The Future of Mathematics

Guest post by Jeremy Avigad (Carnegie Mellon), the latest in Tao's series of AI-and-mathematics guest posts. Tao's note says it "was initially written in a different file format and converted using AI". Avigad says that results which "a year ago, made for perfectly respectable publications can now easily be generated with the help of AI". Credits Matthew Ballard for the observation that AI-generated solutions to open problems "all have a similar character: they are problems that AI could solve by cobbling together available techniques", and argues that reinforcement learning "breeds superhuman cleverness but may miss creativity and higher-level strategizing". His three answers: solve harder problems; think bigger thoughts (Riemann's Habilitation lecture on the foundations of geometry as an example no RL setup could have rewarded; "Whether or not AI can think, it can't think for us"); try new things (people who build proof assistants and train neural networks are "doing mathematics proper, rather than … mere technicians"). He finds community responses on Tao's blog and Proofs and Prompts "generally positive and encouraging". Mentions a longer essay forthcoming in the Notices of the AMS.

Same day, Tao's blog also carried a guest post by Annalisa Buffa (EPFL) advertising a postdoc on formal verification (Lean) and AI-assisted algorithm discovery for numerical analysis of PDEs: https://terrytao.wordpress.com/2026/10/05/postdoc-position-on-formal-verification-and-algorithm-discovery-for-numerical-analysis/

Short quotes only (see Summary). Full text at the URL.