Really happy to share our new paper on using AlphaEvolve for mathematical exploration at scale, written with Javier Gómez-Serrano, Terence Tao, and @GoogleDeepMind's Bogdan Georgiev. We tested it on 67 problems and documented all our successes and failures. 🧵

Very excited that our AlphaProof paper is finally out! It's the final thing I worked on at DeepMind, very satisfying to be able to share the full details now - very fun project and awesome team! https://t.co/OuWDemzAt4

(1) Our team at @GoogleDeepMind has been collaborating with Terence Tao and Javier Gómez-Serrano to use our AI agents (AlphaEvolve, AlphaProof, & Gemini Deep Think) for advancing Maths research. They find that AlphaEvolve can help discover new results across a range of problems.

Find out more in our joint paper: https://t.co/ND2v0AZL3q Terence Tao's blog post: https://t.co/Br9qQzHrHO @UCLA @BrownUniversity

While AlphaEvolve didn't succeed on every problem - and relied on expert human guidance to find the right path in many cases - these findings highlight how mathematicians and AI systems can work together to test hypotheses and discover patterns that might otherwise be missed.

A personal favorite result: avoiding isosceles triangles on a grid. On a 64x64 grid, previous work with @f_charton, @JSEllenberg & Geordie Williamson suggested 112 points were possible, but we couldn't find a construction. AlphaEvolve finally found this elusive set!

In a few cases AlphaEvolve discovered general patterns that solve the problem not just in the cases it was asked to solve, but in all cases. Excitingly, a pipeline combining AlphaEvolve with @GoogleDeepMind's Gemini DeepThink and AlphaProof is able to prove such a generalisation

We tested AlphaEvolve on a wide-ranging portfolio of 67 mathematical problems in combinatorics, geometry and more. It found new constructions that improved upon the best-known results on about 20 of them, such as finding denser ways to pack 11 cubes into a larger cube.

Here’s a reminder of how AlphaEvolve works:

We tested AlphaEvolve on a wide-ranging portfolio of 67 mathematical problems in combinatorics, geometry and more. It found new constructions that improved upon the best-known results on about 20 of them, such as finding denser ways to pack 11 cubes into a larger cube.

Here’s a reminder of how AlphaEvolve works:

We tested AlphaEvolve on a wide-ranging portfolio of 67 mathematical problems in combinatorics, geometry and more. It found new constructions that improved upon the best-known results on about 20 of them, such as finding denser ways to pack 11 cubes into a larger cube.

Here’s a reminder of how AlphaEvolve works:

Official results are in - Gemini achieved gold-medal level in the International Mathematical Olympiad! 🏆 An advanced version was able to solve 5 out of 6 problems. Incredible progress - huge congrats to @lmthang and the team!

Drastic progress on maths with Gemini 2.5! As a math undergrad, I am impressed 🤯 🥈 -> 🥇 ✅ Formal -> Informal ✅ Specialized model -> General model ✅ Available soon ✅ Huge thanks to IMO and congrats to all participants! Blog:

Very excited to share that an advanced version of Gemini Deep Think is the first to have achieved gold-medal level in the International Mathematical Olympiad! 🏆, solving five out of six problems perfectly, as verified by the IMO organizers! It’s been a wild run to lead this

So I've been messing around with this and LLMs. The quality of Mathlib + AI is getting to the point where mathematicians with *minimal* knowledge of Lean should be able to (with AI assistance) *state* (and themselves verify that the statement has the correct mathematical

i built a visualization you can adjust the heights / see how hard it is to improve on google's or Matoslci-Vinuesa's solutions. link below.

there are infinitely many other methods i could try. each requires careful debugging/tuning but i'm limited by my bandwidth and motivation and even with access to every LLM i failed. this is why having infinite compute + an LLM evolve your code wins. it doesn't have to care.

Google released AlphaEvolve. I'm trying to get a sense of whether the problems are hard to solve numerically. Let's focus on problem B.1. i'm going to do this live.