Today a cryptographer said in my presence, "In the movies, the only option for a math guy is to go crazy." Certainly, it seems that math is more often used as a symbol of deep or contorted thinking than as an achievable skill or pastime for a normal person.
But maybe the situation is not quite so bad. Since 1996, Arnold Reinhold has been collecting references to math in a website currently at http://world.std.com/~reinhold/mathmovies.html . Mathematics seems to make a few worthy appearances.
But hardly as many as there might be. What does this say about Anglophone society? I have the impression mathematics is taken more seriously as a pursuit for normal people in South and East Asia, Russia, and Israel — I wonder if the situation better in movies made in those places. Or maybe the movie-making world and the world of mathematical competence are just about mutually exclusive, and so few pathways exist for improving the portrayal of math in the movies.
Actually, I am not bothered so much by depictions of crazy mathematicians. There have been, after all, some great mathematicians with spectactularly quirky personalities, if not outright mental illness — Cantor, Gödel, Boltzmann, and Newton come to mind among the first-rung names, and there are many others elsewhere in the vast nimbus of minds. Being strange or mentally ill does not of itself invalidate a person's thoughts, in any case. (Does that really need to be said?) What bothers me most is the standard cinematic trope of of the math genius who has instant insights and doesn't need to work to prove or develop them. You might call it the Rāmānujan syndrome. Wesley Crusher and Will Hunting are prime examples. It's hard to think of a stereotype more damaging to the development of healthy intellectual skills in normal people.
Something could be done to correct this stereotyping, which I'm sure takes place because of ignorance rather than ill will on the part of scriptwriters and directors. How about a movie or two in which problem-solving is shown as it really is: something carried out by normal people through patient hard work and practice, through a skill that can be cultivated by the sane and the normal. After all, solving problems of one sort or another is something everyone does, and it is rarely a matter of sudden inspiration — instant, complete, and requiring no further labor. Then again, maybe someone thinks that isn't dramatic enough for a movie.