Roger Ebert is right when we reports that the atmosphere and language of David Auburn's Proof is exactly right, that when a professor delivers a eulogy he speaks precisely as professors on such occasions do, and that when a theoretical physicist flirts at a mathematician's wake, he speaks and drinks the way theoretical physicists do.
What's odd, though, and what seems not to have been much discussed, is that Proof can't really be about the discovery of a great proof. The proof is obviously a stand-in for a play, or perhaps a novel: we're not talking about mathematicians here, but writers.
We know this because, in this play (and now in this very fine movie), people care deeply about who created the proof but aren't much exercised about the proof itself. They care about the trappings -- publications, conferences, interviews -- that the proof could bring, but nobody seems to mention that an important new proof must open new avenues for research, new horizons for investigation. Even if the conclusion has been anticipated, the novel methods used to achieve the proof must provide many new opportunities. We should, in short, be in a terrible rush to find out what the proof lets us do today that nobody could do before.
We also have a worrisome and false note when Catherine, who claims to have written the proof and might not be deluded, expects her new lover to accept her authorship because she asserts it -- to believe her, to have faith. They're both mathematicians and they're both grownups, and faith has nothing to do with it. What evidence can we adduce? How can we prove it? A subtext here, running against a tacked-on theme of the play, is that the beautiful, emotionally-fragile, lovable and very female Catherine is really not fit to be a real mathematician: women, after all, want to be believed for their own sake, and if this unfits them for the brutal world of math and science, vive la differénce.
That said, it's pitch-perfect and place-perfect, and the film is wonderfully acted.