systems (simulations, mathematical models), and so on. The combinations are nearly endless—AI methods plus spectroscopy; MRI plus statistical and computational methods; lasers plus machine learning methods; the CRISPR method plus Bayesian inference or simulations (across populations or species); the PCR method plus network modelling (of how viruses spread), and so on. Exploring science's major discoveries, we can imagine countless fusions that hold high potential: combine chromatography with machine learning to predict new compound structures or optimise separations through learned molecular patterns. Link radio telescope data to quasi-experimental and causal inference methods to separate astronomical signals from noise and distortions. Connect centrifuges to AI imaging to train models to detect abnormalities in samples, and so on (Table 6.2). What are other ways a scientific table of methods can help bridge methodologically siloed fields and spur innovation? For researchers with open minds, the possibilities are immense. On one end, data-driven fields that rely heavily on statistical modelling and large datasets—from economics to the science of science—could benefit enormously from adopting a range of physical tools. In medicine, for example, wearable T devices like smartwatches transformed how real-time data are collected on patients to track heart rate, sleep, blood sugar and other health risks. Why not apply this same remarkable technology across the economic and social sciences to run experiments that monitor consumer decisions under stress in economics and emotional states in psychology? Why not increasingly employ neuroimaging tools like MRI to observe how the brain can react to incentives, risks and cooperation or use advanced facial recognition to help interpret emotional responses to economic decisions? These tools could push towards an era of embodied social science, where we do not just study human behaviour, but track its physiological and neural foundations in real time. By expanding our toolbox, highly data-reliant fields can evolve beyond statistical inference and abstract models to collect other rich, real-world experimental data. Another novel example is systematic meta-analysis—a method that synthesises findings across independent studies to reveal overarching trends. In medicine, this method has become indispensable to determine the overall effectiveness of treatments. But why not leverage this transformative method across many fields? It would have a vast impact if fully exploited across fields, from scientometrics and economics, to the science of science and even philosophy of science. For it helps fields move from isolated results scattered across individual papers—or even entire domains plagued by conflicting or inconclusive findings—to establishing greater consensus by synthesising a field's broader findings. Surprisingly, this often reflects low-hanging fruit for generating more reliable, cumulative knowledge—the method is already available and just needs to be applied. On the other end, tool-driven fields that rely heavily on physical instruments to make observations and measurements could advance more rapidly by better harnessing more complex statistical, computational and AI-based methods. Take fields like biology, chemistry and geology that generate images taken with tools like microscopes, x-ray devices, spectrometers and telescopes. Advanced image analysis tools powered by deep machine learning can rapidly analyse images to detect and interpret previously hidden patterns in vast datasets across fields—patterns invisible to the human eye. Take simulation techniques that have been transformative in fields like climate science, computer science and economics. Why not increasingly use cutting-edge AI technology to simulate, model and predict complex systems and processes across fields? Imagine unexplored frontiers across every domain: in the science of science, why not aim to predict how new methods and discoveries spread or how these changes impact new innovation? In public administration, why not simulate the dynamics of institutions and government crises? In philosophy of science, why not model scientific knowledge, practices and communities to see how they gain and lose prominence over time? And so on. If we intentionally cross-pollinate tools and export methods across disciplines, the very structure of scientific knowledge could change. In the future, we may conceive and define disciplines not by what they study but by how they study: by common method and tool clusters. From this method lens, we can already see this in our current scientific landscape. Think of physics, a field that conducts vast research across domains spanning the sciences—from biological systems, ecological networks and weather prediction models, to quantum biology, neurophysics, computational 172 T HE ENGINE OF SCIENTIFIC DISCOVERY chemistry, machine learning and the science of science. These are not studied because they are inherently 'physical' topics, but because physicists often receive more rigorous training in quantitative methods including mathematical and computational modelling, differential equations and network analysis, and in instruments including lasers, particle detectors and high-resolution imaging tools. These equip them to model and simulate complex systems across domains. The reach of physics is defined not by topics, but by the power and portability of their methods that unite these applications. Take also economics, a field that conducts studies on nearly all domains across the social sciences—from happiness, crime, racial bias and political polarisation, to education, transportation systems, energy and climate change. Again, it is not because these topics are intrinsically 'economic' , but because economists often have more extensive training in statistical and causal inference methods—including regression discontinuity designs, instrumental variables, and randomised experiments. These empower them to quantitatively analyse complex social phenomena. Often far from economic or physical theory and far from formal training in the topics they study, it is statistical and mathematical methods that provide the common thread across these diverse applications. Physics often appears to dominate the natural sciences, much like economics dominates the social sciences. Yet within this method-driven framework here, we can see what actually drives this remarkable dominance in science: exportable methods, not subject matter. Powerful tools and their combinations are often the key elements driving progress, not just theory or subject matter. The frontier of science is commonly the unexplored and empty spaces in this evolving periodic table of methods. A deeper insight emerges here about path dependency in science: the discoveries we have achieved so far were made possible by the tools we have come up with so far. The very trajectory of science is shaped by what we have had at our disposal to measure, see and test. If we had created different—or more—methods up to now, science would likely have developed in different—or more—directions. Some of science's leading methods, from statistical methods to randomised controlled experiments, could have turned out differently from how they did. Placebos, double-blinding, p-values or meta-analyses are not inevitable and the only methodological solutions to the problems they help address. Had we invented other techniques first, our understanding of evidence and causation may look different today. Our methods of science are created under particular constraints to solve particular problems. And just as our methods are invented, they have evolved, been merged and vastly expanded—and will turn out differently from how they currently are. Recognising this fact is critical: the future of science hinges not just on new data or new theories, but on our capacity to invent bold new methods. (Yet methods are certainly not arbitrary as they commonly produce consistent, rigorous findings and technologies that improve our lives.) This opens our minds to the undetermined power of the methods we create and the possibility of generating a range of previously unimaginable methods to tackle new real-world problems and challenges we face. T