Professor of Mathematics at UCLA. Interested in deep learning and optimization.
Oct 30 • 4 tweets • 1 min read
I firmly believe we are at a watershed moment in the history of mathematics. In the coming years, using LLMs for math research will become mainstream, and so will Lean formalization, made easier by LLMs. (1/4)
In Chess, Magnus Carlsen said:
“There was a period … where you could very clearly see which players have been using these [AI] and which players didn't. [We] got into it … got an advantage over basically everybody … it just made us understand the game a lot better.” (2/4)
Oct 25 • 14 tweets • 4 min read
I used ChatGPT to solve an open problem in convex optimization.
Actually, the real open problem is to establish point convergence of the Nesterov accelerated gradient (NAG) method. That is, the discrete-time, implementable algorithm.
2/N
Oct 24 • 11 tweets • 4 min read
I used ChatGPT to solve an open problem in convex optimization.
There are 3 proofs in discussion:
v1. ( η ≤ 1/L, discovered by human )
v2. ( η ≤ 1.75/L, discovered by human )
v.GTP5 ( η ≤ 1.5/L, discovered by AI )
Sebastien argues that the v.GPT5 proof is impressive, even though it is weaker than the v2 proof. (2/9)
Jul 19 • 10 tweets • 2 min read
Two cents on AI getting International Math Olympiad (IMO) Gold, from a mathematician.
Background:
Last year, Google DeepMind (GDM) got Silver in IMO 2024.
This year, OpenAI solved problems P1-P5 for IMO 2025 (but not P6), and this performance corresponds to Gold. (1/10)
The two cents: 1. The OpenAI IMO solutions to P1-P5 seem to be correct. 2. P6 is a significantly novel and more difficult problem. P1-P5 are arguably within reach of “standard” IMO problem-solving techniques, but P6 requires creativity. (2/10)
