Proof- Movie

In recent years, there have been several feature films involving mathematicians, and Proof is one of the good examples. Hopkins plays Robert, a man who at one time was a brilliant young mathematician but is beset by mental illness. The diagnosis is not specified, but one can infer that it is schizophrenia. Paltrow plays Catherine, who seems to have inherited her father’s brilliance as well as his instability.

Robert suffers from an illness that causes him to believe that there are encrypted messages being communicated to him via newspapers and magazines. He attempts to do mathematics during his illness but his efforts reveal not brilliance but the tragic depths of his mental illness. Robert is said to have done revolutionary work in three areas before the age of thirty: game theory, algebraic geometry, and nonlinear operator theory. 

Proof is more about the daughter Catherine than it is about the father Robert. Catherina has extraordinary mathematical ability, allowing her to tackle a research problem for which her limited formal education ought not to have prepared her. Catherine is brilliant but she needs a psychiatric help for depression (or is it schizophrenia, like her father?). And she resists treatment.

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And an interesting twists: Catherine is female mathematician. When Catherine asks Hal who is a current PhD student at the University of Chicago, if he knows any female mathematicians, he stammers, and eventually says “There’s a woman at Stanford. I don’t remember her name.” “Sophie Germain?” tests Catherine, in response. “Yeah! I think I’ve met her at meetings,” says Hal, revealing his ignorance. The absence of women in mathematics is a theme in the film, but it is also an inconsistency between the film and reality. Nowadays it would be unthinkable for any PhD student in the field not to know of any women mathematicians.

Proof realistically illustrates the world of mathematics and mathematicians. In Proof, though, the mathematical life is more realistically rendered. Three of the four characters (Robert, Catherine, and Hal) work in mathematics. We see them read and study and write. Robert describes the pleasure he feels when mathematical ideas are flowing. Catherine describes to Hal how she felt when doing mathematics, speaking of “beautiful, elegant proofs, like music”. Hal describes his fear that his own mathematics research doesn’t pass muster when compared with Robert’s.

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After these movies- “Good Will Hunting”, “A Beautiful Mind”, and “Proof”, I suspect that some audiences will draw the following conclusions about mathematicians:

First, mathematicians are disturbed and need psychiatry. Will is emotionally disturbed, John is paranoid and schizophrenic, and Catherine suffers from depression (at least). A reasonable inference is that mathematical talent is itself a psychiatric illness, that madness is a natural result of a mind that can reason mathematically.

Second, mathematicians are arrogant and rude. John is portrayed as obnoxious, such as when he cuts down a colleague by telling him that his ideas have not an ounce of originality in them. Catherine, too, seems rarely to be nice to anyone but her father.

Third, mathematicians are antisocial. Catherine seems to have any friends.  On the other hand, Hal actually describes mathematicians as wild party animals, but that characterization seems to be mostly for laughs, since the stereotype is opposite.

Fourth, mathematicians are competitive and self-promoting. They are more interested in advancing themselves, in being recognized as brilliant, than they are in advancing mathematics.  For instance in Proof, Catherine accuses Hal of stealing mathematical results for his own advancement.

Last, successful mathematicians are young. For example in the movie, Hal worries that he too is over the mathematical hill at age twenty-six. Once mathematicians reach a certain age, Hal in the play suggests that they “might as well teach high school”. In the film, Hal quips “I’m twenty-six. You know “ the downward slope.” About the assumption that mathematical ability is the province of the young, Robert in the play says “this is a stereotype that happens to be true.”