Speaker: Javier Gomez-Serrano, Brown University
Talk: "AI-Driven Mathematical Discovery: Singularities, Algorithms, and Beyond"
Machine learning is transforming mathematical discovery, enabling advances on longstanding open problems. This talk explores two complementary approaches illustrating different paradigms for AI and mathematics.
First, I will present a systematic discovery of unstable singularities in multi-dimensional partial differential equations. While most numerical methods historically found only stable singularities, we discover families of unstable singularities requiring infinitely precise initial conditions. Combining curated machine learning architectures with high-precision optimization and mathematical analysis, we achieve in some cases near machine precision, meeting requirements for rigorous computer-assisted proofs.
Second, I will discuss AlphaEvolve, a general-purpose evolutionary coding agent that uses large language models to autonomously discover old and new mathematical constructions and potentially go beyond them. AlphaEvolve tackles a wide variety of problems across analysis, geometry, combinatorics, and number theory. This illustrates how general-purpose AI systems can systematically successfully explore broad mathematical landscapes at an unprecedented speed, leading us to do mathematics at scale.
These examples reveal complementary roles for machine learning and mathematics in the future: deep, precision-focused small models for specific problems versus broad, systematic exploration across domains via large models.
Bio:
Professor Gomez-Serrano completed his PhD in Mathematics at the Universidad Autónoma de Madrid, where his dissertation won the best of the year award.
His research operates at the intersection of partial differential equations, fluid mechanics, spectral geometry, rigorous computer-assisted proofs, and machine learning. He is recognized for effectively integrating AI into mathematical research. He has utilized Physics-Informed Neural Networks (PINNs) alongside other computational methods to help locate self-similar blow-up profiles in fluid equations. He has collaborated with Google DeepMind to develop AlphaEvolve, an AI system capable of tackling open problems across multiple mathematical fields.
His work has been featured in prominent science/news outlets, including Quanta Magazine, El País, Communications of the ACM, Scientific American, Spektrum.
His innovative work has been recognized with international accolades. In 2025, he received the R.E.Moore Prize for Applications of Interval Analysis, the MCA Prize from the Mathematical Congress of the Americas, and was named a Simons Fellow in Mathematics. Additional distinctions include: The Antonio Ambrosetti Medal (2023), The Antonio Valle Prize (2018), and The Vicent Caselles Mathematical Research Award from the Spanish Royal Mathematical Society and the BBVA Foundation (2017). Currently, his work is backed by an NSF AIMing Grant, which funds the development of machine learning methodologies to solve complex mathematical problems.