Soon after the Great Earthquake struck San Francisco on the morning of April 18, 1906, with fierce fires active or imminent across the city, Eric Temple Bell, then 23, sought to protect his treasured copy of Théorie des Nombres by Édouard Lucas by burying it in the yard of the boarding house in which he had been living. When he dug it up a few days later he found the volume unusable for further study, but he kept it as a memento of that vividly recalled period of his life.
Bell would use his experiences of 1906 as part of his science fiction novel The Time Stream, serialized in 1931, by which time he was a professor of mathematics at the California Institute of Technology, in Pasadena. He would also retain his interest in Lucas, championing the French mathematician’s work and publishing his own research papers inspired by it. The charred copy of Théorie des Nombres has been preserved in the Caltech archives since Bell’s death in 1960.
Although Bell became prolific in both research mathematics and science fiction, it was a third literary genre, not foreshadowed in the 1906 quake, in which he would make his most substantial mark: popularization of mathematics. He ranked the accomplishments of past mathematicians and set standards of aspiration for mathematicians of the future. He effectively defined the contours of the mathematics profession for several generations of mathematicians and non-mathematicians alike. To the exasperation of professional historians, Bell seduced many readers into ignoring blatant falsehoods and bigoted remarks.
With a consistently lively prose style (his fiction writing pales in comparison) and a genius for expounding vivid anecdotes (supported by evidence or not), Bell romped with gusto through the decades and centuries, dispensing caustic commentary. In 1993 he became the subject of a biography himself, by another major mathematics popularizer, Constance Reid, who revealed aspects of Bell’s early life that he had kept hidden even from his wife and only child.
Mathematics has been recognized as an esoteric subject since ancient times, with a few individuals evidently knowing far more, and caring far more, than the majority. Only with the rise of mass education did this imbalance come to be perceived as both a problem and an opportunity. The first half of the 20th century saw a notable flourishing of attempts to make mathematical knowledge more accessible to a wider public, with books and articles emerging with regularity. In the United States in particular, rising levels of education made people more capable of reading such works, at the same time making them realize more fully how far above them the mathematicians were flying.
A special impetus was provided by the work of physicist Albert Einstein. In 1919 his general theory of relativity was dramatically confirmed by the observations conducted during a total solar eclipse, setting off massive publicity throughout the world. The combination of Einstein’s charming personality, frizzy hair, and audacious ideas about space, time, and gravitation fascinated the general public. He was also widely admired (outside his native Germany) for his resolute resistance to the jingoism that had infected so many, including scientists, during the Great War of 1914–18. And the public perceived, vaguely but correctly, that Einstein’s achievement owed something important to mathematics, thus helping to fuel a demand for popular accounts of the subject beyond school books.
The first half of the 20th century saw a notable flourishing of attempts to make mathematical knowledge more accessible to a wider public, with books and articles emerging with regularity.
The professionals were fascinated by Einstein’s work as well. He had sought an appropriate framework for his innovative physical ideas, a flexible language in which to describe with precision the complex interaction of time, space, and matter. He found the tools he needed in 19th-century mathematics, specifically the non-Euclidean geometry of the German mathematician Bernhard Riemann and the tensor calculus of the Italians Gregorio Ricci and Tullio Levi-Civita. Many mathematicians were inspired to explore and further elaborate these fields. Bell remarked in 1922 that had he been 15 years younger he would have devoted himself to the mathematics of general relativity, but he was too committed to the theory of numbers, in which he had built up considerable specialized knowledge of no relevance to physics. Bell contented himself with teaching an occasional course on relativity and providing overviews of the theory in his popular mathematics writings.
His first such effort came early during the Einstein craze, in July 1920, when Scientific American magazine announced a contest to explain general relativity in no more than 3,000 nontechnical words. Bell, then a professor at the University of Washington, was among the 300 contestants who submitted an essay. He did not win the $5,000 prize, but his was one of only 13 essays that were printed in their entirety in the book resulting from the contest. This was Bell’s first effort at transmuting technical details into popular form, although it did not display much of the lively language that would become his trademark. He would go on to write nearly a dozen books explaining science and mathematics to the lay public, the last one finished just as he was dying in 1960.
Bell had been born in Scotland in 1883 and emigrated in 1902 to California, where he obtained a bachelor’s degree in mathematics from Stanford University in just two years. When the earthquake struck in 1906, Bell was teaching at a preparatory school in San Francisco. What biographer Reid discovered was that Bell’s connection to Northern California was of longer standing than he pretended. He had in fact come over from Scotland with his family when he was only 15 months old, living 12 years in San Jose. Bell was also secretive about his father’s occupational history, which included the fish trade in Scotland and fruit growing in California. In neither place was the senior Bell blazingly successful, but there was enough money in the family that when he died in 1896 his son was able to return to England for private secondary schooling. Bell testified later that he was made into a mathematician by the influence of a teacher at the Bedford Modern School. Comparably rigorous schools would have been rare in California at the time.
After his stint in San Francisco, Bell would earn a master’s degree from the University of Washington in 1908 and a PhD from New York City’s Columbia University in 1912. He returned to the University of Washington as a professor from 1912 to 1926, before moving to a professorship at Caltech, where he remained to the end of his career. In moving among Caltech, Columbia, Stanford, and Washington, Bell received an excellent overview of the variety within the burgeoning American university system of the early twentieth century, and of the place of mathematics within this system.
Stanford, like the University of Chicago and Johns Hopkins University, was a post–Civil War private university, based on a great industrial fortune. It was only 10 years old when Bell attended, and was being buffeted by the intrusive meddling of the founder’s widow, but it possessed a small core of stimulating mathematical scholars who inspired Bell. The University of Washington, a state university with origins in the region’s territorial past, featured a Seattle campus situated amid great scenic beauty. It made few claims to academic distinction in Bell’s day, but the head of the mathematics-astronomy department, R. E. Moritz, was building a fine mathematics library, much utilized by Bell. Moreover, Moritz was fascinated by mathematical history, culture, and gossip, as Bell would be fascinated in turn. Columbia was a venerable institution, founded when New York was still a colony of Great Britain.
By the time Bell was a graduate student, its gradual transformation into a modern research university was well launched. In its mathematics department Bell encountered professors whose interests would mark his later career: history (David Eugene Smith), research in number theory (Frank N. Cole), and expository writing about mathematics (Cassius J. Keyser). Finally, Bell joined the California Institute of Technology just as it was rapidly metamorphosing from its previous incarnation as a minor technical school. Under the presidency of physicist Robert Millikan (Nobel laureate, 1923) the former Throop Polytechnic Institute was becoming one of the leading centers of scientific research in the United States. Bell would here come in contact with students, professors, and guest speakers of the highest rank.
A college education was still a rare achievement for Americans in the 1920s and 1930s, but the old centers of learning on the East Coast no longer held a monopoly. The basis was being laid for a nationwide system of higher education, with varying levels of emphasis on teaching and research. In the second half of the twentieth century the PhD would become a prerequisite for almost all professors at universities and four-year colleges, even those claiming primarily a teaching mission. In Bell’s day earning a PhD was less typical, and his research productivity at the University of Washington, with a heavy teaching load, was extraordinary.
Both reviewers lauded Bell’s ability to describe a range of mathematical ideas in concise, understandable language. One attributed the attractiveness of Bell’s mathematical descriptions to his practice as a novelist.
As foreshadowed by the book Bell buried at the time of the San Francisco earthquake, his mathematical research was primarily in the area known as number theory, sometimes referred to as higher arithmetic. Mathematical research by the end of the 19th century was becoming organized into three main specialties: geometry, algebra, and analysis. The first two were vast generalizations of the school subjects going by those names, while the third area designated the elaboration of the differential and integral calculus pioneered in the 17th century. Number theory, focused on the properties of the ordinary counting numbers (1, 2, 3, . . . ), could profitably be pursued with tools from all three of the above branches but was sometimes considered a branch of mathematics unto itself.
Carl Friedrich Gauss, one of the giants of 19th-century mathematics, had famously been quoted as dubbing mathematics the “queen of the sciences” and number theory the “queen of mathematics.” This was a formulation that Bell highly approved of and invoked often. Bell’s first full-length popular mathematics book was The Queen of the Sciences, published in 1931 in conjunction with the Chicago’s Century of Progress Exposition, the World’s Fair of that year. Chapter VII of Bell’s book was on number theory and titled “The Queen of Mathematics.”
Queen of the Sciences surprised its publisher with its popularity among the general public. The mathematical professionals likewise gave it a warm reception; popular mathematics serves not only to entice those outside the field, but also to boost the morale of those already inside. The reviewer in the American Mathematical Monthly, official journal of the Mathematical Association of America, admitted to being “frankly enthusiastic” and professed a desire “to recommend the book to everybody. . . .The apprentice in the guild of mathematicians will be inspired. The university lecturer will put the book down feeling that he has reaffirmed his faith.” The reviewer in the Mathematics Teacher, the official journal of the National Council of Teachers of Mathematics, opined that the book “should be read by every high school teacher.”
Both reviewers lauded Bell’s ability to describe a wide range of mathematical ideas in concise, understandable language. Both reviewers also noted Bell’s other career as a novelist; the true identity of “John Taine,” the pseudonym under which Bell published most of his fiction, had recently been revealed. The Mathematics Teacher reviewer attributed the attractiveness of Bell’s mathematical descriptions to his practice as a novelist.
Encouraged by this response, Bell began to devote a substantial part of his literary efforts to nonfiction. His next such book, published in 1933, was Numerology. This was an eccentric survey of humanity’s tendency to attach mystical significance to striking numerical facts, from the ancient Babylonians, through medieval theologians, to contemporary scientists. Bell meandered from anecdotes about Hollywood (as a professor in nearby Pasadena, he claimed special knowledge) to chitchat about distinguished thinkers, from Plato to Einstein. The whole mishmash, including quick forays into subtle properties of numbers and seemingly serious commentary on the surprising utility of mathematics, was bathed in Bell’s uninhibited style, disdainful of nonsense and flimflam.
In 1934 Bell produced another quirky book, The Search for Truth. It explored the subject of its ambitious title through a mixture of personal recollection (he describes an encounter with philosopher William James in San Francisco only days before the 1906 earthquake) and eclectic displays of erudition, not confined to science and mathematics. The biting comments of an unidentified personage named “Toby” are frequently quoted. Friends recognized Toby as the nickname of Bell’s wife.
Bell tosses off value judgments with flamboyant confidence. Throughout his book, mathematics is depicted as a supremely creative but human endeavor.
Bell next returned to a more sober product, The Handmaiden of the Sciences, which he cast as a companion to his earlier Queen of the Sciences. In the earlier book he had emphasized how mathematical concepts could be developed purely out of intellectual curiosity, irrespective of practical applications, while noting that some apparently useless notions had proved remarkably fruitful for the sciences. In the new book Bell reversed the emphasis, underlining the manifold ways in which mathematics had been explicitly developed as a tool of science, physics especially.
Handmaiden of the Sciences, as with Bell’s earlier nonfiction, was published by the Baltimore firm of Williams and Wilkins. But even as he was working on that manuscript, he had landed a contract for a more ambitious book with the New York publisher Simon and Schuster. Both books would be published in 1937, with the Simon and Schuster volume becoming by far Bell’s most popular title: Men of Mathematics.
Men of Mathematics consists of an introduction and 28 biographical essays treating 33 individual mathematicians and one family of mathematicians (the Bernoullis). One chapter is devoted to three ancient Greeks. The 19th-century Russian Sonya Kovalevsky, the first woman to earn a doctoral degree in mathematics, shares a chapter with her German mentor, Karl Weierstrass. All the other chapters are focused on male European mathematicians who flourished between the 17th century and the early 20th century.
Amid deftly sketched mathematical ideas, Bell delights in colorful anecdotes and amusing foibles: “[Leibniz] was forever disentangling the genealogies of the semi-royal bastards whose descendants paid his generous wages, and proving with his unexcelled knowledge of the law their legitimate claims to the duchies into which their careless ancestors had neglected to fornicate them.” He tosses off value judgments with flamboyant confidence. Throughout, mathematics is depicted as a supremely creative but human endeavor. As one reader remarked in 1945, “Since the appearance of Eric Temple Bell’s Men of Mathematics, mathematicians have shown less fear of the idea of being counted as ‘real persons.'”
Excerpted from Republic of Numbers: Unexpected Stories of Mathematical Americans through History by David Lindsay Roberts. Copyright © David Lindsay Roberts 2019. Reprinted with permission from John Hopkins University Press.