HIGHER MATH.

Having been equally intrigued and inconvenienced by the filming of Ron Howard's A Beautiful Mind on the Princeton campus, it was with great curiosity that I attended a showing at our local theater, located virtually on the site where mathematician John Nash formulated his influential theories.

My first reaction was delight at seeing some of my favorite spots beautifully captured on film, including the large commons room in Rockefeller College where I am an advisor. It is portrayed as an exclusive dining room for faculty, but in fact is a chamber where students are usually found in prone positions as they read books, and where my young sons, often loudly and with smiling forbearance from the students, alternate between playing Ping-Pong and foosball. My second reaction was one of alarm, having never been told about the purported Princeton tradition of giving one's prized pen to a colleague who has achieved some notable achievement. After several days of inquiries, however, I found that none of my senior colleagues had heard of such a practice either, and my pen collection seemed safe.

Upon further reflection, however, I came to be less absorbed by the thrill of seeing familiar places and more troubled by the film's peculiar message. A fundamental tension seems to exist at its core between the content of the mathematical theories for which Nash received the Nobel Prize and the relationship between Nash and his wife, Alicia. It is her love for and devotion to Nash, as portrayed in the film, that allow him to recapture his sanity and pave the way for reception of his deserved accolades.

One scene in particular continues to give me pause. Nash is with a group of friends at a Princeton graduate-student party when he is suddenly struck by an idea that forms the basis of his "rational choice" game theory. In a cinematic version of what would become the "Nash Bargaining Solution," we witness Nash's friends ogling one extremely beautiful blonde woman and four less-ravishing but still attractive brunettes. The other students all intend to seduce the blonde, and one even alludes to Adam Smith's theory of zero-sum game competition--the best man wins, and the others are left out in the cold, literally in this case. Nash, in a sudden flash, realizes that the basis of economic theory does not have to be a zero-sum game, but rather one that might assure mutually beneficial outcomes for all the parties involved (what would later become Nash's "equilibrium" theory). Nash proposes that the students avoid seducing the blonde, since they will get in each others' way and alienate both the blonde and the brunettes. Instead, by ignoring the blonde and concentrating on the brunettes, each will benefit (except, one supposes, the blonde). By seeing the barren outcome of their zero-sum competitive approach, they can adjust their strategy through cooperative bargaining and each, so to speak, enjoy the fruit of his efforts.

Shortly after this fanciful portrayal of Nash's mathematical theories of rational self-interest--ones that now serve as the basis of inquiry in many academic disciplines, ranging from economics to political science--we observe another seduction, this time Alicia's overtures to Nash, her professor. To the amazement and amusement of most of the film's viewers, Alicia not only accepts Nash's quirks and lack of social graces but is attracted to him by an inexplicable desire--one that fosters love, instills devotion, and later makes possible his mental salvation. There is no apparent rational calculation in Alicia's overtures; indeed, as I watched their budding relationship, I found myself in disbelief that she would be attracted to Nash (in spite of Russell Crowe's good looks), and in no small admiration for and incredulity at her irrational dedication.

The irony of the film is that Nash, at least as portrayed in accepting the Nobel Prize for his "rational choice" theory, gratefully thanks his wife for her unwavering love. Yet there is insurmountable incongruity between his theory and the wellsprings of that love.

According to Nash's formula, individual calculation may sometimes grudgingly conclude that achieving our true wish--personal fulfillment--requires mutual calculation and compromise. But in the film, Alicia pursues her true desire not only for the sake of self-fulfillment, but, as with any great love, as a form of self-denial. For Nash, by thinking first of our own interests, we can achieve mutually advantageous situations. For Alicia, by giving herself away, she becomes more fully herself, a person enriched through entwinement in the life of another.

In rational-choice theory, ideal decisions are made only by rational actors--always competitors--who have full information about all aspects governing the choice. But Alicia's love has a mystery at its core, one that is impenetrable to calculated reason and transcends even full information. I came away from the film with the curious realization that Nash was fortunate that not everyone lives by the economic calculus for which he became famous, for without Alicia's selfless and self-fulfilling love, his soul might have been lost.

Patrick J. Deneen teaches in the department of politics at Princeton University.