Part 9 (1/2)

A Slow Fire Burning

CHAPTER 30

Olden Lane and Washi+ngton Square 1956-57 1956-57

Matheinate in eins to live a peculiar life of its own and is better cooverned almost entirely by aesthetical motivationsAs a mathematical discipline travels, or after enerationwhenever this stage is reached, the only re return to the source: the reinfection of more or less directly empirical ideas

- JOHN VON N NEUMANN

THE I INStitUTE FOR A ADVANCED S STUDY, nestled on Princeton's fringes on what had been a farm, was a scholar's dream It was bordered by woods and the Delaware-Raritan Canal, its laere immaculate, and one of its streets was Einstein Drive It was also blessedly free of students The atmosphere in the Fuld Hall common room resembled that of a venerable led scents of leather and pipe tobacco; its doors were never locked and its lights burned far into the night nestled on Princeton's fringes on what had been a farm, was a scholar's dream It was bordered by woods and the Delaware-Raritan Canal, its laere immaculate, and one of its streets was Einstein Drive It was also blessedly free of students The atmosphere in the Fuld Hall common room resembled that of a venerable led scents of leather and pipe tobacco; its doors were never locked and its lights burned far into the night

In 1956, the Institute's permanent faculty were not many more than a dozen mathematicians and theoretical physicists1 They were, however, outnuuished te Oppenheimer to call it ”an intellectual hotel” They were, however, outnuuished te Oppenhei researchers, the Institute was a golden opportunity to escape the onerous de and administration, and, indeed, the tasks of everyday life Everything was provided the visitor: an apart round of seminars, lectures, and, for those so inclined, parties where the booze was plentiful and where one could glilass in an artificial hand, or witness a very drunk Frenchskills by rope-cli researchers, the Institute was a golden opportunity to escape the onerous de and administration, and, indeed, the tasks of everyday life Everything was provided the visitor: an apart round of seminars, lectures, and, for those so inclined, parties where the booze was plentiful and where one could glilass in an artificial hand, or witness a very drunk Frenchskills by rope-cli up and over the fireplace ned to re Paul Cohen, a mathereat place that you had to stay at least two years It took one year just to learn hoork under such ideal conditions” rereat place that you had to stay at least two years It took one year just to learn hoork under such ideal conditions”4 By 1956, Einstein was dead, Godel was no longer active, and von Neu in Bethesda Oppenheimer was still director, but ly isolated As one mathematician said, ”The Institute had become pure, very pure” By 1956, Einstein was dead, Godel was no longer active, and von Neu in Bethesda Oppenheimer was still director, but ly isolated As one mathematician said, ”The Institute had become pure, very pure”5 Cathleen Morawetz, later president of the American Mathematical Society, put it more bluntly: ”The Institute was known to be about the dullest place you could find” Cathleen Morawetz, later president of the American Mathematical Society, put it more bluntly: ”The Institute was known to be about the dullest place you could find”6 By contrast, the Courant Institute of Mathematical Sciences at New York University was ”the national capital of applied azine was soon to inforazine was soon to infory, Courant occupied a nineteenth-century loft less than a block to the east of Washi+ngton Square in a neighborhood that, despite the university's growing presence, was still do concerns Indeed, Courant initially shared the premises - with its fire escapes and creaky old-fashi+oned freight elevator - with a number of hat factories Just a few years old and vibrant with energy, Courant occupied a nineteenth-century loft less than a block to the east of Washi+ngton Square in a neighborhood that, despite the university's growing presence, was still do concerns Indeed, Courant initially shared the premises - with its fire escapes and creaky old-fashi+oned freight elevator - with a nu for the institute had co for a horeat uard, occupied 25 Waverly Place Financing for the institute had co for a horeat uard, occupied 25 Waverly Place9 The institute was the creation of one of reat entrepreneurs, Richard Courant, a German Jewish professor of en in the mid-1950s by the nazis10 Short, rotund, autocratic, and irrepressible, Courant was famous for his fascination with the rich and powerful, his penchant for falling in love with his fe mathematical talent When Courant arrived in 1937, New York University had noof Undaunted, Courant i funds His own stellar reputation, the anti-Semitism of the American educational establishment, and New York's ”deep reservoir of talent,” enabled him to attract brilliant students, most of them New York City Jeere shut out of the Harvards and Princetons Short, rotund, autocratic, and irrepressible, Courant was famous for his fascination with the rich and powerful, his penchant for falling in love with his fe mathematical talent When Courant arrived in 1937, New York University had noof Undaunted, Courant i funds His own stellar reputation, the anti-Semitism of the American educational establishment, and New York's ”deep reservoir of talent,” enabled him to attract brilliant students, most of them New York City Jeere shut out of the Harvards and Princetons11 The advent of World War II brought more money and more students, and by the mid-1950s, when the institute was for more established e The advent of World War II brought more money and more students, and by the mid-1950s, when the institute was for more establishedstars included Peter Lax and his wife, Anneli, Cathleen Synge Morawetz, Juirgen Moser, and Louis Nirenberg, and a its stellar visitors were Lars Hor, ould soonstars included Peter Lax and his wife, Anneli, Cathleen Synge Morawetz, Juirgen Moser, and Louis Nirenberg, and a its stellar visitors were Lars Hor, ould soon move to Harvard

The Courant Institute was practically on Nash's doorstep and, given its lively at at least as much time there as at the Institute for Advanced Study At first Nash would stop by for an hour or two before driving down to Princeton, but he soon found hi the whole day13 He never came too early, for he liked to sleep late after He never ca into the wee hours at the university library working into the wee hours at the university library14 But he was al's penultimate floor But he was al's penultiroup with little taste for the competitiveness of MIT or the snobbery of the Institute, it was happy to have hiers, who recalled that Nash liked to pace around on one of the building's fire escapes, said, ”He was just a delight There was a wit and huhly unstandard There was a wonderful playful quality, a lightness”16 Cathleen Morawetz, the daughter of John Synge, Nash's professor at Carnegie, assumed Nash was just another postdoctoral fellow and found hi,” ”an attractive fellow,” ”a lively conversationalist” Cathleen Morawetz, the daughter of John Synge, Nash's professor at Carnegie, assumed Nash was just another postdoctoral fellow and found hi,” ”an attractive fellow,” ”a lively conversationalist”17 Hormander recalled his first impressions: ”He wore a serious expression Then he'd break out into a sudden smile He was an enthusiast” Hormander recalled his first impressions: ”He wore a serious expression Then he'd break out into a sudden smile He was an enthusiast”18 Peter Lax, who had spent the war at Los Alamos, was interested in Nash's research and ”his oay of looking at things” Peter Lax, who had spent the war at Los Alamos, was interested in Nash's research and ”his oay of looking at things”19 At first, Nash seemed more interested in the political cataclysms of that fall - Nasser nationalized the Suez Canal, proland, France, and Israel, the Russians crushed the Hungarian uprising, and Eisenhower and Stevenson were again battling for the presidency - than in pursuing mathematical conversations ”He'd be in the co of his views of the political situation Fro opinions on the Suez crisis, which was going on at that time”20 Another mathematician re roorab Suez, and Eisenhower had not made his position unmistakably clear (if he ever did), one day at lunch Nash started in on Suez Of course, Nasser wasn't black, but he was dark enough for Nash 'What you have to do with these people is to take a firm hand, and then once they realize you mean it ' ” Another mathematician re roorab Suez, and Eisenhower had not made his position unmistakably clear (if he ever did), one day at lunch Nash started in on Suez Of course, Nasser wasn't black, but he was dark enough for Nash 'What you have to do with these people is to take a firm hand, and then once they realize you hts at Courant were very ress, stimulated by World War II, in certain kinds of differential equations that serve as mathematicalsoe22 By the mid-fifties, as By the mid-fifties, as Fortune Fortune noted,ordinary differential equations using co most nonlinear partial differential equations that crop up when large or abrupt changes occur - such as equations that describe the aerodynamic shock waves produced when a jet accelerates past the speed of sound In his 1958 obituary of von Neumann, who did important work in this field in the thirties, Stanislaw Ula analytically,” saying that they ”defy even qualitative insights by present methods” noted,ordinary differential equations using co most nonlinear partial differential equations that crop up when large or abrupt changes occur - such as equations that describe the aerodynamic shock waves produced when a jet accelerates past the speed of sound In his 1958 obituary of von Neumann, who did important work in this field in the thirties, Stanislaw Ula analytically,” saying that they ”defy even qualitative insights by present methods”23 As Nash was to write that same year, ”The open problems in the area of non-linear partial differential equations are very relevant to applied mathematics and science as a whole, perhaps more so than the open problems in As Nash was to write that same year, ”The open problems in the area of non-linear partial differential equations are very relevant to applied mathematics and science as a whole, perhaps more so than the open problems in any other area of mathematics, and this field seems poised for rapid development It seems clear however that fresh methods must be employed” any other area of mathematics, and this field seems poised for rapid development It seems clear however that fresh methods must be employed”24 Nash, partly because of his contact with Wiener and perhaps his earlier interaction with Weinstein at Carnegie, was already interested in the probleas or liquid over any uneven surface, like water rushi+ng into a bay, heat or electrical charges traveling through round pool, or clouds ski over an air mass It should be possible to model such motion mathematically But it turns out to be extremely difficult As Nash wrote: Turbulence refers to the flow of gas or liquid over any uneven surface, like water rushi+ng into a bay, heat or electrical charges traveling through round pool, or clouds ski over an air mass It should be possible to model such motion mathematically But it turns out to be extremely difficult As Nash wrote: Little is known about the existence, uniqueness and seneral equations of flow for a viscous, co fluid These are a non-linear parabolic system of equations An interest in these questions led us to undertake this work It beca could be done about the continuueneral fluid floithout the ability to handle non-linear parabolic equations and that this in turn required an a priori a priori estimate of continuity esti, a short, e of Courant's, who handed Nash a major unsolved problem in the then fairly new field of nonlinear theory27 Nirenberg, also in his twenties, and already a fore ”He'd often see of a private joke, as if he was laughing at a private joke that he never [told anyone about]” Nirenberg, also in his twenties, and already a fore ”He'd often see of a private joke, as if he was laughing at a private joke that he never [told anyone about]”28 But he was extremely i his eht be theproblem that had been open since the late 1930s But he was extremely i his eht be theproblem that had been open since the late 1930s

He recalled: I worked in partial differential equations I also worked in geometry The problem had to do with certain kinds of inequalities associated with elliptic partial differential equations The problem had been around in the field for some time and a number of people had worked on it Someone had obtained such estimates much earlier, in the 1930s in two dimensions But the probleher di on the probleh he knocked on doors until he was satisfied that the proble claimed30 Lax, as one of those he consulted, commented recently: ”In physics everybody knows the most important problems They are well defined Not so in h, it had to be important in the opinion of others” Lax, as one of those he consulted, commented recently: ”In physics everybody knows the most important problems They are well defined Not so in h, it had to be i to Nirenberg's office to discuss his progress But it eeks before Nirenberg got any real sense that Nash was getting anywhere ”We would meet often Nash would say, 'I seem to need such and such an inequality I think it's true that'” Very often, Nash's speculations were far off the ave that ih” would meet often Nash would say, 'I seem to need such and such an inequality I think it's true that'” Very often, Nash's speculations were far off the ave that ih”32 Nirenberg sent Nash around to talk to Lars Hormander, a tall, steely Sas already one of the top scholars in the field Precise, careful, and ieable, Hormander knew Nash by reputation but reacted even”Nash had learned fro the Holder estimates known for second-order elliptic equations with two variables and irregular coefficients to higher dimensions,” Hormander recalled in 199733 ”He came to see me several times, 'What did I think of such and such an inequality?' At first, his conjectures were obviously false [They were] easy to disprove by known facts on constant coefficient operators He was rather inexperienced in thesestandard techniques He was always trying to extract problems [from conversations with others] He had not the patience to [study them]” ”He came to see me several times, 'What did I think of such and such an inequality?' At first, his conjectures were obviously false [They were] easy to disprove by known facts on constant coefficient operators He was rather inexperienced in thesestandard techniques He was always trying to extract problems [from conversations with others] He had not the patience to [study therope, but with more success ”After a couple s that were not so obviously wrong”34 By the spring, Nash was able to obtain basic existence, uniqueness, and continuity theore novel methods of his own invention He had a theory that difficult problems couldn't be attacked frontally He approached the proble the nonlinear equations into linear equations and then attacking these by nonlinear enius,” said Lax, who followed the progress of Nash's research closely ”I've never seen that done I've always kept it in , maybe it ork in another circuot fartheoreenius36 Hor, a world-class specialist in partial differential equations, ienius to do that” Hor, a world-class specialist in partial differential equations, ienius to do that”37 Courant made Nash a handsome job offer38 Nash's reaction was a curious one Cathleen Synge Morawetz recalled a long conversation with Nash, who couldn't o back to MIT ”He said he opted to go to MIT because of the tax advantage” of living in Massachusetts as opposed to New York Nash's reaction was a curious one Cathleen Synge Morawetz recalled a long conversation with Nash, who couldn't o back to MIT ”He said he opted to go to MIT because of the tax advantage” of living in Massachusetts as opposed to New York39 Despite these successes, Nash was to look back on the year as one of cruel disappoint, Nash discovered that a then-obscure young Italian, Ennio De Giorgi, had proven his continuity theorem a few months earlier Paul Garabedian, a Stanford mathematician, was a naval attache in London It was an Office of Naval Research sinecure40 In January 1957, Garabedian took a long car In January 1957, Garabedian took a long car trip around Europe and looked up young mathematicians ”I saw some oldtimers in Rome,” he recalled ”It was a scene You'd talk mathematics for half an hour Then you'd have lunch for three hours Then a siesta Then dinner nobody i” But in Naples, soi up on his way back through Rouy But I found out he'd written this paper” trip around Europe and looked up young mathematicians ”I saw some oldtimers in Rome,” he recalled ”It was a scene You'd talk mathematics for half an hour Then you'd have lunch for three hours Then a siesta Then dinner nobody i” But in Naples, soi up on his way back through Rouy But I found out he'd written this paper”

De Giorgi, who died in 1996, came from a very poor family in Lecce in southern Italy41 Later he would becoeneration He had no life outside mathematics, no family of his own or other close relationshi+ps, and, even later, literally lived in his office Despite occupying the ious mathematical chair in Italy, he lived a life of ascetic poverty, co, and, as ti preoccupation with mysticism that led hih eneration He had no life outside mathematics, no family of his own or other close relationshi+ps, and, even later, literally lived in his office Despite occupying the ious mathematical chair in Italy, he lived a life of ascetic poverty, co, and, as ti preoccupation with mysticism that led hih i's paper had been published in the ional acadei's results in the Office of Naval Research's European newsletter

Nash's own account, written after he had won the nobel for his work in game theory, conveys the acute disappoint sufficiently infor in the area, it happened that I orking in parallel with Ennio De Giorgi of Pisa, Italy And De Giorgi was first actually to achieve the ascent of the suuratively described proble case of ”elliptic equations”42

Nash's vieas perhaps overly subjective Mathe first is, how one gets to one's destination is often as iet Nash's as alh But this was not how Nash saw it Gian-Carlo Rota, a graduate student at Yale who spent that year at Courant, recalled in 1994: ”When Nash learned about De Giorgi he was quite shocked Soht he cracked up because of that”43 When De Giorgi came to Courant that summer and he and Nash stone” When De Giorgi came to Courant that summer and he and Nash stone”44 Nash left the Institute for Advanced Study on a fractious note In early July he apparently had a serious arguh, at any rate, to warrant a lengthy letter of apology from Nash to Oppenheiize fore discussed quanturessive”45 After calling his own behavior unjustified, Nash nonetheless i ” his own behavior unjustified, Nash nonetheless i ”most physicists (also some mathe of their tendency to treat ”anyone with any sort of questioning attitude or a belief in 'hidden paranorant person” who have studied Quantu of their tendency to treat ”anyone with any sort of questioning attitude or a belief in 'hidden paranorant person”

Nash's letter to Oppenheiun to think seriously of atte's uncertainty principle: Now I ainal 1925 paperThis strikes reat difference between expositions of ”matrix mechanics,” a difference, which froinal46

”I embarked on [a project] to revise quantum theory,” Nash said in his 1996 Madrid lecture ”It was not a priori absurd for a non-physicist Einstein had criticized the indeter”47 He apparently had devoted what little time he spent at the Institute for Advanced Study that year talking with physicists and mathe is not clear: Freeman Dyson, Hans Lewy, and Abraham Pais were in residence at least one of the tery to Oppenhei at the tienda quite clear ”Topaper is its restriction to the observable quantities,” he wrote, adding that ”I want to find a different andunder-picture of a non-observable reality” Nash's letter of apology to Oppenhei at the tienda quite clear ”Topaper is its restriction to the observable quantities,” he wrote, adding that ”I want to find a different andunder-picture of a non-observable reality”49 It was this attempt that Nash would blaering hishis attempt to resolve the contradictions in quantum theory, on which he e and psychologically destabilizing”50

CHAPTER 31

The Bo a loner and innovative? Isn't that fine? But the [lone genius] has the saenius] has the sah school doing science projects, fine But if he s too isolated and he's school doing science projects, fine But if he s too isolated and he's disappointed in soht can precipitate disappointed in soht can precipitate - PAUL H HOWARD, M McLean H Hospital

JuRGEN M MOSER had joined the M I T faculty in the fall of 1957 and was living with his wife, Gertrude, and his stepson, Richy, in a tiny rented house to the west of Boston in Needhae Needham was then more exurb than suburb, still predoazing, all of which Moser, a nature lover, was fond That October and Nove at dusk with eleven-year-old Richy, clireat dirt mound behind their house, and wait for had joined the M I T faculty in the fall of 1957 and was living with his wife, Gertrude, and his stepson, Richy, in a tiny rented house to the west of Boston in Needhae Needham was then more exurb than suburb, still predoazing, all of which Moser, a nature lover, was fond That October and Nove at dusk with eleven-year-old Richy, clireat dirt mound behind their house, and wait for Sputnik - a Sputnik - a tiny silvery dot reflecting the sun's last rays - to pass slowly over Boston tiny silvery dot reflecting the sun's last rays - to pass slowly over Boston1 Having calculated the satellite's precise orbit, Moser always knehen it would appear on the horizon Having calculated the satellite's precise orbit, Moser always knehen it would appear on the horizon

Very often, he would still be thinking of the afternoon's conversation with Nash Nash drove out to Needham often Despite their very different tereat respect for each other Moser, who thought Nash's ieneralized and applied to celestialNash, in turn, was interested in Moser's ideas about nonlinear equations Richard E very much a part of our life He used to coen They would walk and talk together and spend tiinable There could be no interruptions An interruption was an absolute sin, a violation en and Nash met, it was very intense I always had to be quiet”2 Returning to Cae in late summer, Nash and Alicia found an apartment with some difficulty3 They each paid half the rent, for they had decided not to pool their funds They each paid half the rent, for they had decided not to pool their funds4 Alicia got a job as a physics researcher at Technical Operations, one of the s Route 128 Alicia got a job as a physics researcher at Technical Operations, one of the s Route 1285 She also enrolled in a course on quantuht by J CSlater She also enrolled in a course on quantuht by J CSlater

They quickly settled into the pleasant private and social rituals of a newly married academic couple Alicia almost never cooked She would meet Nash on the campus after work, they would eat out with one or more of Nash'sat a lecture, concert, or so6 Aliciapeople, so Mattuck and Bricker, so, and, increasingly, other young couples like theers and his wife, Adrienne, and Gian-Carlo Rota and his wife, Terry Aliciapeople, so Mattuck and Bricker, so, and, increasingly, other young couples like theers and his wife, Adrienne, and Gian-Carlo Rota and his wife, Terry

When they ith other people, Nash talked to the mathematicians, Alicia to the wives or Emma Yet her attention was always focused on Nash: what he was saying, how he looked, how others reacted to him He too, see her That he wasn't especially nice to her, or generous, s happen