1. A Beautiful Movie?

A muscular mathematician
Russell Crowe could certainly snag an Oscar for his convincing portrayal of John Nash, a schizophrenic mathematician in A Beautiful Mind. But what does the film tell us of math  and the people who do math? Quite a little, and quite a lot, according to Terry Millar, a mathematician and associate dean at University of WisconsinMadison who saw the movie at our request. "My personal impression was that it did not reveal much about math, but did say a great deal about mental illness." Topflight mathematicians, he says, "are very odd ducks." Some have dropped out of society or become notorious for sleeping in the classroom. In that respect, Nash was emblematic of the field, Millar says. George Cantor, who developed a theoretical unification of mathematics, he says, "was treated pretty much as a nut by the math community." Like Nash, Cantor was vindicated in the end, Millar adds. "Now the first few pages of any math text will be devoted to set theory assumptions"  which Cantor pioneered. A Beautiful Mind vividly showed Nash's auditory and visual hallucinations. Beyond portraying mental illness, Millar saw the hallucinations as insights into how some mathematicians get with ideas. "These people tend to be very rational in certain contexts, but how they end up doing what they do is not clear. The movie gave you some purchase on what that might be." CroweNash himself said he believed the hallucinations because they seemed to come from the same source as his mathematical insights.
Some zerosum game!
Nash developed a theory to describe economic behavior. In the early 1950s, when Nash entered graduate school, two mathematicians had already described zerosum games with two players. (In a zerosum game, if one player wins, the other loses an equal amount; total wealth does not change.) But economic situations can have dozens or even hundreds of players. And the zerosum condition is unrealistic: by definition, economic growth is an increase in total wealth. Nash's innovation was in describing games with several players without the zerosum restriction. In other words, in a game with six players, three could win $5 each, and the other three could come out even. Eventually, his math described a "Nash equilibrium," a kind of economic paradise where, as the Nobel folks said, "all of the players' expectations are fulfilled and their chosen strategies are optimal." It may sound pretty commonsense, but Nash's insight overturned a bedrock hunk of the economic theory of Adam Smith, founder of the dismal science. Smith argued that greed serves the common good  that individual actors, by seeking their individual benefit, help society as a whole. Nash held that this fundamental tenet of capitalism, however, does not fully describe reality, and that individuals could only maximize their own benefit by thinking about the group.
You could do the math
At any rate, since Blondie was surrounded in the dating arena by four lesser women, the odds favored the four guys (even if they were mathematicians). But Nash saw that if all four men did the Adam Smith thing and wooed the knockout, at least three fellas would lose  big. They would be spurned by Blondie. And, having offended the other women, they would be fated to spend the evening  horrors  talking math with their buddies. A smarter strategy, NashCrowe proposed, would be to ignore Blondie and shower attention on her mortal friends. If each man obeyed Adam Smith, Nash explained, and sought his maximum advantage, most would lose. By thinking about the overall benefits, they would do better. They would reach a Nash equilibrium, and Blondie would be the lonely one, not they. Whitewash?
The New York Times said A Beautiful Mind "can  indeed, should  be intellectually rejected, but you can't quite banish it from your mind" (see "From Math..." in the bibliography). Indeed, this is such a convincing whitewash that you may not want to expose it to the cold light of reality. Why? Because while Nash was a basket case, he was surrounded by dogooders who smoothed the rough path of his life  indeed  make his survival possible. Ironically, the dogooders ignored economic calculations in favor of those emotional ones. But enough of the dismal science. How does Beautiful Mind compare with other recent scienceflicks?




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