Search, Learn, Prove: AI-Driven Discovery Across Pure and Applied Mathematics

PACM Colloquium
Oct 26, 2026
4:30 - 5:30 pm
214 FINE HALL

Abstract:

AI systems are now capable of discovering mathematical objects, algorithms, and arguments that humans could not easily find on their own. The challenge is turning these discoveries into results we can trust. In this talk I will describe several workflows that combine three ingredients: AI-driven search, machine learning, and rigorous verification. I will also explain how my own research has changed over the past eight months. I will illustrate these workflows with examples ranging from fundamental questions in PDE to high-performance scientific computing.

None of this is push-button. These tools reward sustained involvement rather than delegation, and the mathematician has to stay engaged throughout. Correctness is not entirely automatic, even with formal verification. The strongest results come from combining AI with deep domain expertise: the more the mathematician brings to the problem, the further the machine can take it.

Javier Gómez-Serrano - Bio

Javier Gómez-Serrano is a Professor of Mathematics at Brown University. He received his PhD from the Universidad Autónoma de Madrid in 2013. He was an Instructor and then Assistant Professor at Princeton, and a Distinguished Researcher at the University of Barcelona, before joining Brown in 2022.

His research lies at the intersection of analysis, partial differential equations, fluid mechanics, spectral geometry, numerical computation, machine learning, and computer-assisted proofs. He has used physics-informed neural networks to discover new singular solutions in fluid equations, and has worked with Google DeepMind on AlphaEvolve, co-authoring several papers on its applications to mathematics and scientific computing. He has received the R. E. Moore Prize, the MCA Prize, and the Antonio Ambrosetti Medal. His research has been supported by an ERC Starting Grant and an NSF CAREER award, and is currently funded by an NSF AIMing Grant in the context of AI and Mathematics.

Javier Gomez-Serrano

Javier Gomez-Serrano