Part 6 (2/2)
”I'll get it next week,” Nash shot back30 One night, possibly en route to this very talk, Nash was hurtling down the Merritt Parkway31 Poldy Flatto was riding with hiraduate students, knew that Nash orking on the eoat and have the pleasure of watching his reaction, hehtly, was also working on the proble with hiraduate students, knew that Nash orking on the eoat and have the pleasure of watching his reaction, hehtly, was also working on the proble wheel and al whether he had meant to say that Schwartz had solved the problem ”I didn't say that,” Flatto corrected ”I said I heard he orking on it”
”Working on it?” Nash replied, his whole body now the picture of relaxation ”Well, then there's nothing to worry about He doesn't have the insights I have”
Schwartz was indeed working on the same problem Later, after Nash had produced his solution, Schwartz wrote a book on the subject of iot half the idea independently, but I couldn't get the other half It's easy to see an approximate statement to the effect that not every surface can be exactly eot that idea and I was able to produce the proof of the easy half in a day But then I realized that there was a technical problem I worked on it for a month and couldn't see any way to make headway I ran into an absolute stone wall I didn't knohat to do Nash worked on that problem for two years with a sort of ferocious, fantastic tenacity until he broke through it32
Week after week, Nash would turn up in Levinson's office, much as he had in Spencer's at Princeton He would describe to Levinson what he had done and Levinson would show hier, a fellow Moore instructor, recalled: He'd show the solutions to Levinson The first few tiive up As he saw the probleet harder and harder, he applied himself more, and ood he was, sure, but on the other hand he didn't give up even when the problem turned out to be much harder than expected He put more andwhat enables oneprobleeniuses have been sprinters who have solved proble-distance runner If Nash defied von Neuames, he now took on the received wisdom of nearly a century He went into a classical domain where everybody believed that they understood as possible and not possible ”It took enore to attack these problems,” said Paul Cohen, a mathematician at Stanford University and a Fields reat confidence in his own intuition, indifference to criticise but now prominent and impermeable features of his personality - served hiht in his MIT office - froreat confidence in his own intuition, indifference to criticise but now prominent and impermeable features of his personality - served hiht in his MIT office - fro until 3:00 AM AM - and on weekends as well, with, as one observer said, ”no references but his own mind” and his ”supreme self-confidence” Schwartz called it ”the ability to continue punching the wall until the stone breaks” - and on weekends as well, with, as one observer said, ”no references but his own mind” and his ”supreme self-confidence” Schwartz called it ”the ability to continue punching the wall until the stone breaks”
The le-minded attack on the problem comes from Moser: The difficulty [that Levinson had pointed out], to anyone in his right mind, would have stopped them cold and caused them to abandon the problem But Nash was different If he had a hunch, conventional criticise It was totally uncanny nobody could understand how somebody like that could do it He was the only person I ever saith that kind of power, just brute mental power35
The editors of the Annals of Mathematics Annals of Mathematics hardly knehat to make of Nash's manuscript when it landed on their desks at the end of October 1954 It hardly had the look of a mathematics paper It was as thick as a book, printed by hand rather than typed, and chaotic It ineers than to mathematicians So they sent it to a mathematician at Brown University, Herbert Federer, an Austrian-born refugee froh only thirty-four, already had a reputation for high standards, superb taste, and an unusual willingness to tackle difficult manuscripts hardly knehat to make of Nash's manuscript when it landed on their desks at the end of October 1954 It hardly had the look of a mathematics paper It was as thick as a book, printed by hand rather than typed, and chaotic It ineers than to mathematicians So they sent it to a mathematician at Brown University, Herbert Federer, an Austrian-born refugee froh only thirty-four, already had a reputation for high standards, superb taste, and an unusual willingness to tackle difficult htly, as the most solitary of endeavors But when a serious mathematician announces that he has found the solution to an important problem, at least one other serious standing tradition that goes back hundreds of years, will set aside his oork for weeks and months at a time, as one foro of it and straighten everything out”37 Nash's manuscript presented Federer with a sensationally complicated puzzle and he attacked the task with relish Nash's manuscript presented Federer with a sensationally complicated puzzle and he attacked the task with relish
The collaboration between author and referee took e correspondence, many telephone conversations, and numerous drafts ensued Nash did not submit the revised version of the paper until nearly the end of the following sument to Federer was, by Nash's standards, effusive: ”I am profoundly indebted to H Federer, to whom may be traced most of the improvement over the first chaotic for professor at Chicago when Nash gave a lecture on his e theorem, remembers the audience's shocked reaction ”nobody believed his proof at first,” he recalled in 1995 ”People were very skeptical It looked like a [beguiling] idea But when there's no technique, you are skeptical You drea People did not challenge him publicly, but they talked privately”39 (Characteristically, Nash's report to his parents merely said ”talks ell”) (Characteristically, Nash's report to his parents merely said ”talks ell”)40 Gian-Carlo Rota, professor of mathematics and philosophy at MIT, confirreat experts on the subject told raduate students had proposed such an outlandish idea he'd throw him out of his office”41 The result was so unexpected, and Nash's methods so novel, that even the experts had tre what he had done Nash used to leave drafts lying around the MIT co and confused discussion between Aer, and Masatake Kuranishi+ (a mathematician at Columbia University who later applied Nash's result) in which each one tried to explain Nash's result to the other, withoutand confused discussion between Aer, and Masatake Kuranishi+ (a mathematician at Columbia University who later applied Nash's result) in which each one tried to explain Nash's result to the other, without much success43 Jack Schwartz recalled: Nash's solution was not just novel, but very mysterious, a ether In my explication of it I sort of looked at what happened and could generalize and give an abstract form and realize it was applicable to situations other than the specific one he treated But I didn't quite get to the bottom of it either44
Later, Heinz Hopf, professor of mathematics in Zurich and a past president of the International Mathereat loho knew everything about differential geo theorem in New York45 Usually Hopf's lectures were models of crystalline clarity Moser, as in the audience, recalled: ”So we thought, 'NOW we'll understand what Nash did' He was naturally skeptical He would have been an important validator of Nash's work But as the lecture went on, my God, Hopf was befuddled himself He couldn't convey a complete picture He was completely overwhelmed” Usually Hopf's lectures were models of crystalline clarity Moser, as in the audience, recalled: ”So we thought, 'NOW we'll understand what Nash did' He was naturally skeptical He would have been an important validator of Nash's work But as the lecture went on, my God, Hopf was befuddled himself He couldn't convey a complete picture He was coen Moser tried to get Nash to explain how he had overcoinally pointed out ”I did not learn so , 'You have to control this You have to watch out for that' You couldn't follow him But his written paper was complete and correct”47 Federer not only edited Nash's paper to make it more accessible, but also was the first to convince the mathematical community that Nash's theorem was indeed correct Federer not only edited Nash's paper to make it more accessible, but also was the first to convince the mathematical community that Nash's theorem was indeed correct
Martin's surprise proposal, in the early part of 1953, to offer Nash a per the eighteen- Nash's strongest supporters But others, like Warren Aist, were opposed Moore Instructorshi+ps weren't meant to lead to tenure-track positions More to the point, Nash had made plenty of ene Nash's strongest supporters But others, like Warren Aist, were opposed Moore Instructorshi+ps weren't meant to lead to tenure-track positions More to the point, Nash had made plenty of enemies and few friends in his first year and a half His disdainful ues and his poor record as a teacher rubbedway his first year and a half His disdainful ues and his poor record as a teacher rubbedway
Mostly, however, Nash's opponents were of the opinion that he hadn't proved he could produce Whitehead recalled, ”He talked big Some of us were not sure he could live up to his claily, felt similarly Even Nash's champions could not have been completely certain Flatto remembered one occasion on which Nash came to Levinson's office to ask Levinson whether he'd read a draft of his e paper Levinson said, ”To tell you the truth I don't have enough background in this area to pass judgly, felt similarly Even Nash's champions could not have been completely certain Flatto remembered one occasion on which Nash came to Levinson's office to ask Levinson whether he'd read a draft of his e paper Levinson said, ”To tell you the truth I don't have enough background in this area to pass judgment”50 When Nash finally succeeded, A would do His applause was as loud as or louder than anyone else's The bantering beca hiswas the purest, most beautiful tone he had ever heard51
PART TWO
Separate Lives
CHAPTER 21
Singularity
Nash was leading all these separate lives Completely separate lives
- ARTHUR M MATTUCK, 1997
ALL THROUGH HIS CHILDHOOD, adolescence, and brilliant student career, Nash had seeely to live inside his own head, iether His overriding interest was in patterns, not people, and his greatest need was , to the largest possible extent, the resources of his oerful, fearless, fertile mind His apparent lack of ordinary hu, ahis own uniqueness He thought of himself as a rationalist, a free thinker, a sort of Spock of the starshi+p Enterprise Enterprise But now, as he entered early adulthood, this unfettered persona was shown to be partly a fiction or at least partly superseded In those first years at MIT, he discovered that he had some of the sa, and episodic connections that had once sufficed no longer served In five short years, between the ages of twenty-four and twenty-nine, Nash became emotionally involved with at least three other men He acquired and then abandoned a secret mistress who bore his child And he courted - or rather was courted by - a woman who became his wife But now, as he entered early adulthood, this unfettered persona was shown to be partly a fiction or at least partly superseded In those first years at MIT, he discovered that he had some of the sa, and episodic connections that had once sufficed no longer served In five short years, between the ages of twenty-four and twenty-nine, Nash became emotionally involved with at least three other men He acquired and then abandoned a secret mistress who bore his child And he courted - or rather was courted by - a woman who became his wife
As these initial intimate connections multiplied and became ever-present elements in his consciousness, Nash's formerly solitary but coherent existence became at once richer and more discontinuous, separate and parallel existences that reflected an emented and contradictory self The others on whom he now depended occupied different co periods, knew nothing of one another or of the nature of the others' relation to Nash Only Nash was in the know His life resembled a play in which successive scenes are acted by only two characters One character is in all of thees froer to exist when he disappears from the boards
More than a decade later, when he was already ill, Nash hi the MIT years, a e of mathematics: B B squared -I- RTF = 0, a ”very personal” equation Nash included in a 1968 postcard that begins, ”Dear Mattuck, Thinking that you will understand this concept better than most I wish to explain ” The equation represents a three-diin, in four-diularity, the special point, and the other variables are people who affected him - in this instance, men hom he had friendshi+ps or relationshi+ps squared -I- RTF = 0, a ”very personal” equation Nash included in a 1968 postcard that begins, ”Dear Mattuck, Thinking that you will understand this concept better than most I wish to explain ” The equation represents a three-diin, in four-diularity, the special point, and the other variables are people who affected him - in this instance, men hom he had friendshi+ps or relationshi+ps1 Inevitably, the accretion of significant relationshi+ps with others brings with it de to choose Nash had little desire to choose one e, he could avoid, or at least minimize, both dependence and demands To satisfy his own emotional needs for connectedness meant he inevitably made others look to him to satisfy theirs Yet while he was preoccupied with the effect of others on hirasp - his effect on others He had in fact nochild He wished the others to be satisfied with his genius -”I thought I was such a greatback at this period - and, of course, to some extent they were satisfied But when people inevitably wanted or needed more he found the strains unbearable
CHAPTER 22
A Special Friendshi+p Santa Monica, Summer 1952 Santa Monica, Summer 1952
Away from contact with a few special sorts of individuals I am lost, lost completely in the wilderness so, so, so, it's been a hard life in many ways
- JOHN F FORBES N NASH, JR, 1965
AFTER J JOHN N NASH LOST EVERYTHING - family, career, the ability to think about mathematics - he confided in a letter to his sister Martha that only three individuals in his life had ever brought him any real happiness: three ”special sorts of individuals” hom he had formed ”special friendshi+ps” - family, career, the ability to think about mathematics - he confided in a letter to his sister Martha that only three individuals in his life had ever brought him any real happiness: three ”special sorts of individuals” hom he had formed ”special friendshi+ps”1 Had Martha seen the Beatles' filht? ”They see,” he wrote ”Of course they are er like the sort of person I've irls that love the Beatles so wildly since they see to ,” he wrote ”Of course they are er like the sort of person I've irls that love the Beatles so wildly since they see to me”2 Nash's first loves were one-sided and unrequited ”Nash was always for intense friendshi+ps with men that had a romantic quality,” Donald Newman observed in 1996 ”He was very adolescent, alith the boys”3 Some were inclined to see Nash's infatuations' as ”experiments,” or simple expressions of his immaturity - a view that he may well have held himself ”He played around with it because he liked to play around He was very experimental, very try-outish,” said Newman in 1996 ”Mostly he just kissed” Some were inclined to see Nash's infatuations' as ”experiments,” or simple expressions of his immaturity - a view that he may well have held himself ”He played around with it because he liked to play around He was very experimental, very try-outish,” said Newman in 1996 ”Mostly he just kissed”4 Newman, who liked to joke about his past and future fee because Nash was, for a time, infatuated with him - with predictable results ”He used to talk about how Donald looked all the tie because Nash was, for a time, infatuated with him - with predictable results ”He used to talk about how Donald looked all the time,” Mrs New around witharound in Newman's white Thunderbird when Nash kissed hihed it off Newaround in Newman's white Thunderbird when Nash kissed hihed it off7 Nash's first experience of mutual attraction - ”special friendshi+ps,” as he called them - occurred in Santa Monica8 It was the very end of the summer of 1952, It was the very end of the summer of 1952, after Milnor had moved out and Martha had flown back ho in the last days of August, just before he was due to leave for Boston, and very furtive But it was nonetheless decisive because for the first time he found not rejection but reciprocity Thus it was the first real step out of his extreme emotional isolation and the world of relationshi+ps that were purely iinary, a first taste of intiestive of hitherto unsuspected satisfactions after Milnor had moved out and Martha had flown back ho in the last days of August, just before he was due to leave for Boston, and very furtive But it was nonetheless decisive because for the first time he found not rejection but reciprocity Thus it was the first real step out of his extreme emotional isolation and the world of relationshi+ps that were purely iinary, a first taste of intiestive of hitherto unsuspected satisfactions
The only traces of Nash's friendshi+p with Ervin Thorson that remain are his description of him as a ”special” friend in his 1965 letter and a series of elliptical references to ”T” in letters in the late 1960s9 Few if any of Nash's acquaintances met hiht on the couch of their Georgina Avenue apartment, but not his name Few if any of Nash's acquaintances met hiht on the couch of their Georgina Avenue apartment, but not his name10 Thorson, who died in 1992, was thirty years old in 195211 He was a native Californian of Scandinavian extraction Nash described hiineer, but he may in fact have been an applied ist in the Ar the war Afterward, he earned a las Aircraft in 1951, just a few years after Douglas had spun off its R&D division to form the RAND Corporation He was a native Californian of Scandinavian extraction Nash described hiineer, but he may in fact have been an applied ist in the Ar the war Afterward, he earned a las Aircraft in 1951, just a few years after Douglas had spun off its R&D division to for the future of interplanetary travel for the Pentagon, and Thorson, who eventually led a research team, was very likely involved in these efforts At that ti the future of interplanetary travel for the Pentagon, and Thorson, who eventually led a research teareat passion, conceived twenty years before the United States launched His great passion, conceived twenty years before the United States launched Viking, Viking, was the drea Mars, his sister Nelda Trout Mars, his sister Nelda Troutman recalled in 1997
Thorson was, his sister said, ”very high strung, not a social person at all, very bright, knew a lot, very very acadeiven the close ties between Douglas and RAND, which was also heavily involved in studies of space exploration - at a talk or seminar, or perhaps even at one of the parties that John Williaave Nash could easily have las and RAND, which was also heavily involved in studies of space exploration - at a talk or seminar, or perhaps even at one of the parties that John Williaave
If Thorson, who neversister did not know it15 With his family, at any rate, he was unusually closehly classified, but about all aspects of his personal life With his family, at any rate, he was unusually closehly classified, but about all aspects of his personal life16 Given thepressure to root out ho the McCarthy era, Thorson would have had to practice great discretion in any case; his career at Douglas was to last for another fifteen years Given thepressure to root out ho the McCarthy era, Thorson would have had to practice great discretion in any case; his career at Douglas was to last for another fifteen years17 When he abruptly resigned froe of forty-seven because he feared dying Several of his colleagues had recently died of heart attacks and Thorson, who had some sort of mild heart condition, decided he couldn't cope with the stress and overwork anymore He moved back to his hometown of Pomona and became a virtual recluse except for an active involve with his parents for the next twenty-five years until his death When he abruptly resigned froe of forty-seven because he feared dying Several of his colleagues had recently died of heart attacks and Thorson, who had some sort of mild heart condition, decided he couldn't cope with the stress and overwork anymore He moved back to his hometown of Pomona and became a virtual recluse except for an active involve with his parents for the next twenty-five years until his death
Whether Nash and Thorson saw each other again when Nash returned to Santa Monica for a third summer two years later or on one of his trips to Santa Monica during his illness in the early and mid-1960s is not known But Nash continued to think of Thorson and to refer to him obliquely until at least 1968