Some links related to the foundations of math and physics:
- Kevin Hartnett at Quanta has a long article on Jacob Lurie and his work on infinity categories. Unfortunately Lurie didn’t participate in the article himself, so comments are only from others. The article does a good job of giving at least a vague sense of what these very abstract foundational ideas are about, as well as examining the math community’s struggle to absorb them. Lurie’s work on this is spread out over more than 900 pages here and more than 1500 pages here. Recently he has been putting together an online textbook/reference version of this material as Kerodon, which is modeled after and uses much of the same software as Johan de Jong’s Stacks project.
- At Mathematics without Apologies, Michael Harris has some comments on a recent discussion of the Mechanization of Math, held here in New York at the Helix Center. A video of the discussion is available here.
- In the new (November) issue of the AMS Notices John Baez has a review of a recent collection of articles about the foundations of mathematics and physics. The book, Foundations of Mathematics and Physics One Century After Hilbert, contains contributions about both math and physics, although in his review Baez concentrates on issues related to physics. He notes “The elephant in the room is string theory.”
The same issue of the Notices contains an informative long article about Michael Atiyah and his career, written by Alain Connes and Joseph Kouneiher (Kouneiher is the editor of the book reviewed by Baez).