A Beautiful Mind Part 2

... a quaint ceremonious village. - ALBERT E EINSTEIN ... the mathematical center of the universe. - HARALD B BOHR NASH ARRIVED in Princeton, New Jersey, on Labor Day 1948, the opening day of Truman's re-election campaign. in Princeton, New Jersey, on Labor Day 1948, the opening day of Truman's re-election campaign.1 He was twenty years old. He came by train, directly from Bluefield, via Was.h.i.+ngton, D.C., and Philadelphia, wearing a new suit and carrying unwieldy suitcases stuffed with bedding and clothes, letters and notes, and a few books. Impatient and eager now, he got off at Princeton Junction, a nondescript little middle-cla.s.s enclave a few miles from Princeton proper, and hurried onto the d.i.n.ky, the small single-track train that shuttles back and forth to the university. He was twenty years old. He came by train, directly from Bluefield, via Was.h.i.+ngton, D.C., and Philadelphia, wearing a new suit and carrying unwieldy suitcases stuffed with bedding and clothes, letters and notes, and a few books. Impatient and eager now, he got off at Princeton Junction, a nondescript little middle-cla.s.s enclave a few miles from Princeton proper, and hurried onto the d.i.n.ky, the small single-track train that shuttles back and forth to the university.

What he saw was a genteel, prerevolutionary village surrounded by gently rolling woodlands, lazy streams, and a patchwork of cornfields.2 Settled by Quakers toward the end of the seventeenth century, Princeton was the site of a famous Was.h.i.+ngton victory over the British and, for a brief six-month interlude in 1783, the de facto capital of the new republic. With its college-Gothic buildings nestled among lordly trees, stone churches, and dignified old houses, the town looked every inch the wealthy, manicured exurb of New York and Philadelphia that, in fact, it was. Na.s.sau Street, the town's sleepy main drag, featured a row of "better" men's clothing shops, a couple of taverns, a drugstore, and a bank. It had been paved before the war, but bicycles and pedestrians still accounted for most of the traffic. In Settled by Quakers toward the end of the seventeenth century, Princeton was the site of a famous Was.h.i.+ngton victory over the British and, for a brief six-month interlude in 1783, the de facto capital of the new republic. With its college-Gothic buildings nestled among lordly trees, stone churches, and dignified old houses, the town looked every inch the wealthy, manicured exurb of New York and Philadelphia that, in fact, it was. Na.s.sau Street, the town's sleepy main drag, featured a row of "better" men's clothing shops, a couple of taverns, a drugstore, and a bank. It had been paved before the war, but bicycles and pedestrians still accounted for most of the traffic. In This Side of Paradise, This Side of Paradise, F. Scott Fitzgerald had described Princeton circa World War I as "the pleasantest country club in America." F. Scott Fitzgerald had described Princeton circa World War I as "the pleasantest country club in America."3 Einstein called it "a quaint, ceremonious village" in the 1930s. Einstein called it "a quaint, ceremonious village" in the 1930s.4 Depression and wars had scarcely changed the place. May Veblen, the wife of a wealthy Princeton mathematician, Oswald Veblen, could still identify by name every single family, white and black, well-to-do and of modest means, in every single house in town. Depression and wars had scarcely changed the place. May Veblen, the wife of a wealthy Princeton mathematician, Oswald Veblen, could still identify by name every single family, white and black, well-to-do and of modest means, in every single house in town.5 Newcomers invariably felt intimidated by its gentility. One mathematician from the West recalled, "I always felt like my fly was open." Newcomers invariably felt intimidated by its gentility. One mathematician from the West recalled, "I always felt like my fly was open."6 Even the university's mathematics building conjured up images of exclusivity and wealth. "Fine Hall is, I believe, the most luxurious building ever devoted to mathematics," one European emigre wrote enviously.7 It was a gabled, Neo-Gothic red brick and slate fortress, built in a style reminiscent of the College de France in Paris and Oxford University. Its cornerstone contains a lead box with copies of works by Princeton mathematicians and the tools of the trade - two pencils, one piece of chalk, and, of course, an eraser. Designed by Oswald Veblen, a nephew of the great sociologist Thorstein Veblen, it was meant to be a sanctuary that mathematicians would be "loath to leave." It was a gabled, Neo-Gothic red brick and slate fortress, built in a style reminiscent of the College de France in Paris and Oxford University. Its cornerstone contains a lead box with copies of works by Princeton mathematicians and the tools of the trade - two pencils, one piece of chalk, and, of course, an eraser. Designed by Oswald Veblen, a nephew of the great sociologist Thorstein Veblen, it was meant to be a sanctuary that mathematicians would be "loath to leave."8 The dim stone corridors that circled the structure were perfect for both solitary pacing and mathematical socializing. The nine "studies" - not offices!- for senior professors had carved paneling, hidden file cabinets, blackboards that opened like altars, oriental carpets, and ma.s.sive, overstuffed furniture. In a gesture to the urgency of the rapidly advancing mathematical enterprise each office was equipped with a telephone and each lavatory with a reading light. Its well-stocked third-floor library, the richest collection of mathematical journals and books in the world, was open twenty-four hours a day. Mathematicians with a fondness for tennis (the courts were nearby) didn't have to go home before returning to their offices - there was a locker room with showers. When its doors opened in 1921, an undergraduate poet called it "a country club for math, where you could take a bath." The dim stone corridors that circled the structure were perfect for both solitary pacing and mathematical socializing. The nine "studies" - not offices!- for senior professors had carved paneling, hidden file cabinets, blackboards that opened like altars, oriental carpets, and ma.s.sive, overstuffed furniture. In a gesture to the urgency of the rapidly advancing mathematical enterprise each office was equipped with a telephone and each lavatory with a reading light. Its well-stocked third-floor library, the richest collection of mathematical journals and books in the world, was open twenty-four hours a day. Mathematicians with a fondness for tennis (the courts were nearby) didn't have to go home before returning to their offices - there was a locker room with showers. When its doors opened in 1921, an undergraduate poet called it "a country club for math, where you could take a bath."

Princeton in 1948 was to mathematicians what Paris once was to painters and novelists, Vienna to psychoa.n.a.lysts and architects, and ancient Athens to philosophers and playwrights. Harald Bohr, brother of Niels Bohr, the physicist, had declared it "the mathematical center of the universe" in 1936.9 When the deans of mathematics held their first worldwide meeting after World War II, it was in Princeton. When the deans of mathematics held their first worldwide meeting after World War II, it was in Princeton.10 Fine Hall housed the world's most compet.i.tive, up-to-the-minute mathematics department. Next door - connected, in fact - was the nation's leading physics department, whose members, including Eugene Wigner, had driven off to Illinois, California, and New Mexico during the war, lugging bits of laboratory equipment, to help build the atomic bomb. Fine Hall housed the world's most compet.i.tive, up-to-the-minute mathematics department. Next door - connected, in fact - was the nation's leading physics department, whose members, including Eugene Wigner, had driven off to Illinois, California, and New Mexico during the war, lugging bits of laboratory equipment, to help build the atomic bomb.11 A mile or so away, on what had been Olden Farm, was the Inst.i.tute for Advanced Study, the modern equivalent of Plato's Academy, where Einstein, G.o.del, Oppenheimer, and von Neumann scribbled on their blackboards and held their learned discourses. A mile or so away, on what had been Olden Farm, was the Inst.i.tute for Advanced Study, the modern equivalent of Plato's Academy, where Einstein, G.o.del, Oppenheimer, and von Neumann scribbled on their blackboards and held their learned discourses.12 Visitors and students from the four corners of the world streamed to this polyglot mathematical oasis, fifty miles south of New York. What was proposed in a Princeton seminar one week was sure to be debated in Paris and Berkeley the week after, and in Moscow and Tokyo the week after that. Visitors and students from the four corners of the world streamed to this polyglot mathematical oasis, fifty miles south of New York. What was proposed in a Princeton seminar one week was sure to be debated in Paris and Berkeley the week after, and in Moscow and Tokyo the week after that.

"It is difficult to learn anything about America in Princeton," wrote Einstein's a.s.sistant Leopold Infeld in his memoirs, "much more so than to learn about England in Cambridge. In Fine Hall English is spoken with so many different accents that the resultant mixture is termed Fine Hall English... . The air is full of mathematical ideas and formulae. You have only to stretch out your hand, close it quickly and you feel that you have caught mathematical air and that a few formulae are stuck to your palm. If one wants to see a famous mathematician one does not need to go to him; it is enough to sit quietly in Princeton, and sooner or later he must come to Fine Hall." formulae are stuck to your palm. If one wants to see a famous mathematician one does not need to go to him; it is enough to sit quietly in Princeton, and sooner or later he must come to Fine Hall."13 Princeton's unique position in the world of mathematics had been achieved practically overnight, barely a dozen years earlier.14 The university predated the Republic by a good twenty years. It started out as the College of New Jersey in 1746, founded by Presbyterians. It didn't become Princeton until 1896 and wasn't headed by a layman until 1903 when Woodrow Wilson became its president. Even then, however, Princeton was a university in name only -"a poor place," "an overgrown prep school," particularly when it came to the sciences. The university predated the Republic by a good twenty years. It started out as the College of New Jersey in 1746, founded by Presbyterians. It didn't become Princeton until 1896 and wasn't headed by a layman until 1903 when Woodrow Wilson became its president. Even then, however, Princeton was a university in name only -"a poor place," "an overgrown prep school," particularly when it came to the sciences.15 In this regard, Princeton merely resembled the rest of the nation, which "admired Yankee ingenuity but saw little use for pure mathematics," as one historian put it. Whereas Europe had three dozen chaired professors who did little except create new mathematics, America had none. Young Americans had to travel to Europe to get training beyond the B.A. The typical American mathematician taught fifteen to twenty hours a week of what amounted to high school mathematics to undergraduates, struggling along on a negligible salary and with very little incentive or opportunity to do research. Forced to drill conic sections into the heads of bored undergraduates, the Princeton professor of mathematics was perhaps not as well off as his forebears of the seventeenth century who practiced law (Fermat), ministered to royalty (Descartes), or occupied professors.h.i.+ps with negligible teaching duties (Newton). When Solomon Lefschetz arrived at Princeton in 1924, "There were only seven men there engaged in mathematical research," Lefschetz recalled. "In the beginning we had no quarters. Everyone worked at home." In this regard, Princeton merely resembled the rest of the nation, which "admired Yankee ingenuity but saw little use for pure mathematics," as one historian put it. Whereas Europe had three dozen chaired professors who did little except create new mathematics, America had none. Young Americans had to travel to Europe to get training beyond the B.A. The typical American mathematician taught fifteen to twenty hours a week of what amounted to high school mathematics to undergraduates, struggling along on a negligible salary and with very little incentive or opportunity to do research. Forced to drill conic sections into the heads of bored undergraduates, the Princeton professor of mathematics was perhaps not as well off as his forebears of the seventeenth century who practiced law (Fermat), ministered to royalty (Descartes), or occupied professors.h.i.+ps with negligible teaching duties (Newton). When Solomon Lefschetz arrived at Princeton in 1924, "There were only seven men there engaged in mathematical research," Lefschetz recalled. "In the beginning we had no quarters. Everyone worked at home."16 Princeton's physicists were in the same boat, still living in the age of Thomas Edison and Alexander Graham Bell, preoccupied with measuring electricity and supervising endless freshman lab sections. Princeton's physicists were in the same boat, still living in the age of Thomas Edison and Alexander Graham Bell, preoccupied with measuring electricity and supervising endless freshman lab sections.17 Henry Norris Russell, a distinguished astronomer by the 1920s, fell afoul of the Princeton administration for spending too much time on his own research at the expense of undergraduate teaching. In its disdain for scientific research, Princeton was not very different from Yale or Harvard. Yale refused for seven years to pay a salary to the physicist Willard Gibbs, already famous in Europe, on the grounds that his studies were "irrelevant." Henry Norris Russell, a distinguished astronomer by the 1920s, fell afoul of the Princeton administration for spending too much time on his own research at the expense of undergraduate teaching. In its disdain for scientific research, Princeton was not very different from Yale or Harvard. Yale refused for seven years to pay a salary to the physicist Willard Gibbs, already famous in Europe, on the grounds that his studies were "irrelevant."18 While mathematics and physics at Princeton and other American universities were languis.h.i.+ng, a revolution in mathematics and physics was taking place three thousand miles away in such intellectual centers as Gottingen, Berlin, Budapest, Vienna, Paris, and Rome.

John D. Davies, a historian of science, writes of a dramatic revolution in the understanding of the very nature of matter: The absolute world of cla.s.sical Newtonian physics was breaking down and intellectual ferment was everywhere. Then in 1905 an unknown theoretician in the Berne patent office, Albert Einstein, published four epoch-making papers comparable to Newton's instant leap into fame. The most significant was the so-called Special Theory of Relativity, which proposed that ma.s.s was simply congealed energy, energy liberated matter: s.p.a.ce and time, previously thought to be absolute, were dependent on relative motion. Ten years later he formulated the General Theory of Relativity, proposing that gravity was a function of matter itself and affected light exactly as it affected material particles. Light, in other words, did not go "straight"; Newton's laws were not the real universe but one seen through the unreal spectacles of gravity. Furthermore, he set forth a set of mathematical laws with which the universe could be described, structural laws and laws of motion. papers comparable to Newton's instant leap into fame. The most significant was the so-called Special Theory of Relativity, which proposed that ma.s.s was simply congealed energy, energy liberated matter: s.p.a.ce and time, previously thought to be absolute, were dependent on relative motion. Ten years later he formulated the General Theory of Relativity, proposing that gravity was a function of matter itself and affected light exactly as it affected material particles. Light, in other words, did not go "straight"; Newton's laws were not the real universe but one seen through the unreal spectacles of gravity. Furthermore, he set forth a set of mathematical laws with which the universe could be described, structural laws and laws of motion.19

At around the same time, at the University of Gottingen, a German mathematical genius, David Hilbert, had unleashed a revolution in mathematics. Hilbert set out a famous program in 1900 of which the goal was nothing less than the "axiomatization of all of mathematics so that it could be mechanized and solved in a routine manner." Gottingen became the center of a drive to put existing mathematics on a more secure foundation: "The Hilbert program emerged at the turn of the century as a response to a perceived crisis in mathematics," writes historian Robert Leonard. "The effect was to drive mathematicians to 'clean up' Cantorian set theory, to establish it on a firm axiomatic basis, on the foundation of a limited number of postulates... . This marked an important s.h.i.+ft in emphasis towards abstraction in mathematics."20 Mathematics moved further and further away from "intuitive content - in this case, our daily world of surfaces and straight lines - towards a situation in which mathematical terms were leached of their direct empirical content and simply defined axiomatically within the context of the theory. The era of formalism had arrived." Mathematics moved further and further away from "intuitive content - in this case, our daily world of surfaces and straight lines - towards a situation in which mathematical terms were leached of their direct empirical content and simply defined axiomatically within the context of the theory. The era of formalism had arrived."

The work of Hilbert and his disciples - among them such future Princeton stars of the 1930s* and 1940s as Hermann Weyl and John von Neumann - also triggered a powerful impulse to apply mathematics to problems. .h.i.therto considered unamenable to highly formal treatment. Hilbert and others were quite successful in extending the axiomatic approach to a range of topics, the most obvious being physics, in particular the "new physics" of "quantum mechanics," but also to logic and the new theory of games.

But for the first twenty-five years of the century, as Davies writes, Princeton, and indeed the whole American academic community, "stood outside this dramatically swift development."21 The catalyst for Princeton's transformation into a world capital of mathematics and theoretical physics was an accident - an accident of friends.h.i.+p. Woodrow Wilson, like most other educated Americans of his time, despised mathematics, complaining that "the natural man inevitably rebels against mathematics, a mild form of torture that could only be learned by painful processes of drill." The catalyst for Princeton's transformation into a world capital of mathematics and theoretical physics was an accident - an accident of friends.h.i.+p. Woodrow Wilson, like most other educated Americans of his time, despised mathematics, complaining that "the natural man inevitably rebels against mathematics, a mild form of torture that could only be learned by painful processes of drill."22 And mathematics played no role whatever in his vision of Princeton as a real university with a graduate college and a system of instruction that emphasized seminars and discussions instead of drills and rote learning. But Wilson's best friend, Henry Burchard Fine, happened to be a mathematician. When Wilson set And mathematics played no role whatever in his vision of Princeton as a real university with a graduate college and a system of instruction that emphasized seminars and discussions instead of drills and rote learning. But Wilson's best friend, Henry Burchard Fine, happened to be a mathematician. When Wilson set about hiring literature and history scholars as preceptors. Fine asked him, "Why not a few scientists?" As a gesture of friends.h.i.+p more than anything else, Wilson said yes. After Wilson left the presidency of Princeton for the White House in 1912, Fine became dean of science and proceeded to recruit some top-notch scientists, among them mathematicians G. D. Birkhoff, Oswald Veblen, and Luthor Eisenhart, to teach graduate students. They were known around Princeton as "Fine's research men." The undergraduates, not a single one of whom majored in physics or math, complained bitterly of "brilliant but unintelligible lecturers with foreign accents" and "the European, or demi-G.o.d, theory of instruction." about hiring literature and history scholars as preceptors. Fine asked him, "Why not a few scientists?" As a gesture of friends.h.i.+p more than anything else, Wilson said yes. After Wilson left the presidency of Princeton for the White House in 1912, Fine became dean of science and proceeded to recruit some top-notch scientists, among them mathematicians G. D. Birkhoff, Oswald Veblen, and Luthor Eisenhart, to teach graduate students. They were known around Princeton as "Fine's research men." The undergraduates, not a single one of whom majored in physics or math, complained bitterly of "brilliant but unintelligible lecturers with foreign accents" and "the European, or demi-G.o.d, theory of instruction."

Fine's nucleus of researchers might well have scattered after the dean's premature death in 1928 in a cycling accident on Na.s.sau Street had it not been for several dramatic instances of private philanthropy that turned Princeton into a magnet for the world's biggest mathematical stars. Most people think that America's rise to scientific prominence was a by-product of World War II. But in fact the fortunes acc.u.mulated between the gilded eighties and the roaring twenties paved the way.

The Rockefellers made their millions in coal, oil, steel, railroads, and banking - in other words, from the great sweep of industrialization that transformed towns like Bluefield and Pittsburgh in the late nineteenth and early twentieth centuries. When the family and its representatives started to give away some of the money, they were animated by dissatisfaction with the state of higher education in America and a firm belief that "nations that do not cultivate the sciences cannot hold their own."23 Aware of the scientific revolution sweeping Europe, the Rockefeller Foundation and its offshoots started by sending American graduate students, including Robert Oppenheimer, abroad. By the mid-1920s, the Rockefeller Foundation decided that "instead of sending Mahomet to the Mountain, it would fetch the Mountain here." That is, it decided to import Europeans. To finance the effort, the foundation committed not just its income but $19 million of its capital (close to $150 million in today's dollars). While Wickliffe Rose, a philosopher on Rockefeller's board, scoured such European scientific capitals as Berlin and Budapest to hear about new ideas and meet their authors, the foundation selected three American universities, among them Princeton, to receive the bulk of its largesse. The grants enabled Princeton to establish five European-style research professors.h.i.+ps with extravagant salaries, plus a research fund to support graduate and postgraduate students. Aware of the scientific revolution sweeping Europe, the Rockefeller Foundation and its offshoots started by sending American graduate students, including Robert Oppenheimer, abroad. By the mid-1920s, the Rockefeller Foundation decided that "instead of sending Mahomet to the Mountain, it would fetch the Mountain here." That is, it decided to import Europeans. To finance the effort, the foundation committed not just its income but $19 million of its capital (close to $150 million in today's dollars). While Wickliffe Rose, a philosopher on Rockefeller's board, scoured such European scientific capitals as Berlin and Budapest to hear about new ideas and meet their authors, the foundation selected three American universities, among them Princeton, to receive the bulk of its largesse. The grants enabled Princeton to establish five European-style research professors.h.i.+ps with extravagant salaries, plus a research fund to support graduate and postgraduate students.

Among the first European stars to arrive in Princeton in 1930 were two young geniuses of Hungarian origin, John von Neumann, a brilliant student of Hilbert and Hermann Weyl, and Eugene Wigner, the physicist who went on to win a n.o.bel Prize in physics in 1963, not for his vital work on the atom bomb but for research on the structure of the atom and its nucleus. The two shared one of the professors.h.i.+ps endowed by the Rockefeller Foundation, spending half a year in Princeton and the other half in their home universities of Berlin and Budapest. According to Wigner's autobiography, the men were unhappy at first, homesick for Europe's pa.s.sionate theoretical discussion and its coffeehouses - the congenial floating seminars of professors and students where the latest research was discussed. Wigner wondered if they were part of the window dressing, like the faux-Gothic buildings. But von Neumann, an enthusiastic admirer of all things American, adapted more quickly. floating seminars of professors and students where the latest research was discussed. Wigner wondered if they were part of the window dressing, like the faux-Gothic buildings. But von Neumann, an enthusiastic admirer of all things American, adapted more quickly.24 With shrinking opportunities for research in Europe during the Depression, and mounting restrictions on Jews in German universities, they stayed. With shrinking opportunities for research in Europe during the Depression, and mounting restrictions on Jews in German universities, they stayed.

A second act of philanthropy, more serendipitous than the Rockefeller enterprise, resulted in the creation of the independent Inst.i.tute for Advanced Study in Princeton.25 The Bambergers were department store merchants who opened their first store in Newark and who had gone on to make a huge fortune in the dry-goods business. The owners, a brother and sister, sold out six weeks before the stock market crash of 1929. With a fortune of $25 million between them, they decided to show their grat.i.tude to the state of New Jersey. They had in mind perhaps founding a dental school. An expert on medical education, Abraham Flexner, soon convinced them to drop the idea of a medical school and instead to found a first-rate research inst.i.tution with no teachers, no students, no cla.s.ses, but only researchers protected from the vicissitudes and pressures of the outside world. Flexner toyed with the idea of making a school of economics the core of the inst.i.tute but was soon persuaded that mathematics was a sounder choice since it was more "fundamental." Furthermore, there was infinitely greater consensus among mathematicians on who the best people were. Its location was still up in the air. Newark, with its paint factories and slaughterhouses, offered no attractions for the international band of academic superstars Flexner hoped to recruit. Princeton was more like it. Legend has it that it was Oswald Veblen who convinced the Bambergers that Princeton really could be thought of ("in a topological sense," as he put it) as a suburb of Newark. The Bambergers were department store merchants who opened their first store in Newark and who had gone on to make a huge fortune in the dry-goods business. The owners, a brother and sister, sold out six weeks before the stock market crash of 1929. With a fortune of $25 million between them, they decided to show their grat.i.tude to the state of New Jersey. They had in mind perhaps founding a dental school. An expert on medical education, Abraham Flexner, soon convinced them to drop the idea of a medical school and instead to found a first-rate research inst.i.tution with no teachers, no students, no cla.s.ses, but only researchers protected from the vicissitudes and pressures of the outside world. Flexner toyed with the idea of making a school of economics the core of the inst.i.tute but was soon persuaded that mathematics was a sounder choice since it was more "fundamental." Furthermore, there was infinitely greater consensus among mathematicians on who the best people were. Its location was still up in the air. Newark, with its paint factories and slaughterhouses, offered no attractions for the international band of academic superstars Flexner hoped to recruit. Princeton was more like it. Legend has it that it was Oswald Veblen who convinced the Bambergers that Princeton really could be thought of ("in a topological sense," as he put it) as a suburb of Newark.

With zeal and deep pockets matching those of any impresario, Flexner began a worldwide search for stars, dangling unheard-of salaries, lavish perks, and the promise of complete independence. His undertaking coincided with Hitler's takeover of the German government, the ma.s.s expulsion of Jews from German universities, and growing fears of another world war. After three years of delicate negotiation, Einstein, the biggest star of them all, agreed to become the second member of the Inst.i.tute's School of Mathematics, causing one of his friends in Germany to quip, "The pope of physics has moved and the United States will now become the center for the natural sciences." Kurt G.o.del, the Viennese wunderkind of logic, came in 1933 as well, and Hermann Weyl, the reigning star of German mathematics, followed Einstein a year later. Weyl insisted, as a condition of his acceptance, that the Inst.i.tute appoint a bright light from the next generation. Von Neumann, who had just turned thirty, was lured away from the university to become the Inst.i.tute's youngest professor. Practically overnight, Princeton had become the new Gottingen.

The Inst.i.tute professors initially shared the deluxe quarters at Fine Hall with their university colleagues. They moved out in 1939 when the Inst.i.tute's Fuld Hall, a Neo-Georgian brick building perched in the middle of sweeping English lawns surrounded by woods and a pond just a mile or two from Fine, was built. By the time Einstein and the others moved, the Inst.i.tute and Princeton professors had become family and the clans continued to mingle like country cousins. They collaborated on research, edited journals jointly, and attended one another's lectures, seminars, and teas. The Inst.i.tute's proximity made it easier to attract the most brilliant students and faculty to the university, while the university's active mathematics department was a magnet for those visiting or working permanently at the Inst.i.tute. surrounded by woods and a pond just a mile or two from Fine, was built. By the time Einstein and the others moved, the Inst.i.tute and Princeton professors had become family and the clans continued to mingle like country cousins. They collaborated on research, edited journals jointly, and attended one another's lectures, seminars, and teas. The Inst.i.tute's proximity made it easier to attract the most brilliant students and faculty to the university, while the university's active mathematics department was a magnet for those visiting or working permanently at the Inst.i.tute.

By contrast, Harvard, once the jewel of American mathematics, was in "a state of eclipse" by the late 1940s.26 Its legendary chairman G. D. Birkhoff was dead. Some of its brightest young stars, including Marshall Stone, Marston Morse, and Ha.s.sler Whitney, had recently departed, two of them for the Inst.i.tute for Advanced Study. Einstein had used to complain around the Inst.i.tute that "Birkhoff is one of the world's great academic anti-Semites." Whether or not this was true, Birkhoff's bias had prevented him from taking advantage of the emigration of the brilliant Jewish mathematicians from n.a.z.i Germany. Its legendary chairman G. D. Birkhoff was dead. Some of its brightest young stars, including Marshall Stone, Marston Morse, and Ha.s.sler Whitney, had recently departed, two of them for the Inst.i.tute for Advanced Study. Einstein had used to complain around the Inst.i.tute that "Birkhoff is one of the world's great academic anti-Semites." Whether or not this was true, Birkhoff's bias had prevented him from taking advantage of the emigration of the brilliant Jewish mathematicians from n.a.z.i Germany.27 Indeed, Harvard also had ignored Norbert Wiener, the most brilliant American-born mathematician of his generation, the father of cybernetics and inventor of the rigorous mathematics of Brownian motion. Wiener happened to be a Jew and, like Paul Samuelson, the future n.o.bel Laureate in economics, he sought refuge at the far end of Cambridge at MIT, then little more than an engineering school on a par with the Carnegie Inst.i.tute of Technology. Indeed, Harvard also had ignored Norbert Wiener, the most brilliant American-born mathematician of his generation, the father of cybernetics and inventor of the rigorous mathematics of Brownian motion. Wiener happened to be a Jew and, like Paul Samuelson, the future n.o.bel Laureate in economics, he sought refuge at the far end of Cambridge at MIT, then little more than an engineering school on a par with the Carnegie Inst.i.tute of Technology.28 William James, the preeminent American philosopher and older brother of the novelist Henry James, once wrote of a critical ma.s.s of geniuses causing a whole civilization to "vibrate and shake."29 But the man in the street didn't feel the tremors emanating from Princeton until World War II was practically over and these odd men with their funny accents, peculiar dress, and pa.s.sion for obscure scientific theories became national heroes. But the man in the street didn't feel the tremors emanating from Princeton until World War II was practically over and these odd men with their funny accents, peculiar dress, and pa.s.sion for obscure scientific theories became national heroes.

From the start, the European brain drain had an immediate and electrifying effect on American mathematics and theoretical physics. The emigration gathered together a group of geniuses who brought not only broad and deep mathematical know-how, but a set of refres.h.i.+ng new att.i.tudes.30 In particular, the geographical origin of these mathematicians and physicists positioned them to appreciate the implications of the ma.s.sive amount of new work that had been done in Europe since the turn of the century and gave them a great affinity for applications of mathematics to physics and engineering. Many of the newcomers were young and at the height of their research careers. In particular, the geographical origin of these mathematicians and physicists positioned them to appreciate the implications of the ma.s.sive amount of new work that had been done in Europe since the turn of the century and gave them a great affinity for applications of mathematics to physics and engineering. Many of the newcomers were young and at the height of their research careers.

Some historians have called World War II the scientists' war. But because the science required sophisticated mathematics, it was also very much a mathematicians' war, and the war effort tapped the eclectic talents of the Princeton mathematical community.31 Princeton mathematicians became involved in ciphers and code breaking. A crypta.n.a.lytic breakthrough enabled the United States to win a major Princeton mathematicians became involved in ciphers and code breaking. A crypta.n.a.lytic breakthrough enabled the United States to win a major battle at Midway Island, the turning point in the naval war between the United States and j.a.pan. battle at Midway Island, the turning point in the naval war between the United States and j.a.pan.32 In Britain, Alan Turing, a Princeton Ph.D., and his group at Bletchley Park broke the n.a.z.i code without the Germans' knowledge, thus turning the tide in the submarine battle for control of the Atlantic. In Britain, Alan Turing, a Princeton Ph.D., and his group at Bletchley Park broke the n.a.z.i code without the Germans' knowledge, thus turning the tide in the submarine battle for control of the Atlantic.33 Oswald Veblen and several of his a.s.sociates essentially rewrote the science of ballistics at the Aberdeen Proving Ground. Marston Morse, who had recently moved from Harvard to the Inst.i.tute, headed a related effort in the Office of the Chief of Ordnance.34 Another mathematician, the Princeton statistician Sam Wilks, made best daily estimates of the position of the German submarine fleet on the basis of the prior day's sighting. Another mathematician, the Princeton statistician Sam Wilks, made best daily estimates of the position of the German submarine fleet on the basis of the prior day's sighting.35 The most dramatic contributions were in the areas of weaponry: radar, infrared detection devices, bomber aircraft, long-range rockets, and torpedoes with depth charges.36 The new weapons were extremely costly, and the military needed mathematicians to devise new methods for a.s.sessing their effectiveness and the most efficient way to use them. Operations research was a systematic way of coming up with the numbers the military wanted. How many tons of explosive force must a bomb release to do a certain amount of damage? Should airplanes be heavily armored or stripped of defenses to fly faster? Should the Ruhr be bombed, and how many bombs should be used? All these questions required mathematical talent. The new weapons were extremely costly, and the military needed mathematicians to devise new methods for a.s.sessing their effectiveness and the most efficient way to use them. Operations research was a systematic way of coming up with the numbers the military wanted. How many tons of explosive force must a bomb release to do a certain amount of damage? Should airplanes be heavily armored or stripped of defenses to fly faster? Should the Ruhr be bombed, and how many bombs should be used? All these questions required mathematical talent.

The ultimate contribution was, of course, the A-bomb.37 Wigner at Princeton and Leo Szilard at Columbia composed a letter, which they brought to Einstein to sign, warning President Roosevelt that a German physicist, Otto Hahn, at the Kaiser Friedrich Inst.i.tute in Berlin had succeeded in splitting the uranium atom. Lise Meitner, an Austrian Jew who was smuggled into Denmark, performed the mathematical calculations on how an atomic bomb could be constructed from these findings. Niels Bohr, the Danish physicist, visited Princeton in 1939 and transmitted the news. "It was they rather than their American born colleagues who sensed the military implications of the new knowledge," wrote Davies. Roosevelt responded by appointing an advisory committee on uranium in October 1939, two months into the war, which eventually became the Manhattan Project. Wigner at Princeton and Leo Szilard at Columbia composed a letter, which they brought to Einstein to sign, warning President Roosevelt that a German physicist, Otto Hahn, at the Kaiser Friedrich Inst.i.tute in Berlin had succeeded in splitting the uranium atom. Lise Meitner, an Austrian Jew who was smuggled into Denmark, performed the mathematical calculations on how an atomic bomb could be constructed from these findings. Niels Bohr, the Danish physicist, visited Princeton in 1939 and transmitted the news. "It was they rather than their American born colleagues who sensed the military implications of the new knowledge," wrote Davies. Roosevelt responded by appointing an advisory committee on uranium in October 1939, two months into the war, which eventually became the Manhattan Project.

The war enriched and invigorated American mathematics, vindicated those who had championed the emigres, and gave the mathematical community a claim on the fruits of the postwar prosperity that was to follow. The war demonstrated not only the power of the new theories but the superiority of sophisticated mathematical a.n.a.lysis over educated guesses. The bomb gave enormous prestige to Einstein's relativity theory, which before then had been seen as a small correction of the still-valuable Newtonian mechanics.

Princeton rode high on the newfound status of mathematics in American society. It found itself on the leading edge not just of topology, algebra, and number theory, but also of computer theory, operations research, and the new theory of games.38 In 1948, everyone was back and the anxieties and frustrations of the 1930s had been swept away by a feeling of expansiveness and optimism. Science and mathematics were seen as the key to a better postwar world. Suddenly the government, particularly the military, wanted to spend money on pure research. Journals In 1948, everyone was back and the anxieties and frustrations of the 1930s had been swept away by a feeling of expansiveness and optimism. Science and mathematics were seen as the key to a better postwar world. Suddenly the government, particularly the military, wanted to spend money on pure research. Journals started up. Plans were made for another world mathematical congress, the first since the dark days before the war. started up. Plans were made for another world mathematical congress, the first since the dark days before the war.

A new generation was crowding in, eager to drink up the wisdom of the older generation, yet full of ideas and att.i.tudes of its own. There were no women yet, of course - with the exception of Oxford's Mary Cartwright, who was in Princeton that year - but Princeton was opening up. Suddenly, being a Jew or a foreigner, having a working-cla.s.s accent, or graduating from a college that wasn't on the East Coast were no longer automatic bars to a bright young mathematician. The biggest divide on campus was suddenly between "the kids" and the war veterans, who, in their mid-to-late twenties, were starting graduate school alongside twenty-year-olds like Nash. Mathematics was no longer a gentlemen's profession, but a wonderfully dynamic enterprise. "The notion was that the human mind could accomplish anything with mathematical ideas," a Princeton student of that era later recalled. He added: "The postwar years had their threats - the Korean War, the Cold War, China going to the commies - but in fact, in terms of science, there was this tremendous optimism. The sense at Princeton wasn't just that you were close to a great intellectual revolution, but that you were part of it."39

CHAPTER 4

School of Genius Princeton, Fall 1948 Princeton, Fall 1948

Conversation enriches the understanding, but solitude is the school of genius.

- E EDWARD G GIBBON

ON N NASH'S SECOND AFTERNOON in Princeton, Solomon Lefschetz rounded up the first-year graduate students in the West Common Room. in Princeton, Solomon Lefschetz rounded up the first-year graduate students in the West Common Room.1 He was there to tell them the facts of life, he said, in his French accent, fixing them with his fierce gaze. And for an hour Lefschetz glared, shouted, and pounded the table with his gloved, wooden hands, delivering something between a biblical sermon and a drill sergeant's diatribe. He was there to tell them the facts of life, he said, in his French accent, fixing them with his fierce gaze. And for an hour Lefschetz glared, shouted, and pounded the table with his gloved, wooden hands, delivering something between a biblical sermon and a drill sergeant's diatribe.

They were the best, the very best. Each of them had been carefully hand-picked, like a diamond from a heap of coal. But this was Princeton, where real mathematicians did real mathematics. Compared to these men, the newcomers were babies, ignorant, pathetic babies, and Princeton was going to make them grow up, d.a.m.n it!

Entrepreneurial and energetic, Lefschetz was the supercharged human locomotive that had pulled the Princeton department out of genteel mediocrity right to the top.2 He recruited mathematicians with only one criterion in mind: research. His high-handed and idiosyncratic editorial policies made the He recruited mathematicians with only one criterion in mind: research. His high-handed and idiosyncratic editorial policies made the Annals of Mathematics, Annals of Mathematics, Princeton's once-tired quarterly, into the most revered mathematical journal in the world. Princeton's once-tired quarterly, into the most revered mathematical journal in the world.3 He was sometimes accused of caving in to anti-Semitism for refusing to admit many Jewish students (his rationale being that n.o.body would hire them when they completed their degrees), He was sometimes accused of caving in to anti-Semitism for refusing to admit many Jewish students (his rationale being that n.o.body would hire them when they completed their degrees),4 but no one denies that he had brilliant snap judgment. He exhorted, bossed, and bullied, but with the aim of making the department great and turning his students into real mathematicians, tough like himself. but no one denies that he had brilliant snap judgment. He exhorted, bossed, and bullied, but with the aim of making the department great and turning his students into real mathematicians, tough like himself.

When he came to Princeton in the 1920s, he often said, he was "an invisible man."5 He was one of the first Jews on the faculty, loud, rude, and badly dressed to boot. People pretended not to see him in the hallways and gave him wide berth at faculty parties. But Lefschetz had overcome far more formidable obstacles in his life than a bunch of prissy Wasp sn.o.bs. He had He was one of the first Jews on the faculty, loud, rude, and badly dressed to boot. People pretended not to see him in the hallways and gave him wide berth at faculty parties. But Lefschetz had overcome far more formidable obstacles in his life than a bunch of prissy Wasp sn.o.bs. He had been born in Moscow and been educated in France. been born in Moscow and been educated in France.6 In love with mathematics, but effectively barred from an academic career in France because he was not a citizen, he studied engineering and emigrated to the United States. At age twenty-three, a terrible accident altered the course of his life. Lefschetz was working for Westinghouse in Pittsburgh when a transformer explosion burned off his hands. His recovery took years, during which he suffered from deep depression, but the accident ultimately became the impetus to pursue his true love, mathematics. In love with mathematics, but effectively barred from an academic career in France because he was not a citizen, he studied engineering and emigrated to the United States. At age twenty-three, a terrible accident altered the course of his life. Lefschetz was working for Westinghouse in Pittsburgh when a transformer explosion burned off his hands. His recovery took years, during which he suffered from deep depression, but the accident ultimately became the impetus to pursue his true love, mathematics.7 He enrolled in a Ph.D. program at Clark University, the university famous for Freud's 1912 lectures on psychoa.n.a.lysis, soon fell in love with and married another mathematics student, and spent nearly a decade in obscure teaching posts in Nebraska and Kansas. After days of backbreaking teaching, he wrote a series of brilliant, original, and highly influential papers that eventually resulted in a "call" from Princeton. "My years in the west with total hermetic isolation played in my development the role of 'a job in a lighthouse' which Einstein would have every young scientist a.s.sume so that he may develop his own ideas in his own way." He enrolled in a Ph.D. program at Clark University, the university famous for Freud's 1912 lectures on psychoa.n.a.lysis, soon fell in love with and married another mathematics student, and spent nearly a decade in obscure teaching posts in Nebraska and Kansas. After days of backbreaking teaching, he wrote a series of brilliant, original, and highly influential papers that eventually resulted in a "call" from Princeton. "My years in the west with total hermetic isolation played in my development the role of 'a job in a lighthouse' which Einstein would have every young scientist a.s.sume so that he may develop his own ideas in his own way."8 Lefschetz valued independent thinking and originality above everything. He was, in fact, contemptuous of elegant or rigorous proofs of what he considered obvious points. He once dismissed a clever new proof of one of his theorems by saying, "Don't come to me with your pretty proofs. We don't bother with that baby stuff around here."9 Legend had it that he never wrote a correct proof or stated an incorrect theorem. Legend had it that he never wrote a correct proof or stated an incorrect theorem.10 His first comprehensive treatise on topology, a highly influential book in which he coined the term "algebraic topology," "hardly contains one completely correct proof. It was rumored that it had been written during one of Lefschetz' sabbaticals ... when his students did not have the opportunity to revise it." His first comprehensive treatise on topology, a highly influential book in which he coined the term "algebraic topology," "hardly contains one completely correct proof. It was rumored that it had been written during one of Lefschetz' sabbaticals ... when his students did not have the opportunity to revise it."11 He knew most areas of mathematics, but his lectures were usually incoherent. Gian-Carlo Rota, one of his students, describes the start of one lecture on geometry: "Well a Riemann surface is a certain kind of Hausdorff s.p.a.ce. You know what a Hausdorff s.p.a.ce is, don't you? It's also compact, ok. I guess it is also a manifold. Surely you know what a manifold is. Now let me tell you one non-trivial theorem, the Riemann-Roch theorem."12 On this particular afternoon in mid-September 1948, with the new graduate students, Lefschetz was just warming up. "It's important to dress well. Get rid of that thing," he said, pointing to a pen holder. "You look like a workman, not a mathematician," he told one student.13 "Let a Princeton barber cut your hair," he said to another. "Let a Princeton barber cut your hair," he said to another.14 They could go to cla.s.s or not go to cla.s.s. He didn't give a d.a.m.n. Grades meant nothing. They were only recorded to please the "G.o.dd.a.m.n deans." Only the "generals" counted. They could go to cla.s.s or not go to cla.s.s. He didn't give a d.a.m.n. Grades meant nothing. They were only recorded to please the "G.o.dd.a.m.n deans." Only the "generals" counted.15 There was only one requirement: come to tea.16 They were absolutely required to come to tea every afternoon. Where else would they meet the finest mathematics faculty in the world? Oh, and if they felt like it, they were free to visit that "embalming parlor," as he liked to call the Inst.i.tute of Advanced Study, to see if they could catch a glimpse of Einstein, G.o.del, or von Neumann. They were absolutely required to come to tea every afternoon. Where else would they meet the finest mathematics faculty in the world? Oh, and if they felt like it, they were free to visit that "embalming parlor," as he liked to call the Inst.i.tute of Advanced Study, to see if they could catch a glimpse of Einstein, G.o.del, or von Neumann.17 "Remember," "Remember," he kept repeating, "we're not here to baby you." To Nash, Lefschetz's opening spiel must have sounded as rousing as a Sousa march. he kept repeating, "we're not here to baby you." To Nash, Lefschetz's opening spiel must have sounded as rousing as a Sousa march.

Lefschetz's, hence Princeton's, philosophy of graduate mathematics education had its roots in the great German and French research universities.18 The main idea was to plunge students, as quickly as possible, into their own research, and to produce an acceptable dissertation quickly. The fact that Princeton's small faculty was, to a man, actively engaged in research itself, was by and large on speaking terms, and was available to supervise students' research, made this a practical approach. The main idea was to plunge students, as quickly as possible, into their own research, and to produce an acceptable dissertation quickly. The fact that Princeton's small faculty was, to a man, actively engaged in research itself, was by and large on speaking terms, and was available to supervise students' research, made this a practical approach.19 Lefschetz wasn't aiming for perfectly polished diamonds and indeed regarded too much polish in a mathematician's youth as ant.i.thetical to later creativity. The goal was not erudition, much as erudition might be admired, but turning out men who could make original and important discoveries. Lefschetz wasn't aiming for perfectly polished diamonds and indeed regarded too much polish in a mathematician's youth as ant.i.thetical to later creativity. The goal was not erudition, much as erudition might be admired, but turning out men who could make original and important discoveries.

Princeton subjected its students to a maximum of pressure but a wonderful minimum of bureaucracy. Lefschetz was not exaggerating when he said that the department had no course requirements. The department offered courses, true, but enrollment was a fiction, as were grades. Some professors put down all As, As, others all Cs, on their grade reports, but both were completely arbitrary. others all Cs, on their grade reports, but both were completely arbitrary.20 You didn't have to show up a single time to earn them and students' transcripts were, more often than not, works of fiction "to satisfy the Philistines." There were no course examinations. In the language examinations, given by members of the mathematics department, a student was asked to translate a pa.s.sage of French or German mathematical text. But they were a joke. You didn't have to show up a single time to earn them and students' transcripts were, more often than not, works of fiction "to satisfy the Philistines." There were no course examinations. In the language examinations, given by members of the mathematics department, a student was asked to translate a pa.s.sage of French or German mathematical text. But they were a joke.21 If you could make neither heads nor tails of the pa.s.sage - unlikely, since the pa.s.sages typically contained many mathematical symbols and precious few words - you could get a pa.s.sing grade merely by promising to learn the pa.s.sage later. The only test that counted was the general examination, a qualifying examination on five topics, three determined by the department, two by the candidate, at the end of the first, or at latest, second year. However, even the generals were sometimes tailored to the strengths and weaknesses of a student. If you could make neither heads nor tails of the pa.s.sage - unlikely, since the pa.s.sages typically contained many mathematical symbols and precious few words - you could get a pa.s.sing grade merely by promising to learn the pa.s.sage later. The only test that counted was the general examination, a qualifying examination on five topics, three determined by the department, two by the candidate, at the end of the first, or at latest, second year. However, even the generals were sometimes tailored to the strengths and weaknesses of a student.22 If, for example, it was known that a student really knew one article well, but only one, the examiners, if they were so moved, might restrict themselves to that paper. The only other hurdle, before beginning the all-important thesis, was to find a senior member of the faculty to sponsor it. If, for example, it was known that a student really knew one article well, but only one, the examiners, if they were so moved, might restrict themselves to that paper. The only other hurdle, before beginning the all-important thesis, was to find a senior member of the faculty to sponsor it.

If the faculty, which got to know every student well, decided that so-and-so wasn't going to make it, Lefschetz wasn't shy about not renewing the student's support or simply telling him to leave. You were either succeeding or on your way out. As a result, Princeton students who made it past the generals wound up with doctorates after just two or three years at a time when Harvard students were taking six, seven, or eight years.23 Harvard, where Nash had yearned to go for the prestige and magic of its name, was at that time a nightmare of bureaucratic red tape, fiefdoms, and faculty with relatively little time to devote to students. Nash could not possibly have realized it fully that first day, but he was lucky to have chosen Princeton over Harvard. Harvard, where Nash had yearned to go for the prestige and magic of its name, was at that time a nightmare of bureaucratic red tape, fiefdoms, and faculty with relatively little time to devote to students. Nash could not possibly have realized it fully that first day, but he was lucky to have chosen Princeton over Harvard.

That genius will emerge regardless of circ.u.mstance is a widely held belief. The biographer of the great Indian mathematician Ramanujan, for example, claims that the five years that the young Ramanujan spent in complete isolation from other mathematicians, having failed out of school and unable to get as much as a tutoring position, were the key to his stunning discoveries. that the five years that the young Ramanujan spent in complete isolation from other mathematicians, having failed out of school and unable to get as much as a tutoring position, were the key to his stunning discoveries.24 But when writing Ramanujan's obituary, G. H. Hardy, the Cambridge mathematician who knew him best, called that view, held earlier by himself, "ridiculous sentimentalism." After Ramanujan's death at thirty-three, Hardy wrote that the "the tragedy of Ramanujan was not that he died young, but that, during his five unfortunate years, his genius was misdirected, side-tracked, and to a certain extent distorted." But when writing Ramanujan's obituary, G. H. Hardy, the Cambridge mathematician who knew him best, called that view, held earlier by himself, "ridiculous sentimentalism." After Ramanujan's death at thirty-three, Hardy wrote that the "the tragedy of Ramanujan was not that he died young, but that, during his five unfortunate years, his genius was misdirected, side-tracked, and to a certain extent distorted."25 As was to become increasingly obvious over the months that followed, Princeton's approach to its graduate students, with its combination of complete freedom and relentless pressure to produce, could not have been better suited to someone of Nash's temperament and style as a mathematician, nor more happily designed to elicit the first real proofs of his genius. Nash's great luck, if you want to call it luck, was that he came onto the mathematical scene at a time and to a place tailor-made for his particular needs. He came away with his independence, ambition, and originality intact, having been allowed to acquire a truly first-cla.s.s training that was to serve him brilliantly.

Like nearly all the other graduate students at Princeton, Nash lived in the Graduate College. The College was a gorgeous, faux-English edifice of dark gray stone surrounding an interior courtyard that sat on a crest overlooking a golf course and lake. It was located about a mile from Fine Hall on the far side of Alexander Road, about halfway between Fine and the Inst.i.tute for Advanced Study. Especially in winter, when it was dark by the time the afternoon seminar ended, it was a good long walk, and once you were there, you didn't feel like going out again. Its location was the outcome of a fight between Woodrow Wilson and Dean Andrew West.26 Wilson had wanted the graduate students to mix and mingle with the undergraduates. West wanted to re-create the atmosphere of one of the Oxbridge colleges, far removed from the rowdy, sn.o.bbish undergraduate eating clubs on Prospect Street. Wilson had wanted the graduate students to mix and mingle with the undergraduates. West wanted to re-create the atmosphere of one of the Oxbridge colleges, far removed from the rowdy, sn.o.bbish undergraduate eating clubs on Prospect Street.

In 1948, there were about six hundred graduate students, their ranks swelled by the numbers of returning veterans whose undergraduate or graduate careers had been interrupted by the war.27 The College, a bit shabbier than before the war and in need of sprucing up, was full, overflowing really, and a good many less lucky first-year students had been turned away and were being forced to lodge in rented rooms in the village. Almost everyone else had to share rooms. Nash, who lived in Pyne Tower, was lucky to get a private room, one of the perks of his fellows.h.i.+p. The College, a bit shabbier than before the war and in need of sprucing up, was full, overflowing really, and a good many less lucky first-year students had been turned away and were being forced to lodge in rented rooms in the village. Almost everyone else had to share rooms. Nash, who lived in Pyne Tower, was lucky to get a private room, one of the perks of his fellows.h.i.+p.28 About fifteen or twenty of the mathematics students, second- and third-year as well as first-year students, and a couple of instructors lived in the college at the time. About fifteen or twenty of the mathematics students, second- and third-year as well as first-year students, and a couple of instructors lived in the college at the time.

Life was masculine, monastic, and scholarly, exactly as Dean West had envisioned.29 The graduate students ate breakfast, lunch, and dinner together at the cost of fourteen dollars a week. Breakfast and lunch were served in the "breakfast" room, hurried meals that were taken on the run. But dinner, served in Procter The graduate students ate breakfast, lunch, and dinner together at the cost of fourteen dollars a week. Breakfast and lunch were served in the "breakfast" room, hurried meals that were taken on the run. But dinner, served in Procter Hall, a refectory very much in the English style, was a more leisurely affair. There were tall windows, long wooden tables, and formal portraits of eminent Princetonians on the walls; the evening prayer was led by Sir Hugh Taylor, the college's dean, or his second in command, the college's master. There were no candles and no wine, but the food was excellent. Gowns were no longer required as before the war (they were reinstated in the early 1950s, and did not disappear for good until the 1970s), but jackets and ties were required. Hall, a refectory very much in the English style, was a more leisurely affair. There were tall windows, long wooden tables, and formal portraits of eminent Princetonians on the walls; the evening prayer was led by Sir Hugh Taylor, the college's dean, or his second in command, the college's master. There were no candles and no wine, but the food was excellent. Gowns were no longer required as before the war (they were reinstated in the early 1950s, and did not disappear for good until the 1970s), but jackets and ties were required.

The atmosphere at dinner was a combination of male debating society, locker room, and seminary. Though historians, English scholars, physicists, and economists all lived cheek by jowl with the mathematicians, the mathematicians segregated themselves as strictly as if they were living under some legal system of apartheid, always occupying a table by themselves.30 The older, more sophisticated students, namely Harold Kuhn, Leon Henkin, and David Gale, met for sherry in Kuhn's rooms before dinner. Conversation at dinner, sometimes but not always mathematical, was more expansive than at teatime. The talk, one former student recalls, frequently revolved around "politics, music, and girls." Political debate resembled discussions about sports, with more calculation of odds and betting than ideology. In that early fall, the Truman-Dewey race provided a great deal of entertainment. Being a more diverse group, the graduate students were more evenly split between the candidates than the Princeton undergraduates; 98 percent of the undergraduates at Princeton, it turned out, were Dewey supporters. One graduate student even wore a Wallace b.u.t.ton for Henry Wallace, the candidate supported by the American Labor party, a Communist front organization. The older, more sophisticated students, namely Harold Kuhn, Leon Henkin, and David Gale, met for sherry in Kuhn's rooms before dinner. Conversation at dinner, sometimes but not always mathematical, was more expansive than at teatime. The talk, one former student recalls, frequently revolved around "politics, music, and girls." Political debate resembled discussions about sports, with more calculation of odds and betting than ideology. In that early fall, the Truman-Dewey race provided a great deal of entertainment. Being a more diverse group, the graduate students were more evenly split between the candidates than the Princeton undergraduates; 98 percent of the undergraduates at Princeto