Joint Distinguished Interdisciplinary and Applied Mathematics and Mathematics Colloquium
Title: AI-Driven Mathematical Discovery: Singularities, Algorithms, and Beyond
Speaker: Javier Gómez-Serrano (Brown University)
Date, Time, Location: Wednesday, March 25th @4:30 PM – 5:30 PM in Math Hall 520
Abstract:
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. On the one hand, 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. On the other, 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. Together, 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.
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