A Beautiful Mind Page 8
While mathematics and physics at Princeton and other American universities were languishing, a revolution in mathematics and physics was taking place three thousand miles away in such intellectual centers as Göttingen, 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 classical 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 mass was simply congealed energy, energy liberated matter: space 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 Göttingen, 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.” Göttingen 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 shift 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.”
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 hitherto 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 friendship. 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 about hiring literature and history scholars as preceptors. Fine asked him, “Why not a few scientists?” As a gesture of friendship 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-God, 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 Nassau 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 accumulated 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 professorships 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 Nobel 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 professorships 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 passionate 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.24 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 Institute 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 gratitude 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 institution with no teachers, no students, no classes, 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 institute 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 mass 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 Institute’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 Gödel, 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 Institute appoint a bright light from the next generation. Von Neumann, who had just turned thirty, was lured away from the university to become the Institute’s youngest professor. Practically overnight, Princeton had become the new Göttingen.
The Institute professors initially shared the deluxe quarters at Fine Hall with their university colleagues. They moved out in 1939 when the Institute’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 Institute 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 Institute’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 Institute.
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 Hassler Whitney, had recently departed, two of them for the Institute for Advanced Study. Einstein had used to complain around the Institute 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 Nazi 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 Nobel 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 Institute of Technology.28
William James, the preeminent American philosopher and older brother of the novelist Henry James, once wrote of a critical mass 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 passion 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 refreshing new attitudes.30 In particular, the geographical origin of these mathematicians and physicists positioned them to appreciate the implications of the massive 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 cryptanalytic 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 Japan.32 In Britain, Alan Turing, a Princeton Ph.D., and his group at Bletchley Park broke the Nazi 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 associates essentially rewrote the science of ballistics at the Aberdeen Proving Ground. Marston Morse, who had recently moved from Harvard to the Institute, 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.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 assessing 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 Institute 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 émigrés, 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 analysis 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 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 attitudes 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-class 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