Part 2 (2/2)

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 community31 PrincetonA cryptanalytic breakthrough enabled the United States to win a major PrincetonA cryptanalytic breakthrough enabled the United States to win apoint in the naval war between the United States and japan battle at Midway Island, the turning point in the naval war between the United States and japan32 In Britain, Alan Turing, a Princeton PhD, and his group at Bletchley Park broke the nazi code without the Ger the tide in the submarine battle for control of the Atlantic In Britain, Alan Turing, a Princeton PhD, and his group at Bletchley Park broke the nazi code without the Ger the tide in the submarine battle for control of the Atlantic33 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 Ordnance34 Another mathematician, the Princeton statistician Sam Wilks, made best daily estimates of the position of the Ger Another mathematician, the Princeton statistician Sam Wilks, made best daily estimates of the position of the Ger35 The most dramatic contributions were in the areas of weaponry: radar, infrared detection devices, boe rockets, and torpedoes with depth charges36 The neeapons were extremely costly, and the military neededtheir effectiveness and the most efficient way to use the up with the numbers the military wanted How many tons of explosive force e? 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 neeapons were extremely costly, and the military neededtheir effectiveness and the most efficient way to use the up with the numbers the military wanted How many tons of explosive force e? 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 ultiner at Princeton and Leo Szilard at Colun, warning President Roosevelt that a German physicist, Otto Hahn, at the Kaiser Friedrich Institute in Berlin had succeeded in splitting the uraniuled into Denmark, performed the mathematical calculations on how an atos Niels Bohr, the Danish physicist, visited Princeton in 1939 and transmitted the news ”It was they rather than their Aues who sensed the e,” wrote Davies Roosevelt responded by appointing an advisory committee on uranium in October 1939, two months into the hich eventually becaner at Princeton and Leo Szilard at Colun, warning President Roosevelt that a German physicist, Otto Hahn, at the Kaiser Friedrich Institute in Berlin had succeeded in splitting the uraniuled into Denmark, performed the mathematical calculations on how an atos Niels Bohr, the Danish physicist, visited Princeton in 1939 and transmitted the news ”It was they rather than their Aues who sensed the e,” wrote Davies Roosevelt responded by appointing an advisory committee on uranium in October 1939, two months into the hich eventually becaorated American res, 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 ave enore to Einstein's relativity theory, which before then had been seen as a small correction of the still-valuable Newtonian h on the newfound status of mathee not just of topology, algebra, and number theory, but also of coames38 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 postorld 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 postorld Suddenly the government, particularly the military, wanted to spend money on pure research Journals started up Plans were ress, the first since the dark days before the war started up Plans were ress, the first since the dark days before the war

A new generation was crowding in, eager to drink up the wisdoeneration, yet full of ideas and attitudes of its own There were no women yet, of course - with the exception of Oxford's Mary Cartwright, as in Princeton that year - but Princeton was opening up Suddenly, being a Jew or a foreigner, having a working-class accent, or graduating froer autoest divide on campus was suddenly between ”the kids” and the war veterans, who, in their side twenty-year-olds like Nash Matheentlemen's profession, but a wonderfully dynamic enterprise ”The notion was that the hu 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, Soloraduate students in the West Common Rooraduate students in the West Common Room1 He was there to tell the thelared, shouted, and pounded the table with his gloved, wooden hands, delivering soeant's diatribe He was there to tell the thelared, shouted, and pounded the table with his gloved, wooden hands, delivering soeant'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 mathenorant, pathetic babies, and Princeton was going to etic, Lefschetz was the supercharged human locoenteel ht to the top2 He recruited matheh-handed and idiosyncratic editorial policies made the He recruited matheh-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 world3 He was so to ad that nobody would hire therees), He was so to ad that nobody would hire therees),4 but no one denies that he had brilliant snap judgment He exhorted, bossed, and bullied, but with the ai his students into real h like himent He exhorted, bossed, and bullied, but with the ai his students into real h 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 hiave him wide berth at faculty parties But Lefschetz had overcome far more formidable obstacles in his life than a bunch of prissy Wasp snobs He had He was one of the first Jews on the faculty, loud, rude, and badly dressed to boot People pretended not to see hiave him wide berth at faculty parties But Lefschetz had overcome far more formidable obstacles in his life than a bunch of prissy Wasp snobs He had been born in Moscow and been educated in France been born in Moscow and been educated in France6 In love with mathematics, but effectively barred from an academic career in France because he was not a citizen, he studied engineering and ee twenty-three, a terrible accident altered the course of his life Lefschetz orking 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 ee twenty-three, a terrible accident altered the course of his life Lefschetz orking 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, ram at Clark University, the university famous for Freud's 1912 lectures on psychoanalysis, soon fell in love with and married another mathe 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 ith total hermetic isolation played in hthouse' which Einstein would have every young scientist assume so that he may develop his own ideas in his oay” He enrolled in a PhD program at Clark University, the university famous for Freud's 1912 lectures on psychoanalysis, soon fell in love with and married another mathe 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 ith total hermetic isolation played in hthouse' which Einstein would have every young scientist assume so that he may develop his own ideas in his oay”8 Lefschetz valued independent thinking and originality above everything He was, in fact, conteorous proofs of what he considered obvious points He once dis, ”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 theoreend had it that he never wrote a correct proof or stated an incorrect theorehly influential book in which he coined the tery,” ”hardly contains one completely correct proof It was ru one of Lefschetz' sabbaticalswhen his students did not have the opportunity to revise it” His first cohly influential book in which he coined the tery,” ”hardly contains one completely correct proof It was ru one of Lefschetz' sabbaticalswhen 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 space You knohat a Hausdorff space is, don't you? It's also couess it is also a manifold Surely you knohat a manifold is Now let me tell you one non-trivial theorem, the Riemann-Roch theorem”12 On this particular afternoon in raduate students, Lefschetz was just war,” he said, pointing to a pen holder ”You look like a workman, not a mathematician,” he told one student13 ”Let a Princeton barber cut your hair,” he said to another ”Let a Princeton barber cut your hair,” he said to another14 They could go to class or not go to class He didn't give a da They were only recorded to please the ”Goddao to class or not go to class He didn't give a da They were only recorded to please the ”Goddaenerals” counted15 There was only one requirement: come to tea16 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 ”e parlor,” as he liked to call the Institute of Advanced Study, to see if they could catch a glimpse of Einstein, Godel, 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 ”e parlor,” as he liked to call the Institute of Advanced Study, to see if they could catch a glimpse of Einstein, Godel, or von Neu, ”we're not here to baby you” To Nash, Lefschetz's opening spielas a Sousa , ”we're not here to baby you” To Nash, Lefschetz's opening spielas a Sousa raduate reat German and French research universities18 The e students, as quickly as possible, into their own research, and to produce an acceptable dissertation quickly The fact that Princeton's sed in research itself, was by and large on speaking terms, and was available to supervise students' research, e students, as quickly as possible, into their own research, and to produce an acceptable dissertation quickly The fact that Princeton's sed in research itself, was by and large on speaking terms, and was available to supervise students' research,for perfectly polished diaarded too much polish in a matheoal was not erudition,out inal and i for perfectly polished diaarded too much polish in a matheoal was not erudition,out inal and important discoveries

Princeton subjected its students to a maximum of pressure but a wonderfulwhen he said that the department had no course requirements The department offered courses, true, but enrollrades Sorade reports, but both were corade reports, but both were cole time to earn them and students' transcripts were, more often than not, works of fiction ”to satisfy the Philistines” There were no course exaiven by members of the mathee 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 exaiven by members of the mathee of French or German mathematical text But they were a joke21 If you could e - unlikely, since the passages typically contained et a passing grade e later The only test that counted was the general exa 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 soths and weaknesses of a student If you could e - unlikely, since the passages typically contained et a passing grade e later The only test that counted was the general exa 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 soths and weaknesses of a student22 If, for example, it was known that a student really knew one article well, but only one, the exaht restrict the 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 exaht restrict the 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 tothe student's support or si or on your way out As a result, Princeton students who enerals wound up with doctorates after just two or three years at a tiht years23 Harvard, where Nash had yearned to go for the prestige and htmare 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 htmare 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 eardless of circureat Indian mathematician Ramanujan, for exa Ramanujan spent in co failed out of school and unable to get asdiscoveries that the five years that the young Ramanujan spent in co failed out of school and unable to get asdiscoveries24 But riting Rae 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 Ra his five unfortunate years, his genius was misdirected, side-tracked, and to a certain extent distorted” But riting Rae 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 Ra his five unfortunate years, his genius was misdirected, side-tracked, and to a certain extent distorted”25 As was to becoly obvious over the raduate students, with its combination of complete freedom and relentless pressure to produce, could not have been better suited to someone of Nash's tened 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 cainality intact, having been allowed to acquire a truly first-class training that was to serve hiraduate 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 Institute for Advanced Study Especially in winter, when it was dark by the ti walk, and once you were there, you didn't feel like going out again Its location was the outcoht between Woodrow Wilson and Dean Andrew West26 Wilson had wanted the graduate students to raduates West wanted to re-create the ates, far re clubs on Prospect Street Wilson had wanted the graduate students to raduates West wanted to re-create the ates, far re clubs on Prospect Street

In 1948, there were about six hundred graduate students, their ranks swelled by the nuraduate careers had been interrupted by the war27 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 rooe Almost everyone else had to share rooet a private rooe, 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 rooe Almost everyone else had to share rooet a private room, one of the perks of his fellowshi+p28 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 envisioned29 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 lish style, was awooden tables, and formal portraits of e prayer was led by Sir Hugh Taylor, the college's dean, or his second in coe's master There were no candles and no wine, but the food was excellent Goere 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 lish style, was awooden tables, and formal portraits of e prayer was led by Sir Hugh Taylor, the college's dean, or his second in coe's master There were no candles and no wine, but the food was excellent Goere 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 at society, locker roolish scholars, physicists, and economists all lived cheek by joith the ated theal syste a table by themselves30 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, irls” Political debate resembled discussions about sports, with y In that early fall, the Tru a raduate 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 button for Henry Wallace, the candidate supported by the Aanization 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, irls” Political debate resembled discussions about sports, with y In that early fall, the Tru a raduate students were more evenly split between the candidates than the Princeton undergraduates; 98 percent of the undergraduates at Princeto