Examining science's major discoveries and methods across fields offers us a unique opportunity to probe the fundamental nature of scientific progress. This approach captures science's major theoretical, experimental and methodological breakthroughs—rather than just focusing on select theoretical breakthroughs. While there is no clear cut-off for what counts as a small discovery, there is strong consensus within the scientific community on science's major discoveries. To assess scientific progress, we classify discoveries, methods and tools across fields into three categories: those that have been updated (extended) with new evidence, those that have not been updated, and those that have been entirely replaced (abandoned or subject to a paradigm shift for being incorrect). Discoveries, methods and tools across fields are defined as contributing to cumulative scientific progress if they have not been abandoned. The classification is based on descriptions within the six mentioned encyclopaedias of science, Nobel prize documents or the seven mentioned R science textbooks. The description for about four-fifths of major breakthroughs is drawn from two sources—Nobel prize documents (such as prize summaries and press releases) and Encyclopaedia Britannica where entries are written by scientific experts as established knowledge (and so are not self-reported by discoverers). One measure of scientific progress: scientific methods and their cumulative nature We begin by first testing the fundamental hypothesis of paradigm shifts in science by examining scientific methods and tools—a yet unexplored perspective. If science were truly defined by abrupt revolutions, we would expect to see major tools discarded over time. But what does the evidence show? Take the ten central methods and tools most used to make all 533 nobel-prize discoveries: statistical/mathematical methods, spectrometers, (electron) microscopes, x-ray methods, chromatography, centrifuges, electrophoresis, lasers, particle accelerators and particle detectors. These powerful instruments are the backbone of science that have shaped entire fields. And remarkably, each has been continuously refined, upgraded and expanded to increase power, accuracy, precision and efficiency, at times over centuries. None have been abandoned. Instead, we apply them widely across disciplines, enabling us to spark dozens of new discoveries. Among all 149 nobel-prize-winning method discoveries—the major methods and tools awarded the prize—we find a striking trend: 99% have been updated, 1% have not been updated and none have been abandoned. These extraordinary tools like the PCR method, electron microscope, radiocarbon dating method and electrophoresis have been fine-tuned over time. In fact, we find no major methods or tools we employ across fields—from calculus and controlled experimental methods to telescopes and thermometers—that have been entirely discarded. Our most prominent scientific methods and tools do not undergo abrupt breaks but are deeply cumulative. Microscopes—our classic example of a powerful discovery tool—have evolved cumulatively over centuries. From the earliest microscopes relying on light and lenses to electron and scanning probe microscopes, we keep extending the field of microscopy and so our ability to observe the microscopic world. Our best light microscopes today do not compete as an entirely different paradigm to the first light microscope, with the same function of visualising miniscule objects. Our methods of arithmetic today do not represent a break from those the Sumerians developed, but build on it. Major methods and instruments used across fields do not go through competing method paradigms. We instead expand our best tools over time into even more powerful tools of discovery, forming the foundation of science and our ability to do science. In fact, our best tools are the very building blocks making up a continually stronger and more refined foundation of science. (So a possible paradigm shift that would abandon them would so fundamentally change how we conceive science that we could likely no longer call what we do science.) Think of statistical methods for example. Over hundreds of years, they have been developed and expanded by pioneers like the German Carl Gauss, French PierreSimon Laplace, British Karl Pearson and Ronald Fisher and many others. R methods share a common purpose: to extract meaningful patterns from data and make inferences. Today, our cumulative statistical methods test hypotheses, analyse vast data and make systematic predictions in fields from physics and biology to economics. Statistics has arguably received most attention in ongoing debates on improving how results are reported and published. The replication crisis, the push for open science and developments in Bayesian statistics all contribute to upgrading statistical methods. Far from replacing the foundations of statistics, these reforms only strengthen them. Some tools, like mercury thermometers and barometers, are expanded into new tools, like electronic thermometers and barometers, offering greater accuracy and safety. Although cathode ray tubes have largely been physically phased out of physics and electronics labs, their core function—visualising electrical signals—remains unchanged today. Cathode ray tubes were gradually outdated with more advanced digital oscilloscopes, fulfilling the same purpose but with greater precision and efficiency. Looking at the bigger picture, a key trend emerges here: many methods and tools are each applied in sparking five or more discoveries, often across different fields, underscoring the cumulative tool-driven nature of science. In short, with our best tools deeply intertwined across fields, they are the scaffolding of scientific progress. A second measure of scientific progress: scientific discoveries and their cumulative nature We next test the fundamental hypothesis of paradigm shifts in science by probing scientific discoveries. Analysing science's over 750 major discoveries, we find a pattern: about 83% have been extended using new methods and evidence, about 16% have not been extended, while only in a few exceptional cases—1%—has a discovery been abandoned. What were once the leading discoveries of the time have generally been built on and updated with new methods and more accurate evidence, making up over four in five discoveries. The discovery of DNA sequencing in 1977 by the American Walter Gilbert and British Frederick Sanger was for example vastly extended with improved electrophoresis and sequencing machines. The discovery of the nature of isotopes in 1913 by the British Frederick Soddy was updated once the neutron was discovered, made possible by new particle detectors. The discovery of hormonal treatment for prostatic cancer in 1940 by the Canadian Charles Huggins was expanded with new methods that paved the way for more sophisticated hormone therapies and improved patient outcomes. Far from abrupt paradigm shifts that render past knowledge obsolete, the vast majority of nobel-prize-winning discoveries has been built upon with new and more cutting-edge methods and later discoveries. So about one in six discoveries has stood the test of time and has not (yet) been extended but remains largely unchanged. The nobel-prize-winning discoveries of the first exoplanet, the detection of the neutrino and the isolation of fluorine are examples. Often, these are one-off breakthroughs that establish the existence of a new phenomenon. The electron and the double-helix structure of DNA are other such foundational discoveries in the sense that other breakthroughs build on them but do not directly revise them. Ultimately, only 1% of discoveries have been entirely replaced by new methods and evidence, reflecting only eight superseded discoveries among science's over 750 major discoveries. Surprisingly, three of them were awarded a Nobel prize, but their findings were later abandoned. One case is the initial findings of the Danish Johannes Fibiger in 1913 that ingesting a roundworm caused cancer in rats. While his work was initially celebrated, later methods and research revealed that the real cause was actually a lack of vitamin A. The worm larvae only led to tissue damage where cancer could then develop. Another case is the development of leucotomy by the Portuguese Egas Moniz as a treatment for mental illnesses in 1935. Yet this surgical technique, involving cutting into the brain's prefrontal lobe, also could cause major personality changes as an unpredictable 'side effect'. So it was abandoned as new methods and medications for treating mental illness emerged in the 1950s. Today, it stands as a cautionary tale of early surgical interventions in mental health. The third case comes from economics: the economic theory of portfolio management by the American Harry Markowitz in 1952. Yet he later 'warns the reader that the 1952 piece should be considered only a historical document—not a reflection of my current views about portfolio theory', since he later discarded his initial theory because of methodological errors and changes in his views about mean and variance. Even in these eight exceptional cases, the discoveries, theories and methods applied served as reference points—stepping stones enabling us to build on and supersede them. So in these few cases, scientific progress can still be conceived as cumulative, since mismeasurements and mistakes also contribute to the overall picture by triggering correction. Science is self-correcting. Revolutionary leaps that represent a complete rupture from what we currently know are rare in science—unless we search for exceptional differences over millennia as in the most famous example of a paradigm shift from Ptolemy to Copernicus. The last step or discovery often seems to be the most impressive or revolutionary. But it is only possible by building on methods and resulting discoveries that come before. Comparison across fields reveals insight into the evolutionary nature of science. Astronomy stands out again with the highest share of nobel-prize discoveries that have not been updated, making up about four out of ten discoveries in the field. Pulsars (neutron stars) and the accelerating expansion of the universe for example, once discovered, have not been updated given the very nature of these discoveries. Yet we have expanded nearly all discoveries in economics and social sciences. Why? For these fields deal with highly complex and fast evolving systems. The key here is that we update or replace discoveries commonly by using a new method or tool that offers a new perspective and evidence. New tools provide the lens through which we can revisit and revise earlier findings. Overall, less than 1% of nobel-prize discoveries have been abandoned and slightly more at 2% for major non-nobel discoveries across history, highlighting comparable results across the two groups. This provides us with evidence against the popular hypothesis that revolutionary paradigm shifts dominate science. Let us take a closer look at the classic and most widely discussed paradigm shift: the transition from the model of our universe from Ptolemy to Copernicus. The ancient Greek Claudius Ptolemy's geocentric model proposed that the Earth was the centre of our universe, with the sun revolving around it. The Prussian-Polish Nicolaus Copernicus' heliocentric model proposed the opposite: that the sun is the centre of our universe, around which the Earth orbits. For over a millennium, Ptolemy's model reigned. Then Copernicus came and used observational data—collected with tools like the quadrant and astrolabe—and mathematical calculations. These were laid out in his book De revolutionibus orbium coelestium that later shook the foundations of astronomy and was published just a few months before his death. Yet the shift from Ptolemy's model to Copernicus' model occurred gradually, once evidence backed by new tools supported the heliocentric model. At the University of Padua in Italy, Galileo refined and confirmed Copernicus' model through new discoveries. Galileo's newly invented telescope played a crucial role: it enabled discovering the phases of Venus and the moons of Jupiter and compellingly proved that celestial bodies could orbit something other than Earth. The heliocentric theory gained greater acceptance once we could test hypotheses rigorously using standards of modern science including predictive accuracy and we invented new tools like the telescope. Once invented, we were no longer blind to incorrect models but could disprove them. The older an abandoned theory is, the less likely it was developed and confirmed using rigorous scientific methods and tools that cumulatively build on each other over time. What seems like a sudden, radical idea we generally make possible by measuring and observing the world with ever more refined tools that enable new perspectives and greater precision. What if science does not move forward mainly through theory shifts, but through new tools that allow us to see what we could not see before—and not just in theory-heavy fields but across scientific fields? Groundbreaking discoveries—whether we call them paradigm shifts or not—are commonly driven by new and better methods and tools that enable us to study and understand the world in new ways. Our tools do not just endure changes in theory; they commonly cause them—by providing a new lens to the world. A third measure of scientific progress: scientific fields and their cumulative nature We now test the fundamental hypothesis of paradigm shifts in science by exploring scientific fields, such as genetics, computer science and electricity. Take the development of the field of electricity for example—one of the most transformative forces in modern society. A critical first step was taken in 1752 when the American Benjamin Franklin famously demonstrated that lightning is a form of electricity. He discovered the nature of electricity using leyden jars (a device for storing static electricity) invented a few years earlier in 1745. The breakthrough, explaining how electricity flows from lightning through a metal kite, sparked new questions. It led to the Italian Luigi Galvani developing an animal electricity theory in 1791 by also using leyden jars—a theory of how electricity causes frogs' muscles to contract. Building on this theory and its limitations, the Italian Alessandro Volta created the first electric battery in 1800—a steady source of electric current that marked a transformative advance. For it enabled us to better study electricity and produce electricity-powered technology. Volta's breakthrough powered new discoveries, with the Danish Hans Ørsted applying the newly created battery to discover that an electric current generates a magnetic field in 1820. Building on the work of Volta, Ørsted and Faraday, the French André-Marie Ampère was then able to develop the law of electromagnetism in 1827 by using a magnetic conductor he invented in 1822. This mathematical theory explained the relationship between electricity and magnetism. In the same year, the German Georg Ohm introduced the mathematical concept of electrical resistance, establishing Ohm's Law, by using a galvanometer. The next giant leap came in 1831 when the British Michael Faraday created an electric generator using electromagnetic induction. This was key in laying the foundation for electrical power generation. Through Faraday's work and using mathematical methods, the Scottish James Maxwell could then take the pivotal next step to unify what was known about electricity and magnetism into a theory of electromagnetic radiation in 1865. Maxwell's highly influential theory revealed that electric and magnetic waves are on the same electromagnetic spectrum—governing everything from radio waves and light to x-rays. These collective methods and knowledge fuelled the Serbian Nikola Tesla's development of alternating current (an induction motor) in 1883. This fascinating breakthrough brought electric power plants and electricity to our cities on a mass scale. Building on the accumulated tools and evidence, the British Joseph Thomson ultimately unexpectedly discovered the electron in 1897 using a cathode ray tube he designed the previous year. These pioneering scientists had an expanding and powerful toolbox at their disposal. A key insight emerges: each of these scientists since 1820 applied the newly developed galvanometer, battery and/or electric generator to spark their discoveries. The fact that major discoveries could not be made without first generating these innovative tools and resulting discoveries offers compelling evidence of the deeply cumulative nature of scientific progress. Even the most revolutionary ideas arise from a chain of incremental steps. Taking a broader step back, the German physicist Albert Einstein then built upon these methods to be able to achieve a critical breakthrough in 1905: the special theory of relativity and the famous equationE = mc2, reshaping the field of physics. While Einstein's theory is often seen as a classic example of just a theoretical discovery, it was deeply rooted in the existing methods and experimental findings of his time. We can trace the methods he heavily relied on directly or indirectly: advanced mathematical methods—including Maxwell's equations—and Michelson's measurements of the speed of light using the newly invented interferometer in 1881. Without these tools, he could not have formulated his theory (a topic we return to in Chapter 6). Einstein's innovation lies in interpreting and logically restructuring the existing experimental results and methods. New tools, such as particle accelerators and atomic clocks, enabled later experimental tests that confirmed and expanded his predictions with extraordinary precision. Strikingly, genetics and computer science, like electricity, reveal how we develop complex knowledge through deeply interlinked methods, tools and resulting discoveries that build on each other and often span more than a century. The history of electricity, genes and computers exemplifies how we apply interconnected tools to trigger interconnected discoveries in fields across the sciences. In fact, no major fields—from biology and nuclear physics to medicine and mechanical engineering—have been entirely discarded. Our highly connected system of science is the outcome of these deeply collective feedbacks. In chemistry, assembling the periodic table of elements has been an enormous collaborative and cumulative effort over time, forming the foundation of the field. In biology, most of what we know builds on the theory of evolution and the mechanisms of evolution, laying the backbone of the field. Yet it would be odd if we did not see a big change in theory in the classic examples between Ptolemy and Copernicus, or between Aristotle's, Newton's and Einstein's view of physical reality spanning two millennia. These changes did not emerge from nowhere. Scholars in the 16th and 17th century, including Copernicus and Newton, turned to Ptolemy's geocentric astronomy and Aristotle's laws of motion as the very theories they tested, disproved and built on. Several centuries later, Einstein then relied on Newton's laws of motion and theory of gravity as a reference point to build on. Yet Newton's classical mechanics still remains useful today to describe everyday, macroscopic objects. Even the rare historical cases of abandoned discoveries reveal elements of cumulative knowledge we used to go beyond them. By studying discoveries systematically, we can overcome what seems to be discontinuity in some select theories in the past, especially about physical reality, and view them as stepping stones.