Natesh Pillai

1. Scaffolding affects the search so much 2. What interests humans is currently decided by humans. This is not just an AI problem in my view

My hometown.

@atheorist very interesting! thanks!

Today my colleagues and I released a paper on the formalization of d=4 Quantum Field Theory in Lean. We believe that formal verification has the potential not only to radically reshape how mathematical research is conducted, but also to transform research in theoretical physics.

@littmath This eigen value repulsion equation is similar to the one in random matrix theory and Dyson Brownian motion etc

There is an associated (non-linear!) differential equation--see e.g. below--controlling this action. We prove an analogue of Katz's theorem for these equations: the arithmetic of this differential equation controls the action of \pi_1(S,s) on representations of \pi_1(X_s).

New paper with Josh Lam, about which I'm really excited! I want to try to briefly explain what the point is in this thread.

Amazing! Congrats!!!

@EdgarDobriban Amazing!!

AI is getting great at math, but how good is it at solving real research problems in areas outside of those covered by Erdős problems? Towards gauging this, I have started putting together a list of unsolved research problems in mathematical statistics and machine learning, sourced from recent papers in a leading statistics journal, the Annals of Statistics (with some bonus COLT open problems: solveall.org. Currently >100 problems. In my view, much of the value of AI for researchers in the mathematical sciences stems from helping with their own research problems. These are problems without known solutions. There are many math benchmarks, but few with the following properties: (1) of a realistic research-level, so that solving them can potentially lead to a publication in a top journal (problems discussed in papers already, not contest math, not Millenium problems, not problems created for a benchmark, not problems that have a known solution); I'd say Erdős problems are the best example of this. (2) cover problems outside of the usual focus (combinatorics, number theory, ... ) of Erdős problems. Especially under-represented are domains of applied math, along with statistics, operations research, etc. I'm interested in statistics and ML, so that's where I started, but this could grow over time. Hope this can grow into something useful to the community! Happy to hear your thoughts...

@SebastienBubeck We do know the proof is unlikely to be short.

I used to think that I would not see a proof of P vs NP in my lifetime, but now with AI I'm not sure anymore, and that's pretty cool!

@aramHmarkosyan Amazing to see this :)

Our next step toward publicly executable mathematics! We are hiring across spectrum of eng and research roles!

@CarinaLHong Thank you for this. Super useful.

AXLE - our core infrastructure - is available to the community for free today. axle.axiommath.ai Check it out!

@kevinweil Amazing. Can't wait to try it out.

💥 GPT 5.4 is launching today! It's our best model ever, and it's also the most capable scientific model we've ever released. GPT 5.4 Pro in particular is 🤯 based on early testing with scientists and mathematicians.

andrew.cmu.edu/user/avigad/Pa… Nice article on AI and math. But don’t need to reinvent the wheel. Just look at the AI use in competitive chess and follow suit. #chesspunks

@roydanroy Yes I agree. But we Don’t need to reinvent the wheel. All of the above points are common place in competitive chess which is the first domain AI had a similar effect. We should own it. 100%. My worlds colliding. #chesspunks

How are mathematicians facing the wave of rapidly advancing AI-for-math capabilities? Jeremy Avigad (CMU prof and co-author on the original 2015 system description paper for Lean) just posted a paper with his thoughts in the wake of the Math, Inc. announcement on sphere packing. andrew.cmu.edu/user/avigad/Pa… There are a lot of interesting passages in here, including a bit of the back story of the Math, Inc. bomb drop and how it was initially received by the humans working on the formalization project. But, as for how mathematics proceeds, here's the key last passage: "We need to remember our strengths: mathematicians are problem solvers and theory builders extraordinaire. Rather than fight the use of AI in mathematics, we should own it. It is not enough to keep up with current events and design benchmarks for AI researchers; we need to play an active role in deploying the technology and molding it to our purposes. We also need to learn how to raise our students with the wisdom to use the new technologies appropriately, and we need to be careful that we still manage to impart core mathematical intuitions and understanding. Figuring out how to use AI effectively to achieve our mathematical goals won’t be easy, but mathematicians have always embraced challenges—indeed, the harder, the better. If we face AI head-on and stay true to our values, mathematics will thrive. We just need to show up and get to work." The next few years should be a golden era for mathematics. For those of us working on the frontier, I hope we do well by our mathematician colleagues.

@littmath Welcome!

This has been public for a bit but (some personal news) I don't think I've mentioned it on here: I'll be the "Benedict H. Gross Distinguished Visitor" at the Harvard math department for the fall semester.

🤣

@davidalmog25 @HarvardHBS welcome!

I am excited to share that I will be joining @HarvardHBS as an Assistant Professor in the Technology and Operations Management unit beginning in the 2026 to 2027 academic year.

@RenierCast Sad indeed. Legend.

Sad to hear about the passing of Jan Timman. A true chess hero.

@atheorist @boazbaraktcs That’s not the opinion of entire Harvard community for sure. People will be denial for a while before adapting.

@boazbaraktcs I was pretty shocked that the SA article implied this is a nothingburger when potentially 5/10 of the questions were solved in a week.. very strange reporting on their end

Sorry friends but this is not the verdict. We don’t know yet how many questions were solved by AI but even if it was 10/10 (as it surely will in a few months) it wouldn’t replace mathematicians but it will radically change how they work.

@patrickshafto This is not my take for sure.

This is a strange take. Replacing mathematicians doesn't seem like the highest order bit. That mathematicians have put in the effort to create the assessment answers the most important question: AI is good at math and getting better. Dismiss this at your peril.

Wow! I didn’t know he gave a proof for this! Especially since he wasn’t known for proofs. Are there other proofs he gave?

🤣 didn’t know that joke