Last week I finished reading a really interesting book by Cedric Villani, who won the Fields Prize in mathematics (the discipline's equivalent of the Nobel Prizes), for his work on (bear with me on this) Landau damping and the Boltzmann equation. Birth of a Theorem describes how Villani and his collaborator came up with the proof. It's quite unforgiving on the mathematics, which I found unintelligible (it turns out that Villani intended the mathematics to be unintelligible), but really informative about the phenomenology of mathematical creativity -- and perhaps about creativity in general.

My take on Villani's account is this: He was thinking about the problem pretty much all the time, though not always in a focused way. And, though the problem was "modular," in that it had quite a few almost-independent moving parts, he didn't approach its solution in a linear way. That is, he didn't work on the first step until he got the solution and then move on to the second and then the third steps. Instead, he moved among the different "sections" of the proof seemingly randomly (although he doesn't quite say this, he was able to work on Step Seven by assuming for the moment that they'd figured out Steps One through Six). Workshops turn out to be a good incentive for creativity -- but seemingly only if at least some of the people in the audience are (almost) as knowledgeable as the presenter. There's a lot of other stuff that resonated with me, such as the fact that he likes to work with popular (French) music in the background, such as this by Catherine Riberio. (Here's a lecture by Villani describing the creative process.)

I thought the book was a fascinating description of creativity, and mentioned it at the faculty lunch table. But, when I responded to a question about what Villani had created, the answer -- "a proof about Landau damping" -- brought the conversation to a stop, and not merely (I think) because I couldn't explain what Landau damping was. (After all, I referred to the book as about creativity, not about Landau damping.)

A day or two later, I went to a program on Handel's music as illuminated by his circle of friends in London. Ellen Harris, the author of a book on that topic, gave a talk that I found interesting mostly because of her description of the archival detective work she had to do to trace the friendship circle. The talk was followed by a performance of excerpts from some of Handel's operas (which I found less interesting). I'm quite confident that, had I introduced the topic of the program into the lunchtime conversation, my colleagues would have gone along -- even though, at some level, the Handel program was also about creativity.

Two generations ago the novelist and physicist C.P. Snow wrote about the two cultures, of the humanities and the sciences. Apparently the two cultures persist, at least at Harvard Law School. I suppose you can get some interest in cutting-edge applied sciences like neuroscience and robotics (the latter of which is basically engineering, I think), but basic science is a black hole, so to speak -- an occasional source of metaphors like that one, but not something of real intellectual interest. I have a cynical hunch about why the divide persists: Basic science and mathematics are about about the real truths about the universe, whereas law -- isn't.

But, I did end my first-year course this year with a short description of Yitang Zhang (and a picture of Odell Beckham, Jr.). The lesson -- Do Good Work.