A Beautiful Mind

Although it will later lead to him receiving the Nobel Prize, Nash’s work on game theory is not yet respected enough to earn him a faculty position at a top university, so he begins working on a paper that should “win him recognition as a pure mathematician” (128).

The paper concerns manifolds, topological spaces which, “from the vantage point of any spot on such an object, the immediate vicinity looks like perfectly regular and normal Euclidean space” (128). Manifolds are extremely varied and may, “in one dimension […] be a straight line, in two dimensions a plane, or the surface of a cube, a balloon, or a doughnut” (128). Although all two-dimensional objects have been “defined topologically” (129), many “three- and four-dimensional objects – of which there is literally an infinite assortment” (129) are yet to receive such definitions.

Nash uses visiting professor Donald Spencer as his “sounding board for completing the paper” (129). Initially, he is skeptical of Nash’s efforts but, after months of meetings in which he would “shoot holes in Nash’s arguments” (130), he begins to see progress. Eventually, he respects not only Nash’s mathematics but also the fact that the problem itself is “highly original,” remarking later that, “Nobody else could have thought of this problem” (130).

Nash’s finished paper reveals that a class of manifolds are “closely related to a simpler class of objects called real algebraic varieties, something previously unsuspected” (131) by the mathematical community. This is also seen as highly original and “establishe[s] Nash as pure mathematician of the first rank” (132).

However, despite his successes, Nash is disappointed to learn that he will not be offered a faculty position at Princeton, largely because some of the mathematics department find him too strange, “aggressive, abrasive, and arrogant” (132) to employ. Instead, he accepts a position at MIT. 

MIT’s history revolves around engineering, and when Nash takes a position, this is still very much reflected in the institution. Courses are still geared more towards engineering than more “pure” mathematics and sciences, and the academic community is “dominated by an old guard not of high-society intellectuals but of middle-class Republicans and engineers” (134).

Nash slightly resents his position here, viewing himself as “a swan among ducks” (134). However, increased funding and changing perspectives mean that things are already changing and “mathematics [is] on the verge of becoming an important department” (134). Nash’s time here will help bring this change about, adding to MIT’s growing reputation.

Nash also finds greater acceptance at MIT. Norbert Weiner, a brilliant, eccentric polymath, can be so distracted and distant that he sometimes has to ask, “When we met, was I walking to the faculty club or away from it?” (136) in order to ascertain whether he has eaten lunch that day. He also suffers from “periods of manic excitability followed by severe depressions” (136).

His own experiences giving him perspective and empathy, Weiner is enthusiastically supportive of Nash. Nash, in turn, sees Weiner, “a genius who was at once adulated and isolated, as a kindred spirit and fellow exile” (136).

Nash makes a closer companion in Norman Levinson, a mathematician who serves as “a combination of sounding board and father substitute” (137) as well as “a role model for Nash” (138). Like Weiner, Levinson has mental health difficulties, and suffers “from hypochondria and from wide mood swings, long manic periods of intense creative activity followed by months, sometimes years, of depression” (137). 

Although far less restrictive than many positions, Nash still finds his teaching duties at MIT to be “irksome” as he does “everything that interfere[s] with his research or smack[s] of routine” (139). The lectures he does give are “closer to free association than exposition” (139), following his own interests and original approaches with little interest in “whether the students [learn] or not” (139).

Known as “a bit of a gamester” (140), Nash’s teaching style has “more to do with laying mind games than pedagogy” (140), and he often includes pranks and trick questions in his examinations. This frustrates some of his students and they occasionally play pranks back on him as revenge.

Nash maintains his strange behavior at MIT, often “pacing in Building Two’s cavernous hallways whistling Bach” (141). However, he is also more sociable, spending much of his time in the mathematics common room jumping into conversations and playing games.

Nash’s increased sociability might be explained by the fact that the other staff and the students are also somewhat unusual. They all place “a certain premium on eccentricity and outrageousness” (142), acting and dressing in unconventional ways. In fact, one graduate student later recalled, “At the time, we thought of eccentricity and being good in math as going together” (142).

Not to be outdone, Nash also “adopt[s] a touch of flamboyance about his dress” (143) and begins to take on extra quirks such as “creat[ing] his own vocabulary” and talking “a great deal about experimenting with mind altering drugs like heroin” (142). In this atmosphere, Nash gains “a real social life” (145) for the first time, eating and drinking with others and attending parties with other faculty members.

Despite this, he still seems to need to stand out, striving “to constantly underscore his own uniqueness, superiority, and self-sufficiency” (145). He remains highly competitive and prone to withering putdowns, exuding an attitude of social superiority that sometimes borders on being anti-Semitic.