This got me a bit puzzled: why would a comment on this post link to a BBC documentary on Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing?
Given that I don’t know as much about the history of mathematics as I probably should, and that I was too tired late last night to do anything more intellectually challenging, I ended up clicking through and watching all 10 parts of the documentary.
The mathematics involved – Cantor’s hierarchy of different-sized infinities, Boltzmann’s statistical mechanics and entropy, Gödel’s incompleteness theorem – is described remarkably well. An expert might quibble about how some of the explanations are ambiguous and imprecise, especially where it concerns Gödel’s work, but that’s a relatively small price to pay for being able to communicate the excitement, audacity and impact of mathematical ideas to a lay audience. The images and animations are, for the most part, well done and helpful. Several mathematicians and scientists (including Roger Penrose) were interviewed for the documentary, and I am guessing that experts were consulted quite extensively about the mathematical content.
That’s only one part of it, though. The movie chooses to focus on Cantor, Boltzmann, Gödel and Turing not only for their groundbreaking contributions to mathematics, but also for the mental anguish and personal tragedy in their lives. Boltzmann and Turing committed suicide, Cantor and Gödel suffered from mental illness and were hospitalized for it, and Gödel ended up starving himself to death. Now, I understand that these are undisputed historical facts. I also understand that troubled characters make for a more interesting movie. But I’m tired of watching the media portray mathematicians as socially challenged and mentally unstable, not to mention poorly dressed. You’d never know that it is quite possible for a great mathematician to be a well adjusted and fully functional human being, to have a long, happy and accomplished life, or to face and overcome adversity without developing a mental illness.