Part 9 (2/2)

Their friends accepted Nash's new status as a race So-willed,” others quite the opposite Rogers recalled in 1996 that ”Alicia subordinated herself to John She wasn't there to compete with him She was totally dedicated to his support”7 Some of their acquaintances found their relationshi+p oddly cool, but others cae suited Nash well and that Alicia was having a good effect on hiers recalled Zipporah Levinson agreed: ”John ard Alicia made him behave” Some of their acquaintances found their relationshi+p oddly cool, but others cae suited Nash well and that Alicia was having a good effect on hiers recalled Zipporah Levinson agreed: ”John ard Alicia raphs of Alicia taken in thosewoman It was, as Alicia would say raphs of Alicia taken in thosewoman It was, as Alicia would say many years later, ”a very nice time of my life”9 Nash continued to work on the problem he had solved the previous year at Courant There were soun to write, laying out a full account of what he had done, was in very rough shape10 ”It was,” a colleague said in 1996, ”as if he were a composer and could hear the music, but he didn't knorite it down or exactly how to orchestrate it” ”It was,” a colleague said in 1996, ”as if he were a composer and could hear the music, but he didn't knorite it down or exactly how to orchestrate it”11 As it turned out, it would take most of the year, and a collective effort, before the final product - which soard as Nash's most important work - was finally ready to be submitted to a journal As it turned out, it would take most of the year, and a collective effort, before the final product - which soard as Nash's most important work - was finally ready to be submitted to a journal

To complete, it, Nash came as close as he ever had or would to an active collaboration with otherthe ato professor fro MIT that ter of nonlinear theory It was very difficult”12 Nash knocked on doors, asked questions, speculated out loud, fished for ideas, and at the end of the day, got a dozen or so h in his probleh to solve little pieces of his puzzle ”It was a kind of factory,” Carleson, who contributed a neat little theorem on entropy to Nash's paper, said ”He wouldn't Nash knocked on doors, asked questions, speculated out loud, fished for ideas, and at the end of the day, got a dozen or so h in his probleh to solve little pieces of his puzzle ”It was a kind of factory,” Carleson, who contributed a neat little theorem on entropy to Nash's paper, said ”He wouldn't tell us what he was after, his grand design It was aos to cooperate” tell us what he was after, his grand design It was aos to cooperate”13 Besides Moser and Carleson, Nash also turned to Eli Stein, now a professor of mathematics at Princeton University but then an MIT instructor ”He wasn't interested in what I was doing,” recalled Stein ”He'd say, You're an analyst You ought to be interested in this' ”14 Stein was intrigued by Nash's enthusiasm and his constant supply of ideas He said, ”We were like Yankees fans getting together and talking about great gareat players It was very ereat intuition, he saw that certain things ought to be true He'd come into uments were plausible but he didn't have proofs for the individual leed Stein to prove the leed Stein to prove the leuments based on plausibility,” said Stein in 1995 ”If you build an edifice based on one plausible proposition after another, the whole thing is liable to collapse after a few steps But somehow he kneouldn't And it didn't”16 Nash's thirtieth year was thus looking very bright He had scored a major success He was adulated and lionized as never before17Fortune htest young stars of azine was about to feature hi stars ofseries on the ”New Math”18 And he had returned to Ca wife Yet his good fortune seeap between his a, he felt more frustrated and dissatisfied than ever He had hoped for an appointe as a ood fortune seeap between his a, he felt more frustrated and dissatisfied than ever He had hoped for an appointment at Harvard or Princeton19 As it was, he was not yet a full professor at MIT, nor did he have tenure He had expected that his latest result, along with the offer from Courant, would convince the department to award him both that winter As it was, he was not yet a full professor at MIT, nor did he have tenure He had expected that his latest result, along with the offer from Courant, would convince the departs after only five years would be unusual, but Nash felt that he deserved nothing less Getting these things after only five years would be unusual, but Nash felt that he deserved nothing less21 But Martin had alreadyto put him up for promotion so soon Nash's candidacy was controversial, Martin had told him, just as his initial appointment had been But Martin had alreadyto put him up for promotion so soon Nash's candidacy was controversial, Martin had told him, just as his initial appointment had been22 A number of people in the departue Martin felt Nash's case would be stronger once the full version of the parabolic equations paper appeared in print Nash, however, was furious A number of people in the departue Martin felt Nash's case would be stronger once the full version of the parabolic equations paper appeared in print Nash, however, was furious

Nash continued to brood over the De Giorgi fiasco The real blow of discovering that De Giorgi had beaten hi to share the credit for hisbelief that the sudden appearance of a coinventor would rob hi he most coveted: a Fields Medal

Forty years later, after winning a nobel, Nash referred in his autobiographical essay, in his typically elliptical fashi+on, to his dashed hopes: It seei or Nash had failed in the attack on this problem (or a priori a priori estimates of Holder continuity) then that the lone clinized with the mathematics' Fields medal (which has traditionally been restricted to persons less than 40 years old) estimates of Holder continuity) then that the lone clinized with the mathematics' Fields medal (which has traditionally been restricted to persons less than 40 years old)23

The next Fields Medal would be awarded in August 1958, and as everyone knew, the deliberations had long been under way

To understand how deep the disappointment was, one must know that the Fields Medal is the nobel Prize of matheranted by his peers, the trophy of trophies24 There is no nobel in mathematics, and mathematical discoveries, no matter how vital to nobel disciplines such as physics or economics, do not in the, rarer than the nobel In the fifties and early sixties, it arded once every four years and usually to just two recipients at a time nobels, by contrast, are awarded annually, with aseach prize Tradition dee, a practice designed to honor the spirit of the prize charter, which stipulates that the purpose of the honor is ”to encourage young mathematicians” and ”future work” There is no nobel in mathematics, and mathematical discoveries, no matter how vital to nobel disciplines such as physics or economics, do not in the, rarer than the nobel In the fifties and early sixties, it arded once every four years and usually to just two recipients at a time nobels, by contrast, are awarded annually, with aseach prize Tradition dee, a practice designed to honor the spirit of the prize charter, which stipulates that the purpose of the honor is ”to encourage young mathematicians” and ”future work”25 The incentive, incidentally, is of an intangible variety, as the cash involved, in contrast to the nobel, is negligible, a few hundred dollars Yet since the Fields is an instant ticket in midcareer to endowed chairs at top universities, a disadvantage is more apparent than real The incentive, incidentally, is of an intangible variety, as the cash involved, in contrast to the nobel, is negligible, a few hundred dollars Yet since the Fields is an instant ticket in midcareer to endowed chairs at top universities, a disadvantage is more apparent than real

The prize is administered by the International Matheanizes the quadrennial world resses, and the selection of Fields anization put it, ”one of theresponsibilities”26 Like the nobel deliberations, the Fields selection process is shrouded in greatest secrecy Like the nobel deliberations, the Fields selection process is shrouded in greatest secrecy

The seven-member prize committee for the 1958 Fields awards was headed by Heinz Hopf, the dapper, genial, cigar-seometer fro theorem, and included another prominent Geren, and then at Courant27 The deliberations got under way in late 1955 and were concluded early in 1958 (The medalists were informed, in strictest secrecy, in May 1958 and actually awarded their ust) The deliberations got under way in late 1955 and were concluded early in 1958 (The medalists were informed, in strictest secrecy, in May 1958 and actually awarded their ust) All prize deliberations involve ele the composition of the committee As one mathematician who took part in a subsequent committee said, ”People aren't universalists They're horse trading”28 In 1958, there were a total of thirty-six nominees, as Hopf was to say in his award ceremony speech, but the hot contenders numbered no more than five or six In 1958, there were a total of thirty-six nominees, as Hopf was to say in his award ceremony speech, but the hot contenders numbered no more than five or six29That year the deliberations were unusually contentious and the prizes, which ultiist, and Klaus F Roth, a number theorist, were awarded on a four-three vote'30 ”There were lots of politics in that prize,” one person close to the deliberations said recently ”There were lots of politics in that prize,” one person close to the deliberations said recently31 Roth was a shoo-in; he had solved a fundamental problem in nu Siegel, had worked on early in his career ”It was a question of Thorn versus Nash,” said Moser, who heard reports of the deliberations from several of the participants Roth was a shoo-in; he had solved a fundamental problem in nu Siegel, had worked on early in his career ”It was a question of Thorn versus Nash,” said Moser, who heard reports of the deliberations froht very hard for Nash, but he didn't succeed,” recalled Lax, who had been Friedrichs's student and who heard Friedrichs's account of the deliberations ”He was upset As I look back, he should have insisted that a third prize be given” ”Friedrichs fought very hard for Nash, but he didn't succeed,” recalled Lax, who had been Friedrichs's student and who heard Friedrichs's account of the deliberations ”He was upset As I look back, he should have insisted that a third prize be given”33 Chances are that Nash did not make the final round His work on partial differential equations, of which Friedrichs would have been aware, was not yet published or properly vetted He was an outsider, which one person close to the deliberations thought ”ht have hurt him” Moser said, ”Nash was somebody who didn't learn the stuff He didn't care He wasn't afraid of et looked at so positively by other people”34 Besides, there was no great urgency to recognize him at this juncture; he was just twenty-nine Besides, there was no great urgency to recognize him at this juncture; he was just twenty-nine

No one could know, of course, that 1958 would be Nash's last chance ”By 1962, a Fields for Nash would have been out of the question,” Moser said recently ”It would never have happened I'ht about him anymore”35 A measure of how badly Nash wanted to win the distinction conferred by such a prize is the extraordinary lengths to which he went to ensure that his paper would be eligible for the Bocher Prize, the only award ree to the Fields The Bocher is given by the American Mathematical Society only once every five years36 It was due to be awarded in February 1959, which meant that the deliberations would take place in the latter part of 1958 It was due to be awarded in February 1959, which meant that the deliberations would take place in the latter part of 1958

Nash submitted his manuscript to Acta Mathematica, Acta Mathe of 1958 the Swedishof 195837 It was a natural choice, since Carleson was the editor and was convinced of the paper's great importance Nash let Carleson knoanted the paper published as quickly as possible and urged Carleson to give it to a referee who could vet the paper in a ave the manuscript to Hor it, verified all the theoreet it into print as quickly as possible But as soon as Carleson informed Nash of the forone conclusion, Nash withdrew his paper It was a natural choice, since Carleson was the editor and was convinced of the paper's great importance Nash let Carleson knoanted the paper published as quickly as possible and urged Carleson to give it to a referee who could vet the paper in a ave the manuscript to Hor it, verified all the theoreet it into print as quickly as possible But as soon as Carleson informed Nash of the forone conclusion, Nash withdrew his paper

When the paper subsequently appeared in the fall issue of the American Journal of Mathematics, American Journal of Mathematics, Hormander concluded that Nash had always intended to publish the paper there, since the Bocher restricted eligible papers to those published in American journals - or, worse, had submitted the paper to both journals, Hormander concluded that Nash had always intended to publish the paper there, since the Bocher restricted eligible papers to those published in American journals - or, worse, had submitted the paper to both journals, a clear-cut breach of professional ethics ”It turned out that Nash had just wanted to get a letter of acceptance from a clear-cut breach of professional ethics ”It turned out that Nash had just wanted to get a letter of acceptance froet fast publication in the to be able to get fast publication in the American Journal of Mathery at what he felt was ”very iry at what he felt was ”very ih, that Nash had si that doing so would exclude it fro this fact, he illing to antagonize Carleson and Horibility Heso would exclude it fro this fact, he illing to antagonize Carleson and Horibility He may therefore not have used Acta Acta quite so unscrupulously Withdrawing the paper after it had been pro the paper after it had been promised to Acta, Acta, and after it had been refereed, would have been unprofessional, but not as clear a violation of ethics as Horests However, it still showed how verya prize meant to Nash and after it had been refereed, would have been unprofessional, but not as clear a violation of ethics as Horests However, it still showed how verya prize meant to Nash

CHAPTER 32

Secrets Summer 1958 Su: everything was revealed tothose spacious hours

- GERARD DE N NERVAL

NASH TURNED THIRTY that June Forline between youth and adulthood, but a back at this time in his life, Nash would refer to a sudden onset of anxiety, ”a fear” that the best years of his creative life were over that June Forline between youth and adulthood, but a back at this time in his life, Nash would refer to a sudden onset of anxiety, ”a fear” that the best years of his creative life were over1 What an irony that mathematicians, who live so much more in their minds than most of humanity, should feel somathematician watches the calendar with a sense of trepidation and foreboding equal to or greater than that of any y The Mathey by G H Hardy sets the standard for all lale piece of first-rate mathematics done by a mathematician over fifty by G H Hardy sets the standard for all lale piece of first-rate e anxiety is most intense, mathematicians say, as thirty draws near ”People say that for better or worse you will probably do your best work by the tienius ”I tend to think that you are at your peak around thirty I' you won't equal it I would like to think that you could But I don't think you will ever do better That's e anxiety is most intense, mathematicians say, as thirty draws near ”People say that for better or worse you will probably do your best work by the tienius ”I tend to think that you are at your peak around thirty I' you won't equal it I would like to think that you could But I don't think you will ever do better That's ”3 Von Neumann used to say that ”the primary mathematical powers decline at about twenty-six,” after which the mathematician must rely on ”a certain more prosaic shrewdness” Von Neumann used to say that ”the primary mathematical powers decline at about twenty-six,” after which the mathematicianthe irony is that the act of creating new mathematics, which appears so solitary from the outside, feels from the inside like an intraets the crowded field And one's relative standing, vis-a-vis past and present coain, Hardy best conveyed whathi to be anything but aany passion for mathematics as a boy ”I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively” boys, and this seemed to be the way in which I could do so most decisively”5 More ae-conscious than most - or perhaps sie-conscious person I've ever met,” recalled Felix Browder in 1995 ”He would tell e relative to his and everybody else's” More ae-conscious than most - or perhaps sie-conscious person I've ever met,” recalled Felix Browder in 1995 ”He would tell e relative to his and everybody else's”6 His deterested not just a desire to avoid reginess to take time out of the race His deterested not just a desire to avoid reginess to take time out of the race

Thethat tierated, but they are quite capable of producing real crises, as the history of mathematics amply attests Artin, for exa to catch hold of so that would equal his early accomplishments7 Steenrod slipped into a deep depression When one of his students published a note on ”Steenrod's Reduced Powers” - the reference was, of course, mathematical, not personal - other mathematicians smirked and said, ”Oh, yes, Steenrod's reduced powers!” Steenrod slipped into a deep depression When one of his students published a note on ”Steenrod's Reduced Powers” - the reference was, of course, mathematical, not personal - other mathematicians smirked and said, ”Oh, yes, Steenrod's reduced powers!”8 Nash's thirtieth birthday produced a kind of cognitive dissonance One can al commentator inside Nash's head: ”What, thirty already, and still no prizes, no offer froreat enius? Ha, ha, ha!”

Nash'sself-doubt and dissatisfaction alternated with periods of heady anticipation Nash had a distinct feeling that he was on the brink of some revelation And it was this sense of anticipation, asto a professional level of comparative in working on two great proble of 1958, Nash had confided to Eli Stein that he had ”an idea of an idea” about how to solve the Riemann Hypothesis10 That su, and other experts in nu their opinion That su, and other experts in nu their opinion11 He worked in his office in Building Two for hours, night after night He worked in his office in Building Two for hours, night after night

Even when a genius makes such an announcement, the rational response is skepticisrail of pure mathematics ”Whoever proves or disproves it will cover hilory,” wrote E T Bell in 1939 ”A decision one way or the other disposing of Riereater interest to mathematicians than a proof or disproof of Fermat's Last Theorem”12 Enrico Bombieri, at the Institute for Advanced Study, said: ”The Riemann Hypothesis is not just a problem It is the the problem It is the most important proble extrerasp” problem It is the most important proble extrerasp”13 Whole numbers that are evenly divisible only by themselves and one - socalled prime numbers - have exerted a fascination for mathematicians for two thousand years or more The Greek mathematician Euclid proved that there were infinitely hteenth century - Euler, Legendre, and Gauss - began a quest, still under way, to estiiven a whole number thousand years or more The Greek mathematician Euclid proved that there were infinitely hteenth century - Euler, Legendre, and Gauss - began a quest, still under way, to estiiven a whole nu of iants - G H Hardy, Nor others - have attempted, unsuccessfully, to prove the Rieiants - G H Hardy, Nor others - have attempted, unsuccessfully, to prove the Rieon the Riemann Hypothesis a reprint of a faulty proof of the conjecture by a Gottingen ht he'd solved the proble,” the young mathematician had said, and Polya delivered the reprint the followingwith a note: ”If you want to clio to Zere Polya once gave a youngon the Riemann Hypothesis a reprint of a faulty proof of the conjecture by a Gottingen ht he'd solved the proble,” the young mathematician had said, and Polya delivered the reprint the followingwith a note: ”If you want to clio to Zermatt where those who have tried are buried”16 Before World War I, a Geren, for whoever proved or disproved the hypothesis The prize was never awarded and, indeed, vanished in the inflation of the 1920s17 Nash's first encounter with Georg Friedrich Bernhard Riemann and his famous conjecture took place when Nash was fourteen, probably lying on the den floor in front of the radio, reading Bell's Men of Mathematics Men of Mathematics18 Riemann, the sickly son of an i to follow in his father's footsteps when a sympathetic headmaster, who sensed that the boy was ave hiendre's Theorie des Nombres Theorie des No Rie, ”That is certainly a wonderful book I have mastered it” This episode, which took place in 1840, was likely the origin of Rie interest in the riddle of prime numbers and, as Bell theorizes, Rieinated in his later atte Rie, ”That is certainly a wonderful book I have mastered it” This episode, which took place in 1840, was likely the origin of Rie interest in the riddle of prime numbers and, as Bell theorizes, Rieinated in his later attee of thirty-three, Riee paper, ”Ueber die Anzahl der Priebenen Groesse” ”Ueber die Anzahl der Priebenen Groesse” (”On the nunitude”), in which he laid out his faes, if not the outstanding challenge to pure iven nitude”), in which he laid out his faes, if not the outstanding challenge to pure mathematics”

Here is how Bell explains the conjecture: The probleive a formula which will state how iven nu to solve this Rieation of the infinite series 1 + 1/2S + 1/3S + 1/4S +in whi