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Astrophysicist Mario Livio on the "Brilliant Blunders" That Changed Our Understanding of the Universe

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 We all make mistakes. Nobody’s perfect. Not even some of the greatest geniuses in history, as Mario Livio tells us in part one of this excerpt from
 <a href="http://www.mariolivio.com/">
 Brilliant Blunders: Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe.
 </a>
 The book is a marvelous exploration of scientific error and breakthrough that focuses on five scientific giants who made significant advances in their fields through error, proving that mistakes are essential to progress.
 

<h1>
 Brilliant Blunders (Book Excerpt: Part 1)
 </h1>

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<figcaption>Oscar Wilde
 
 </figcaption>
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 When the mercurial Bobby Fischer, perhaps the most famous chess player in the history of the game, finally showed up in Reykjavik, Iceland, in the summer of 1972 for his world championship match against Boris Spassky, the anticipation in the chess world was so thick you could cut it with a chainsaw. Even people who had never shown any interest in chess before were holding their breath for what had been dubbed “the Match of the Century.” Yet in the twenty-ninth move of the very first game, in a position that appeared to be leading to a dead draw, Fischer chose a move that even amateur chess players would have rejected instinctively as a mistake. This may have been a typical manifestation of what is known as “chess blindness”—an error that in the chess literature is denoted by “??”—and would have disgraced a five-year old in a local chess club. Particularly astonishing was the fact that the mistake was committed by a man who’d smashed his way to the match with the Russian Spassky after an extraordinary sequence of twenty successive wins against the world’s top players. (In most world-class competitions, there are easily as many draws as outright victories.) Is this type of “blindness” something that happens only in chess? Or are other intellectual enterprises also prone to similarly surprising mistakes?
 
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 Oscar Wilde once wrote, “Experience is the name everyone gives to their mistakes.” Indeed, we all make numerous mistakes in our everyday lives. We lock our keys inside the car, we invest in the wrong stock (or sometimes in the right stock, but at the wrong time), we grossly overestimate our ability to multitask, and we often blame the absolutely wrong causes for our misfortunes. This misattribution, by the way, is one of the reasons that we rarely actually learn from our mistakes. In all cases, of course, we realize that these were mistakes only after we have made them—hence, Wilde’s definition of “experience.” Moreover, we are much better at judging other people than at analyzing ourselves. As psychologist and Nobel laureate in economics Daniel Kahneman has put it, “I am not very optimistic about people’s ability to change the way they think, but I am fairly optimistic about their ability to detect the mistakes of others.”
 

 Even attentively and carefully constructed processes, such as those involved in the criminal justice system, fail occasionally—sometimes heartbreakingly so. Ray Krone of Phoenix, Arizona, for instance, spent more than ten years behind bars and faced the death penalty after having been convicted
 
 twice
 
 of a brutal murder he did not commit. He was eventually fully exonerated (and the real killer implicated) by DNA evidence.
 

 The focus of this book, however, is not on such mistakes, no matter how grave they may be: it is on major
 
 scientific blunders
 
 . By “scientific blunders,” I mean particularly serious conceptual errors that could potentially jeopardize entire theories and game plans, or could, in principle at least, hold back the progress of science.
 
<aside class="pulledquote">
 Great blunders are often made, like large ropes, of a multitude of fibres. Take the cable thread by thread, take separately
 
 all the little determining motives, you break them one after another, and you say: that is all. Wind them and twist them together they become an enormity.
 
 —VICTOR HUGO, LES MISÉRABLES
 </aside>

 Human history teems with stories of momentous blunders in a wide range of disciplines. Some of these consequential errors go all the way back to the Scriptures, or to Greek mythology. In the book of Genesis, for instance, the very first act of Eve—the biblical mother of all living humans—was to yield to the crafty serpent and to eat the forbidden fruit. This monumental lapse in judgment led to no less than the banishment of Adam and Eve from the Garden of Eden, and—at least according to the thirteenth-century theologian Thomas Aquinas—even to humans being eternally denied access to absolute truth. In the Greek mythology, Paris’s misguided elopement with the beautiful Helen, the wife of the king of Sparta, brought about the total destruction of the city of Troy. But these examples don’t even begin to scratch the surface. Throughout history, neither renowned military commanders nor famous philosophers or groundbreaking thinkers were immune to serious blunders. During World War II, the German field marshal Fedor von Bock foolishly repeated Napoléon’s ill-fated attack on Russia in 1812. Both officers failed to appreciate the insurmountable powers of “General Winter”—the long and harsh Russian winter for which they were woefully unprepared. The British historian A. J. P. Taylor once summarized Napoléon’s calamities this way: “Like most of those who study history, he [Napoléon] learned from the mistakes of the past how to make new ones.”
 

 In the philosophical arena, the great Aristotle’s erroneous ideas on physics (such as his belief that all bodies move toward their “natural” place) fell just as wide off the mark as did Karl Marx’s awry predictions on the imminent collapse of capitalism. Similarly, many of Sigmund Freud’s psychoanalytic speculations, be it on the “death instinct”—a supposed impulse to return to a pre-life state of quietude— or on the role of an infantile Oedipus complex in the neuroses of women, have been found to be pathetically amiss, to put it mildly.
 

 You may think, OK, people made mistakes, but surely, when it comes to some of the greatest scientists of the past two centuries— such as the twice Nobel laureate Linus Pauling or the formidable Albert Einstein—they were correct at least in those theories for which they are best known, right? After all, hasn’t the intellectual glory of modern times been precisely in the establishment of science as an empirical discipline, and of error-proof mathematics as the “language” of fundamental science? Were, then, the theories of these illustrious minds and of other comparable thinkers truly free of serious blunders? Absolutely not!
 

 The purpose of this book is to present in detail some of the surprising blunders of a few genuinely towering scientists, and to follow the unexpected consequences of those blunders. At the same time, my goal is also to attempt to analyze the possible causes for these blunders and, to the extent possible, to uncover the fascinating relations between those blunders and features or limitations of the human mind. Ultimately, however, I hope to demonstrate that the road to discovery and innovation can be constructed even through the unlikely path of blunders.
 

 As we shall see, the delicate threads of evolution interweave all the particular blunders that I have selected to explore in detail in this book. That is, these are serious blunders related to the theories of the evolution of life on Earth, the evolution of the Earth itself, and the evolution of our universe as a whole.
 
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Astrophysicist Mario Livio on Blunders of Evolution and the Evolution of Blunders

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 We all make mistakes. Nobody’s perfect. Not even some of the greatest geniuses in history, as Mario Livio tells us in part one of this excerpt from
 <a href="http://www.mariolivio.com/">
 Brilliant Blunders: Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe.
 </a>
 The book is a marvelous exploration of scientific error and breakthrough that focuses on five scientific giants who made significant advances in their fields through error, proving that mistakes are essential to progress.
 

<h1>
 Blunders of Evolution and Evolution of Blunders (Book Excerpt: Part 2)
 </h1>

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<figcaption>Charles Darwin, Original Mistake-Maker.
 
 </figcaption>
</figure>

 

 
 
 One of the definitions of the word “evolution” in the Oxford English Dictionary reads: “The development or growth, according to its inherent tendencies, of anything that may be compared to a living organism. Also, the rise or origination of anything by natural development, as distinguished from its production by a specific act.” This was not the original meaning of the word. In Latin, evolution referred to the unrolling and reading of a book that existed in the form of a scroll. Even when the word started to gain popularity in biology, it was used initially only to describe the growth of an embryo. The first utilization of the word “evolution” in the context of the genesis of species can be found in the writings of the eighteenth-century Swiss naturalist Charles Bonnet, who argued that God had pre-organized the birth of new species in the germs of the very first life-forms he created.
 

 In the course of the twentieth century, the word “evolution” has become so intimately associated with Darwin’s name that you may find it hard to believe that in the first, 1859 edition of his masterwork,
 
 On the Origin of Species
 
 , Darwin does not mention the word “evolution” as such even once! Still, the very last word of
 
 The Origin
 
 is “evolved.”
 

 In the time that has passed since the publication of
 
 The Origin
 
 , evolution has assumed the broader meaning of the definition above, and today we may speak of the evolution of such diverse things as the English language, fashion, music, and opinions, as well as of sociocultural evolution, software evolution, and so on. (Check out how many web pages are devoted just to “the evolution of the hipster.”) President Woodrow Wilson emphasized once that the correct way to understand the Constitution of the United States was through evolution: “Government is not a machine, but a living thing . . . It is accountable to Darwin, not to Newton.”
 
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 My focus on the evolution of life, of the Earth, and of the universe should not be taken to mean that these are the only scientific arenas in which blunders have been committed. Rather, I have chosen these particular topics for two main reasons. First, I wanted to critically review the blunders made by some of the scholars that appear on almost everybody’s short list of great minds. The blunders of such luminaries, even if of a past century, are extremely relevant to questions scientists (and, indeed, people in general) face today. As I hope to show, the analysis of these blunders forms a living body of knowledge that is not only captivating in its own right but also can be used to guide actions in domains ranging from scientific practices to ethical behavior. The second reason is simple: The topics of the evolution of life, of the Earth, and of the universe have intrigued humans—not just scientists—since the dawn of civilization, and have inspired tireless quests to uncover our origins and our past. The human intellectual curiosity about these subjects has been at least partially at the root of religious beliefs, of the mythical stories of creation, and of philosophical inquiries. At the same time, the more empirical, evidence-based side of this curiosity has ultimately given birth to science. The progress that humankind has made toward deciphering some of the complex processes involved in the evolution of life, the Earth, and the cosmos is nothing short of miraculous. Hard to believe, but we think that we can trace cosmic evolution back to when our universe was only a fraction of a second old. Even so, many questions remain unanswered, and the topic of evolution continues to be a hot-button issue even today.
 
<aside class="pulledquote">
 “The progress that humankind has made toward deciphering some of the complex processes involved in the evolution of life, the Earth, and the cosmos is nothing short of miraculous.”
 </aside>

 It took me quite a while to decide which major scientists to include in this journey through deep intellectual and practical waters, but I eventually converged on the blunders of five individuals. My list of surprising “blunderers” includes the celebrated naturalist Charles Darwin; the physicist Lord Kelvin (after whom a temperature scale is named); Linus Pauling, one of the most influential chemists in history; the famous English astrophysicist and cosmologist Fred Hoyle; and Albert Einstein, who needs no introduction. In each case, I will address the central theme from two rather different—but complementary—perspectives. On one hand, this will be a book about some of the theories of these great savants and the fascinating relations among those theories, viewed in part from the unusual vantage point of their weaknesses and sometimes even failures. On the other, I will scrutinize briefly the various types of blunders and attempt to identify their psychological (or, if possible, neuroscientific) causes. As we shall see, blunders are not born equal, and the blunders of the five scientists on my list are rather different in nature. Darwin’s blunder was in not realizing the full implications of a particular hypothesis. Kelvin blundered by ignoring unforeseen possibilities. Pauling’s blunder was the result of overconfidence bred by previous success. Hoyle erred in his obstinate advocacy of dissent from mainstream science. Einstein failed because of a misguided sense of what constitutes aesthetic simplicity. The main point, however, is that along the way, we shall discover that blunders are not only inevitable but also an essential part of progress in science. The development of science is not a direct march to the truth. If not for false starts and blind alleys, scientists would be traveling for too long down too many wrong paths. The blunders described in this book have all, in one way or another, acted as catalysts for impressive breakthroughs—hence, their description as “brilliant blunders.” They served as the agents that lifted the fog through which science was progressing, in its usual succession of small steps occasionally punctuated by quantum leaps.
 

 I have organized the book in such a way that for each scientist, I first present the essence of some of the theories for which this individual is best known. These are very concise summaries intended to provide an introduction to the ideas of these masters and an appropriate context for the blunders, rather than to represent comprehensive descriptions of the respective theories. I have also chosen to concentrate only on one major blunder in each case instead of reviewing a laundry list of every possible mistake that these pundits may have committed during their long careers.
 

 —
 

 Despite their blunders, and perhaps even because of them, the five individuals I have followed and sketched in this book have produced not just innovations within their respective sciences but also truly great intellectual creations. Unlike many scientific works that target only professionals from within the same discipline as their audience, the oeuvres of these masters have crossed the boundaries between science and general culture. The impact of their ideas has been felt far beyond their immediate significance for biology, geology, physics, or chemistry. In this sense, the work of Darwin, Kelvin, Pauling, Hoyle, and Einstein comes closer in spirit to achievements in literature, art, and music—both cut a broad swath across erudition.
 

 There is no better way to end a book on blunders than with an important reminder—a plea for humility, if you like—that nobody can express more eloquently than Darwin:
 
<blockquote>

 We must, however, acknowledge, as it seems to me, that man with all his noble qualities, with sympathy which feels for the most debased, with benevolence which extends not only to other men but to the humblest living creature, with his god-like intellect which has penetrated into the movements and constitution of the solar system—with all these exalted powers—Man still bears in his bodily frame the indelible stamp of his lowly origin.
 
</blockquote>
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Brilliant Blunders: How the Big Bang Beat Out the Steady State Universe

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 On March 28, 1949, at 6:30 in the evening, astrophysicist Fred Hoyle gave one of his authoritative radio lectures on
 
 The Third Programme
 
 , a cultural broadcast on the BBC’s that featured such intellectuals as philosopher Bertrand Russell and playwright Samuel Beckett. At one point, as he was trying to contrast his own scenario—one of continuous creation of matter in the universe—with the opposing theory, which claimed that the universe had a distinct and definite beginning, Hoyle made what was to become a controversial statement:
 
<blockquote>

 We now come to the question of applying the observational tests to earlier theories. These theories were based on the hypothesis that
 
 all the matter in the universe was created in one big bang at a particular time in the remote past
 

 [emphasis added]
 
 . It now turns out that in some respect or other all such theories are in conflict with the observational requirements.
 
</blockquote>

 This lecture marked the birth of the term “big bang,” which has since been inextricably attached to the initial event from which our universe sprouted. Contrary to popular belief, Hoyle did not use the term in a derogatory manner. Rather, he was simply attempting to create a mental picture for his listeners.
 

 Hoyle’s most enduring works were in the areas of nuclear astrophysics and stellar evolution. Yet most of those who remember him from his popular books and prominent radio programs know him as a cosmologist and co-originator of the idea of a steady state universe. (The steady state model predicted that galaxies that are billions of light-years away should look, statistically speaking, just like nearby galaxies, even though we see the former as they were billions of years ago because of the time it takes their light to reach us.)
 

 He started from the observational fact that the universe is expanding. This immediately raised a question: If galaxies are continuously rushing away from each other, does that mean that space is becoming more and more empty? Hoyle answered with a categorical no. Instead, he proposed, matter is continually being created throughout space so that new galaxies and clusters of galaxies are constantly being formed at a rate that compensates precisely for the dilution caused by the cosmic expansion. In this way, Hoyle reasoned, the universe is preserved in a steady state. He once commented wittily, “Things are the way they are because they were the way they were.”
 

 The idea of matter being continuously created out of nothing may appear crazy at first. However, as Hoyle was quick to point out, no one knew where matter had appeared from in the big bang cosmology, either. The only difference, he explained, was that in the big bang scenario all the matter was created in one explosive beginning, while in the steady state model matter has been created at a constant rate throughout an infinite time and is still being created at the same rate today. Hoyle contended that the concept of continuous creation of matter (when put in the context of a specific theory) was much more attractive than creation of the universe in the remote past, since the latter implied that observable effects had arisen from “causes unknown to science.”
 

 The big bang and steady state models made distinctly different predictions about the distant universe. When we observe galaxies that are billions of light-years away, we get a picture of those galaxies as they were billions of years ago. In a continuously evolving universe (the big bang model), this means that we observe that particular part of the universe when it was younger and therefore different. In the steady state model, on the other hand, the universe has always existed in the same state. Consequently, the remote parts of the universe are expected to have precisely the same appearance as the local cosmic environment.
 

 The first signs of trouble for the steady state model came not from optical telescopes but from radio astronomy. One of the pioneers in this endeavor was a physicist from the Cavendish Laboratory at Cambridge: Martin Ryle.
 

 Unlike Hoyle, whose father was a wool and textiles merchant, Ryle came from a privileged background—his father was physician to King George VI—and he had received the best of what private education could offer. After some pioneering radio observations of the Sun in the late 1940s, Ryle and his group embarked on an ambitious program to detect radio sources beyond the solar system. Following some impressive improvements to the observational techniques that allowed them to discard background radiation from the Milky Way, Ryle and his colleagues discovered several dozen “radio stars” distributed more or less isotropically across the sky. Unfortunately, since most of the sources did not have visible counterparts, there was no way to determine their distances precisely.
 

 Ryle began picking apart the steady state model by evaluating one of its testable predictions—that distant parts of the universe should look exactly the same as the local cosmic environment. He started to collect a large sample of radio sources, and to count how many of them there were at different intensity intervals. Since he had no way of knowing the actual distances to most sources (they were beyond the detection range of optical telescopes), Ryle made the simplest assumption: namely, that the observed weaker radio sources were, on average, more distant than the sources of the strong signals. He found that there were dramatically more weak sources than strong ones. In other words, it seemed that the density of sources at distances of billions of light-years (and therefore representing the universe billions of years ago) was much higher than the current density nearby. This was clearly at odds with a model of a never-changing universe, but it could be made consistent with a cosmos evolving from a big bang, if one assumed (correctly, as we now recognize) that galaxies were more prone to emit intense radio signals in their youth than at present, in their older age.
 

 By the early 1960s, Ryle’s group had at its disposal even an entirely new radio observatory, funded by the Mullard electronics company. By then, Ryle and Hoyle had become engaged in a series of intellectual skirmishes, culminating in one particularly unpleasant incident. Hoyle later described this traumatic experience in his autobiographical book
 
 Home Is Where the Wind Blows
 
 . It all started with what appeared to be an innocent phone call from the Mullard company in early 1961. The person at the other end of the line invited Hoyle and his wife to attend a press conference at which Ryle was expected to present new results that were supposed to be of great interest to Hoyle. When they arrived at the Mullard headquarters in London, Hoyle’s wife, Barbara, was escorted to a seat in the front now, while Hoyle was led to a chair on stage, facing the media. He had no doubt that the announcement would be related to the counting of radio sources according to their intensity, but he couldn’t believe that he would have been invited if the results were to contradict the steady state theory.
 

 Unfortunately, what Hoyle found utterly unthinkable did happen. When Ryle appeared, rather than making a brief announcement, as advertised, he launched into a technical, jargon-filled lecture on the results of his larger, fourth survey. He finished by claiming confidently that the results now showed unambiguously a higher density of radio sources in the past, therefore proving the steady state theory wrong. The shocked Hoyle was merely asked to comment on the results. Incredulous and humiliated, he barely mumbled a few sentences and rushed away from the event. The media frenzy that followed in the subsequent days disgusted Hoyle to the point that he avoided phone calls for a week and was absent even from the following Royal Astronomical Society meeting on February 10. Even Ryle realized that the press conference had crossed the border of common decency. He called Hoyle to apologize, adding that when he agreed to the Mullard event, he “had no idea how bad it would be.”
 

 On the purely scientific front, however, despite these disturbing failures in etiquette, Ryle’s arguments grew increasingly compelling, and by the mid-1960s, the vast majority of the astronomical community agreed that the proponents of the steady state theory had lost the battle.
 

 The discovery of extremely active galaxies, in which the accretion of mass onto central, supermassive black holes releases sufficient radiation to outshine the entire galaxy, cemented the evidence against a steady state universe. These objects, known as quasars, were luminous enough to be observed by optical telescopes. The observations allowed astronomers to use Hubble’s law to determine the distance to these sources, and to show convincingly that quasars were indeed more common in the past than at present. There was no escape from the conclusion that the universe was evolving and that it had been denser in the past. At that point, the floodgates opened, and the challenges to the steady state model kept pouring in.
 

 In spite of Hoyle’s valiant efforts, beginning in the mid-1960s most scientists stopped paying attention to the steady state theory. Hoyle’s continuing attempts to demonstrate that all the confrontations between the theory and emerging observations could be explained away looked increasingly contrived and implausible. Worse yet, he seemed to have lost that “fine judgment” that he had once advocated, which was supposed to distinguish him from “merely becoming a crackpot.” Even as late as the year 2000, at the age of 85, he published a book entitled
 
 A Different Approach to Cosmology: From a Static Universe Through the Big Bang Towards Reality
 
 , in which he and his collaborators, Jayant Narlikar and Geoff Burbidge, explained the details of the quasi–steady state theory and their objections to the big bang. To express their contemptuous opinion of the scientific establishment, they presented in one of the book’s pages a photograph of a flock of geese walking on a dirt road with the caption, “This is our view of the conformist approach to the standard (hot big bang) cosmology. We have resisted the temptation to name some of the leading geese.” Perhaps the best thing said about the book appeared in the review by Britain’s
 
 Sunday Telegraph
 
 , and it referred not so much to the contents of the book as to Hoyle’s fiery personality: “Hoyle systematically reviews the evidence for the Big Bang theory, and gives it a good kicking . . . it’s hard not to be impressed with the audacity of the demolition job . . . I can only hope that I possess one- thousandth of Hoyle’s fighting spirit when I, like him, have reached my 85th year.”
 

 Hoyle’s blunder was in his apparently pigheaded, almost infuriating refusal to acknowledge the theory’s demise even as it was being smothered by accumulating contradictory evidence, and in his use of asymmetrical criteria of judgment with respect to the big bang and steady state theories. What was it that caused this intransigent behavior?
 

 A few statements made by Hoyle himself provide the best evidence. In
 
 Home Is Where the Wind Blows
 
 , he wrote the following striking paragraph:
 
<blockquote>

 The problem with the scientific establishment goes back to the small hunting parties of prehistory. It must then have been the case that, for a hunt to be successful, the entire party was needed. With the direction of prey uncertain, as the direction of the correct theory in science is initially uncertain, the party had to make a decision about which way to go, and then they all had to stick to the decision, even if it was merely made at random. The dissident who argued that the correct direction was precisely opposite from the chosen direction had to be thrown out of the group, just as the scientist today who takes a view different from the consensus finds his papers rejected by journals and his applications for research grants summarily dismissed by state agencies. Life must have been hard in pre-history, for the more a hunting party found no prey in its chosen direction, the more it had to continue in that direction, for to stop and argue would be to create uncertainty and to risk differences of opinion breaking out, with the group then splitting disastrously apart. This is why the first priority among scientists is not to be correct but for everybody to think the same way. It is this perhaps instinctive primitive motivation that creates the establishment.
 
</blockquote>

 One can hardly imagine a stronger advocacy for dissent from mainstream science. Hoyle echoes here the words of the influential second-century physician Galen of Pergamum: “From my very youth I despised the opinion of the multitude and longed for truth and knowledge, believing that there was for man no possession more noble or divine.” However, as Martin Rees, Astronomer Royal for Britain, has pointed out, isolation has its price. Science progresses not in a straight line from A to B but in a zigzag path shaped by critical reevaluation and faultfinding interaction. The continuous evaluation provided by the scientific establishment that Hoyle so despised is what creates the checks and balances that keep scientists from straying too far in the wrong direction. By imposing upon himself academic isolation, Hoyle denied himself these corrective forces.
 

 I have noted several times that the idea of a steady state universe was brilliant at the time it was proposed. In retrospect, the steady state universe, with its continuous creation of matter, shares many features with currently fashionable models of an inflationary universe: the conjecture that the cosmos experienced a faster-than-light growth spurt when it was a fraction of a second old. In some respects, the steady state universe is simply a universe in which inflation always occurs.
 

 Hoyle’s brilliance was also revealed in the fact that he belonged to that small group of scientists capable of investigating two mutually inconsistent theories in parallel. In spite of continuing to hold out against the big bang for his entire life, Hoyle actually contributed important studies to big bang nucleosyntheses, in particular concerning the cosmic helium abundance and the synthesis of elements at very high temperatures. Hoyle’s theories, even when eventually proven wrong, were always dynamizing, and they unfailingly energized entire fields and catalyzed new ideas.
 


 From
 
<a href="http://www.amazon.com/Brilliant-Blunders-Einstein-Scientists-Understanding/dp/1469286041">
 Brilliant Blunders
 </a>

 by Mario Livio. Copyright ©2013 by
 <a href="http://mariolivio.com" target="_blank">
 Mario Livio
 </a>
 . Repreinted by permission of Simon &amp; Schuster, Inc.
 

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Math: Discovered, Invented, or Both?

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 “The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”
 


 Eugene Wigner wrote these words in his 1960 article “
 <a href="http://math.northwestern.edu/~theojf/FreshmanSeminar2014/Wigner1960.pdf">
 The Unreasonable Effectiveness of Mathematics in the Natural Sciences
 </a>
 .” The Nobel prize-winning physicist’s report still captures the uncanny ability of mathematics not only to describe and explain, but to predict phenomena in the physical world.
 
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 How is it possible that all the phenomena observed in classical electricity and magnetism can be explained by means of just four mathematical equations? Moreover, physicist James Clerk Maxwell (after whom those four equations of electromagnetism are named) showed in 1864 that the equations predicted that varying electric or magnetic fields should generate certain propagating waves. These waves—the familiar electromagnetic waves (which include light, radio waves, x-rays, etc.)—were eventually detected by the German physicist Heinrich Hertz in a series of experiments conducted in the late 1880s.
 

 And if that is not enough, the modern mathematical theory which describes how light and matter interact, known as quantum electrodynamics (QED), is even more astonishing. In 2010 a group of physicists at Harvard University determined the magnetic moment of the electron (which measures how strongly the electron interacts with a magnetic field) to a precision of less than one part in a trillion. Calculations of the electron’s magnetic moment based on QED reached about the same precision and the two results agree! What is it that gives mathematics such incredible power?
 

 The puzzle of the power of mathematics is in fact even more complex than the above examples from electromagnetism might suggest. There are actually two facets to the “unreasonable effectiveness,” one that I call
 
 active
 
 and another that I dub
 
 passive
 
 . The active facet refers to the fact that when scientists attempt to light their way through the labyrinth of natural phenomena, they use mathematics as their torch. In other words, at least some of the laws of nature are formulated in directly applicable mathematical terms. The mathematical entities, relations, and equations used in those laws were developed for a specific application. Newton, for instance, formulated the branch of mathematics known as calculus because he needed this tool for capturing motion and change, breaking them up into tiny frame-by-frame sequences. Similarly, string theorists today often develop the mathematical machinery they need.
 

 Passive effectiveness, on the other hand, refers to cases in which mathematicians developed abstract branches of mathematics with absolutely no applications in mind; yet decades, or sometimes centuries later, physicists discovered that those theories provided necessary mathematical underpinnings for physical phenomena. Examples of passive effectiveness abound. Mathematician Bernhard Riemann, for example, discussed in the 1850s new types of geometries that you would encounter on surfaces curved like a sphere or a saddle (instead of the flat plane geometry that we learn in school). Then, when Einstein formulated his theory of General Relativity (in 1915), Riemann’s geometries turned out to be precisely the tool he needed!
 

 At the core of this math mystery lies another argument that mathematicians, philosophers, and, most recently, cognitive scientists have had for a long time: Is math an invention of the human brain? Or does math exist in some abstract world, with humans merely discovering its truths? The debate about this question continues to rage today.
 

 Personally, I believe that by asking simply whether mathematics is discovered or invented, we forget the possibility that mathematics is an intricate combination of inventions
 
 and
 
 discoveries. Indeed, I posit that humans invent the mathematical concepts—numbers, shapes, sets, lines, and so on—by abstracting them from the world around them. They then go on to discover the complex connections among the concepts that they had invented; these are the so-called theorems of mathematics.
 

 I must admit that I do not know the full, compelling answer to the question of what is it that gives mathematics its stupendous powers. That remains a mystery.
 


 Go Deeper
 
 

 Editor’s picks for further reading
 



 NOVA:
 <a href="http://www.pbs.org/wgbh/nova/physics/great-math-mystery.html">
 The Great Math Mystery
 </a>
 
 Is math invented by humans, or is it the language of the universe? NOVA takes on this question in a new film premiering April 15, 2015 at 9pm on most PBS stations.
 

 NOVA:
 <a href="http://www.pbs.org/wgbh/nova/physics/describing-nature-math.html">
 Describing Nature with Math
 </a>
 
 How do scientists use mathematics to define reality? And why? Peter Tyson investigates two millennia of mathematical discovery.
 

 The Washington Post:
 <a href="http://www.washingtonpost.com/wp-dyn/content/article/2009/02/05/AR2009020502876.html">
 The Structure of Everything
 </a>
 
 Learn more about the “unreasonable effectiveness of mathematics” in this review of Mario Livio’s book “Is God a Mathematician?”
 
</section>

Mario Livio explores math’s uncanny ability to describe, explain, and predict phenomena in the physical world.

Mario Livio

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Astrophysicist Mario Livio on the "Brilliant Blunders" That Changed Our Understanding of the Universe

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Math: Discovered, Invented, or Both?

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