Federal Project Grant Award Summary

Brown University received a $300,000 Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), effective September 1, 2026 through August 31, 2029. The project, "Forging New Paradigms in Analysis and Partial Differential Equations: A Synergy of Artificial Intelligence and Computer-Assisted Proofs," advances fundamental mathematics research by developing and validating computer-based and artificial intelligence tools as rigorous instruments for scientific discovery. The research encompasses three primary research directions: analysis of the incompressible Euler equation and related models; investigation of the generalized surface quasi-geostrophic equation and active scalar models; and applications to spectral geometry and mathematical physics, including eigenvalue problems.

The project's methodological approach combines traditional mathematics with modern computational techniques, including interval arithmetic and computer-assisted proofs to obtain rigorous quantitative results in complex regimes, physics-informed neural networks to discover high-precision self-similar and blow-up profiles, and large language model applications to address open problems at scale. Integral to the award is an extensive education and training component that engages students from high school through the postdoctoral level in active mathematical research, develops new courses and programs, and disseminates findings to both specialist and general audiences. The project directly supports the NSF's mission to promote scientific progress and strengthen the Nation's scientific enterprise through advancement of mathematical and physical sciences.