“An accumulation of facts is no more a science than a heap of stones is a house.” - Poincaré LLMs are now proving results that have resisted mathematicians for decades. Finding interesting theorems without human guidance is a new bottleneck. We show that we can teach an LLM to do it! TL;DR: → a quantitative notion of interestingness → 4.3× higher interestingness → a self-expanding discovery loop [1/5]

ah nevermind they made it in a retarded way

"interestingness = proof difficulty / description length"

Assuming "abduction" exists as a distinct, long range cognitive task generated spontaneously in humans from the repetition of lower level cognitive tasks (e.g. deduction/induction) immediately sends you to the most devestatingly pessimismistic view of the future.

This is an important report! To facilitate discussion, I am pasting below the main recommendations: 1. Programs should add new training opportunities to teach skills that are becoming increasingly relevant. These may include: collaboration, formulating questions, interdisciplinary work, use of AI tools, and formalization. 2. Skill in communication to both expert and broad audiences should be part of the training in a PhD program and an explicit degree expectation. 3. While homework can provide a useful way for students to learn course material, assessment should be based on in-person written or oral assessments. 4. Programs should provide access to AI tools for all graduate students, with use never mandatory and methods subject to the standards of the advisor and department. 5. Advisors should hold regular detailed discussions with their students about expectations for AI use. 6. Three ethical rules: (i) maintain responsibility for the correctness and understanding of the mathematics that appears under your name, (ii) always disclose AI use, and (iii)obtain explicit agreement from all involved parties before entering material into an AI 7. A mathematics PhD program should require rigorous in-person assessment of research plans and progress by multiple faculty at least annually, including meaningful feedback for the student. 8. A thesis should be an original scholarly contribution. This should be understood broadly; for instance, the thesis need not record the first proof of a statement. 9. A PhD should not be awarded primarily on the basis of the text of the dissertation. The text should serve as the foundation for a rigorous thesis defense that requires complete mastery of the thesis content.

I'm sorry to say I think he is a fossil. Editors at Compositio/Advances/Math Z/Transactions/JLMS are using AI to autoreview paper submissions now. There is no going back from here

It just keeps getting worse 🤯 👀

More mathematicians needed terrytao.wordpress.com/2026/…

More mathematicians needed terrytao.wordpress.com/2026/…

Unique ergodicity of hedgehogs! I am particularly pleased to announce this new paper where I solve a long standing conjecture.... (a conjecture of mine!) In 1995 I conjectured the unique ergodicity of Hedgehogs. This conjecture closes a decade long program of study of the dynamics on hedgehogs since their discovery more than 30 years ago. They were discovered around 1992-1993. The motivation was to translate linearization results in the Siegel problem to Arnold linearization results for analytic circle diffeomorphisms. The reference publication with the first properties and the key construction making the link with analytic circle diffeomorphisms is my article in Acta Mathematica in 1997. The rigidity of the dynamics on hedgehogs make it a unique set of results in Dynamics. For example, as for rotations, we have the q_n iterates of f in K that converge uniformly to the identity. It is the first time that we are able to control and prove rigidity results on such a pathological invariant set. I remind that hedgehogs are topologically and metrically very complex. They have empty interior, they are not locally connected and we can have examples with positive 2 dimensional measure, but also of Hausdorff dimension 1, with smooth combs inside, and the fixed point can even be non-accessible (many of these results are due to KIngshook Biswas). arxiv.org/abs/2609.28797