I used Opus 5.5 to formally verify the Claude Agent SDK using Lean. A couple short prompts = 16 PRs fixing various bugs and race conditions. Video attached. TLA+ also works well. I sometimes combine Lean and TLA+ to look for issues around data flow, concurrency, and state mgmt. I don't know either language well, but Claude is excellent at both. This approach is super useful for formally modeling your code and finding bugs that a human probably wouldn't have spotted. Is formal verification the future of coding (or at least, bug finding)?

We’re working with an independent advisory group of mathematicians to help OpenAI responsibly share advances in AI and mathematics. The group will advise on how we assess and communicate new mathematical results, uphold academic and professional standards, and build tools that support mathematical research and learning. Through this work, we want mathematicians to be at the center of shaping how AI supports mathematical understanding and how its benefits reach the wider community.

Today we introduce Open Math Model: open models and tools for mathematics. Built for everyday research, shaped by the mathematical community, and developed in the open. Read our co-founder Terence Tao’s blog:

Thanks @srush_nlp ! Really fun to reread the Named Tensor posts in light of TorchLean! A lot of the questions there around tensor semantics, private dimensions, lifting PyTorch modules, and checked pre/postconditions are exactly the kind of things we’d love to push much further. TorchLean has also grown quite a bit recently; I’ll write up the new features + some of these directions soon!

I've written an essay on how I think the mathematics profession should adapt to highly capable AI systems. It's hosted here on "Proofs and Prompts": though you should also feel free to complain/comment on my website here:

Ben Shelton after losing to Zverev in the U.S. Open final “First and most importantly I wanna thank God. My successes are a gift. The failures are a gift. Being here playing in front of you guys is a gift. Sascha, congrats on these two weeks man. Your 2nd Grand Slam title. Two in one year. You’re one of the very best players in the world. Maybe the best player in the world this year. What you’re doing is incredible. The way you’re serving, moving, and playing. You work harder than anyone I know. You put more hours on the court than anyone I know. You and your team do things the right way. Sincerely happy for you guys to hold this title. It’s been a long time coming here.”

The Andrews–Curtis Conjecture (ACC) Challenge Discovery Track is live! Turn computational search into verifiable progress on a longstanding conjecture in group theory. Find short move sequences for 10,115 presentations. Join:

Indeed, it seems that the Caltech undergrads in question are showing remarkable perseverance adapting to this brave new world. Many senior academics should take note, lest the Planck funeral march become deafening. It's always important to understand the counterfactual: do you want students empowered to use models at scale, or (as the null-hypothesis) just the labs internally? I strongly encourage everyone to read their thoughtful response to the letter:

My guest post on Terence Tao's famous blog: Thank you Terry for giving us this opportunity and talking about our work from the very moment we launched on September 7th even before @OpenAI did. In the post, I go into how our method takes a different starting point: designing physics-AI (PINN) to discover singular candidates rather than human constructed ones. Making PINN optimization work for the first time for unforced Euler in R^3, converting that numerical solution to certified bounds which are then used in analytical stability arguments: we develop new tools to bridge numerical computation with analysis, and we believe it has much broader applications in theory. Physics-AI in the form of Neural Operators have already been successful in so many applications, including training the first AI-based high-resolution weather model, and most recently making density functional theory in quantum chemistry quasi-linear time. There is a wealth of new research to be done here!

Lean has a new checker: con-leche, a CONsistent LEan CHEcker. This is an external checker for Lean that is proven (in Lean) to be consistent, meaning it does not accept a proof of False. Joachim Breitner (@nomeata) is the mastermind behind the project.