A Beautiful Mind

by Sylvia Nasar

  Such guilt would be a heavy burden to bear. More likely, it was not just the feeling of guilt, but also the more potent threat of losing his mother’s love on the heels of the actual loss of his father, that would have placed tremendous pressure on Nash to act. Virginia felt that Nash was duty bound to legitimize his relationship to his son. John Sr. had an abhorrence of scandal and a strong belief in doing one’s duty. Whether, by the time of her husband’s death, Virginia still persisted in the demand that Nash marry Eleanor isn’t clear. It may be that her contact with Eleanor — including the evidence of Eleanor’s lower-class origins, her lack of education, or her threats to make trouble for Nash — convinced her that even a temporary marriage was out of the question. She may have feared that Eleanor would never agree to a divorce. Or simply, she may have realized that she had no way of forcing Nash to do something that he did not wish to do.

  If Virginia reacted so to Nash’s mistress and- illegitimate son, how might she react to the far more disturbing facts of Nash’s liaisons with other men? As a practical matter, the likelihood of her ever finding out about the arrest seemed negligible. Yet that too must have crossed Nash’s mind. His confidence that he could keep his secret lives completely separate and keep his parents in the dark as well was jolted by Eleanor’s betrayal. He must have felt on his neck the hot breath of other potential discoveries.

  In addition to commuting to the Institute in Princeton, Nash was spending a good deal of time at New York University, whose campus began a block north of Bleecker Street, at the Courant Institute of Mathematical Sciences. One afternoon, very soon after his father’s funeral, Nash stopped at the desk of the beautiful Natasha Artin, the wife of Emil Artin and one of Richard Courant’s assistants. A famously gorgeous creature, Natasha had a doctorate from the University of Berlin, where she’d been a student of Artin’s before they married. Everyone knew that she was the latest object of Courant’s infatuation. Nash liked to chat with her on his way up to tea.

  “I wonder how easy it is to get a divorce in New Jersey,” he said out of the blue one day to her.14 Natasha immediately took this for a declaration that he intended to get married. She found it quite typical of Nash to investigate the exit doors even as he was hovering near the entrance.

  On another occasion, Nash gave a lecture at Chicago and had dinner afterward with Leo Goodman, a mathematician he knew from the graduate-school days in Princeton. He told Goodman that he thought Alicia would make a fine wife. Why? Because she watched so much television. That meant, he felt, that she wouldn’t require much attention from him.15 The exchange brings to mind Eleanor’s oft-repeated remark about Nash: “he always wanted something for nothing.”

  Alicia has insisted that she cannot remember when Nash proposed or whether he did so in person or by letter.16 They simply had an understanding, she said. But Alicia’s actions that fall belie her later account. After Nash had left Cambridge in June, Alicia stayed on, desperately unhappy. All this suggests the opposite of any “understanding.”

  Alicia’s letter to Joyce Davis on October 23, 1956, does not mention Nash at all. Presumably, if they’d gotten formally engaged by that date, Alicia would have announced the fact to Joyce.

  As you might know I’ve been looking for a job in New York and had applied to several places. At first I was afraid things might prove difficult but so far I’ve already had offers from Brookhaven, as a junior physicist with the reactor group, and from the Nuclear Development Corporation of America also in the reactor field. I’m accepting the latter at $450 per month. I’m told I might get $500 some other place but I think N.D.C. offers good experience and I’ve always wanted to do nuclear physics specifically.17

  It’s possible that Alicia would have left school and gotten a job regardless of the state of her relationship with Nash. She was increasingly unenthusiastic about attending graduate school. “I’m tired of the studying and procrastinating routine… . All I know is I want to ’LIVE.’ ” Since she had gone to high school in New York, it would have been natural for her to think of returning there to work. But Alicia herself said later that she moved to New York on Nash’s account. She may have gone there in the hopes of renewing her relationship with him. She may have gone at his express invitation.

  Alicia moved into the Barbizon Hotel, the legendary hotel for young women that is the setting of Sylvia Plath’s fifties novel The Bell far. References were required to obtain lodging there. And the rooms, tiny and white with metal beds, were only for sleeping, Alicia complained in a PS to Joyce.18 “This hotel — the Amazon — was for women only,” writes Plath, who spent the summer of 1952 in residence, “and they were mostly girls my age with wealthy parents who wanted to be sure their daughters would be living where men couldn’t get at them and deceive them; and they were all going to posh secretarial schools like Katy Gibbs, where they had to wear hats and stockings and gloves to class, or … simply hanging around in New York waiting to get married to some career man or other.”19

  Whether or not Alicia came to New York as Nash’s fiancée at the end of October, she visited Nash’s family in Roanoke that Thanksgiving.20 Nash did not give her a ring, however. He had some idea, typically odd and pennypinching, that he wanted to buy one in Antwerp, directly from a diamond wholesaler.21

  Virginia found Alicia charming and dignified and was impressed by Alicia’s obvious devotion to Nash, but at the same time she thought her quite different from the sort of girl she had imagined for her son’s bride.22 She thought the relationship between the two strange. Alicia was a physicist who talked about her job at a nuclear reactor company and displayed no interest in anything domestic, a young woman completely out of Virginia’s ken. While Virginia and Martha busied themselves in the kitchen, Alicia and Nash spent most of Thanksgiving Day sitting on the floor of Virginia’s living room poring over stock quotations. Martha’s reaction was similar to her mother’s. (At Virginia’s insistence, and thinking it might turn Alicia’s head in the right direction, Martha took Alicia shopping in Roanoke one afternoon to buy a hat.)

  The wedding took place on an unexpectedly mild, gray February morning in Washington, D.C., at St. John’s, the yellow-and-white Episcopal church across Pennsylvania Avenue from the White House.23’ Nash, by then an atheist, balked at a Catholic ceremony. He would have been happy to get married in city hall. Alicia wanted an elegant, formal affair. It was a small wedding. There were no mathematicians or old school friends present, only immediate family. Charlie, his brother-in-law, whom Nash hardly knew, was best man. Martha was matron of honor. Bride and groom were both late, having been held up at the portrait photographers. Nash and Alicia drove to Atlantic City for a weekend honeymoon on the way back to New York. It wasn’t a success. Alicia hadn’t been feeling well, Nash wrote in a postcard to his mother.24

  In April, two months later, Alicia and Nash threw a party to celebrate their marriage. They were living in a sublet apartment on the Upper East Side, around the corner from Bloomingdale’s. About twenty people came, mostly mathematicians from Courant and the Institute for Advanced Study and several of Alicia’s-cousins, including Odette and Enrique. “They seemed very happy,” Enrique Larde later recalled. “It was a great apartment. They were just showing off their new marriage. He looked very handsome. It seemed very romantic.”25

  PART THREE

  A Slow Fire Burning

  30

  Olden Lane and Washington Square 1956-57

  Mathematical ideas originate in empirics… . But, once they are so conceived, the subject begins to live a peculiar life of its own and is better compared to a creative one, governed almost entirely by aesthetical motivations… . As a mathematical discipline travels, or after much “abstract” inbreeding, [it] is in danger of degeneration… . whenever this stage is reached, the only remedy seems to me to be the rejuvenating return to the source: the reinfection of more or less directly empirical ideas.

  — JOHN VON NEUMANN

  THE INSTITUTE FOR ADVANCED STUDY, nestled on P
rinceton’s fringes on what had been a farm, was a scholar’s dream. It was bordered by woods and the Delaware-Raritan Canal, its lawns were 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 men’s club, with its newspaper racks and mingled 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 physicists.1 They were, however, outnumbered sixfold by a host of distinguished temporary visitors from around the globe, prompting Oppenheimer to call it “an intellectual hotel.”2 For young researchers, the Institute was a golden opportunity to escape the onerous demands of teaching and administration, and, indeed, the tasks of everyday life. Everything was provided the visitor: an apartment less than a few hundred yards from an office, an unending round of seminars, lectures, and, for those so inclined, parties where the booze was plentiful and where one could glimpse Lefschetz balancing a martini glass in an artificial hand, or witness a very drunk French mathematician displaying his mountaineering skills by rope-climbing up and over the fireplace mantel.3

  Some found the idyllic setting, carefully designed to remove all impediments to creativity, vaguely disquieting. Paul Cohen, a mathematician at Stanford University, remarked, “It was such a great place that you had to stay at least two years. It took one year just to learn how to work under such ideal conditions.”4 By 1956, Einstein was dead, Gödel was no longer active, and von Neumann lay dying in Bethesda. Oppenheimer was still director, but much humbled by the McCarthyite inquisitions and increasingly 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.”6

  By contrast, the Courant Institute of Mathematical Sciences at New York University was “the national capital of applied mathematical analysis,” as Fortune magazine was soon to inform its readers.7 Just a few years old and vibrant with energy, Courant occupied a nineteenth-century loft less than a block to the east of Washington Square in a neighborhood that, despite the university’s growing presence, was still dominated by small manufacturing concerns. Indeed, Courant initially shared the premises — with its fire escapes and creaky old-fashioned freight elevator — with a number of hat factories.8 Financing for the institute had come from the Atomic Energy Commission, which had been hunting for a home for its giant Univac 4 computer. At the time, this great mass of vacuum tubes, with its armed guard, occupied 25 Waverly Place.9

  The institute was the creation of one of mathematics’ great entrepreneurs, Richard Courant, a German Jewish professor of mathematics who had been driven out of Göttingen in the mid-1950s by the Nazis.10 Short, rotund, autocratic, and irrepressible, Courant was famous for his fascination with the rich and powerful, his penchant for falling in love with his female “assistants,” and his unerring eye for young mathematical talent. When Courant arrived in 1937, New York University had no mathematics worth speaking of. Undaunted, Courant immediately set about raising 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 Jews who were shut out of the Harvards and Princetons.11 The advent of World War II brought more money and more students, and by the mid-1950s, when the institute was formally founded, it was already rivaling more established mathematical centers like Princeton and Cambridge.12 Its young stars included Peter Lax and his wife, Anneli, Cathleen Synge Morawetz, Jüirgen Moser, and Louis Nirenberg, and among its stellar visitors were Lars Hörmander, a future Fields medalist, and Shlomo Sternberg, who would soon move to Harvard.

  The Courant Institute was practically on Nash’s doorstep and, given its lively atmosphere, it was not surprising that Nash was soon spending 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 himself staying the whole day.13 He never came too early, for he liked to sleep late after working into the wee hours at the university library.14 But he was almost always there for teatime in the lounge on the building’s penultimate floor.15

  As for the Courant crowd, a friendly, open group with little taste for the competitiveness of MIT or the snobbery of the Institute, it was happy to have him. Tilla Weinstein, a mathematician at Rutgers, 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 humor about him that was thoroughly 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 him “very charming,” “an attractive fellow,” “a lively conversationalist.”17 Hörmander 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 own way of looking at things.”19

  At first, Nash seemed more interested in the political cataclysms of that fall — Nasser nationalized the Suez Canal, prompting an invasion by England, 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 common room,” one Courant visitor recalled, “talking and talking of his views of the political situation. From the afternoon teas, I remember him as voicing very strong opinions on the Suez crisis, which was going on at that time.”20 Another mathematician remembered a similar conversation in the institute dining room: “When the British and their allies were trying to grab 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 …’ ”21

  The leading lights at Courant were very much at the forefront of rapid progress, stimulated by World War II, in certain kinds of differential equations that serve as mathematical models for an immense variety of physical phenomena involving some sort of change.22 By the mid-fifties, as Fortune noted, mathematicians knew relatively simple routines for solving ordinary differential equations using computers. But there were no straightforward methods for solving 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 Ulam called such systems of equations “baffling 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 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 problem of turbulence.25 Turbulence refers to the flow of gas or liquid over any uneven surface, like water rushing into a bay, heat or electrical charges traveling through metal, oil escaping from an underground pool, or clouds skimming 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 smoothness of solutions of the general equations of flow for a viscous, compressible, and heat conducting
fluid. These are a non-linear parabolic system of equations. An interest in these questions led us to undertake this work. It became clear that nothing could be done about the continuum description of general fluid flow without the ability to handle non-linear parabolic equations and that this in turn required an a priori estimate of continuity.26

  It was Louis Nirenberg, a short, myopic, and sweet-natured young protégé of Courant’s, who handed Nash a major unsolved problem in the then fairly new field of nonlinear theory.27 Nirenberg, also in his twenties, and already a formidable analyst, found Nash a bit strange. “He’d often seemed to have an internal smile, as if he was thinking of a private joke, as if he was laughing at a private joke that he never [told anyone about].”28 But he was extremely impressed with the technique Nash had invented for solving his embedding theorem and sensed that Nash might be the man to crack an extremely difficult outstanding problem 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 problem was open for [almost] thirty years in higher dimensions.29

  Nash began working on the problem almost as soon as Nirenberg suggested it, although he knocked on doors until he was satisfied that the problem was as important as Nirenberg claimed.30 Lax, who was one of those he consulted, commented recently: “In physics everybody knows the most important problems. They are well defined. Not so in mathematics. People are more introspective. For Nash, though, it had to be important in the opinion of others.”31