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.
This particular documentary goes further, pointing to links between the content of the mathematical work of the four men and their mental anguish. The connection is for the most part made in terms of parallels, similarities, associations and juxtapositions rather than actual implications. To its credit, the documentary does not state anywhere that Cantor’s consideration of the multiple infinities drove him insane. Instead, a major theme of the documentary emerges slowly: the struggle between determinism and chaos, the inevitability of uncertainty and our reluctance to accept it, be it in mathematics, in politics or in our personal lives.
While this is a valid general philosophical point, it troubles me that the viewer is likely to come away with the impression that these men’s minds were damaged by their mathematical ideas. That would be wrong. Turing’s mathematics had nothing to do with his suicide. He was in perfectly good mental health until the courts declared him otherwise for being gay and subjected him to barbaric “treatments”. Cantor may have been disturbed by the philosophical implications of his work, but it is just as likely that having to face hostility and personal attacks for many years took a toll on him. The same could be said of Boltzmann. The text of the documentary is perfectly clear on that. Unfortunately, its general tone lingers much longer.
At the beginning of the documentary, the narrator says that the stories of the four mathematicians “have an important message for us today”. He then goes on to develop his points about certainty – in life and mathematics – and the impossibility thereof. He concludes by asking: have we grown up enough to accept uncertainty? Or will we “pledge blind allegiance to yet another certainty”? That was an exact quote, and in case you weren’t sure what this was about, it is paired up with 9/11-suggestive images. In case you still didn’t get it, the last time the documentary had mentioned “certainty” in a political context involved Hitler and the Nazi Germany. That, I thought, feels tacked-on and takes the extrapolation a bit too far. A weak ending to an otherwise good documentary.