News flash: DeepMind and "the beauty of pure mathematics"

Time is no longer simply the medium all histories take place; it gains a historical quality. Consequently, history no longer occurs in, but through time. Time becomes a dynamic and historical force in its own right. (Reinhard Koselleck, Futures Past, p. 246)

The publication in Nature of a collaborative article by two groups of mathematicians, working in different fields, along with a team from DeepMind, the Google initiative behind AlphaGo, was not intended to be an ordinary mathematical event. The title of the article — “Advancing mathematics by guiding human intuition with AI” — expresses an ambition that goes well beyond the technical questions in representation theory or knot theory at the origin of the mathematical end of this collaboration. The simultaneous appearance of the Nature article in open access, of a second article in Nature’s “News and Views” section commenting on the first article, a third article on the implications of the first article by Nature’s top mathematical writer Davide Castelvecchi, a DeepMind blog post and Twitter thread, an article in TheConversation and a YouTube appearance by New Horizons Prize winner Geordie Williamson, the best known of the mathematical co-authors, as well as literally dozens of articles in the news media — many of which, I suspect, were themselves written by AI — is the sign of the intention of at least some of the authors, and certainly of the DeepMind team, to endow this moment with a “historical quality.”

The language used to talk about the mechanization of mathematics is the main topic of this newsletter — not the technical means of bringing about this mechanization. So before the moment fades — although I don’t think it will be allowed to fade — I will be writing a first attempt to understand what the event means for the discourse around mechanization of mathematics, and specifically of mathematical intuition. This means that the installment I had planned for two weeks from now, in response to Kantor’s challenge with regard to the Poincaré Conjecture, will be postponed for at least two weeks. It turns out, though, that the DeepMind/Nature event fits well — even too well — in the sequence about the Poincaré Conjecture.

Comments and questions are welcome at the Mathematics without Apologies blog.