AI is expanding the capacity to generate mathematical arguments, numerical algorithms, andscientific software. The IPAM workshop explored how these capabilities might translate intoreliable scientific knowledge. A central opportunity is to connect AI for mathematics andscience with mathematics for reliable, efficient AI. Potential advances include certifiedsolutions […]

Fusion energy represents one of the most complex scientific and engineering challenges, characterized by multi-scale, multi-physics problems spanning wide ranges of physical and temporal scales. First-principles, high-fidelity simulations require the world’s largest supercomputers running for days or weeks to simulate a single plasma realization, severely […]

Electrochemistry bridges chemistry, materials science, biomolecular science, and mathematics to explain how electrical and chemical processes interact at the atomic scale. It underpins critical technologies—including batteries, fuel cells, electrolyzers, metal separation, and green-chemical synthesis—and provides a scientific foundation for sustainable technologies addressing renewable-energy integration, carbon […]

This document summarizes the activities and outcomes of the Long Program “Non-commutative Optimal Transport,” which was held at the Institute of Pure and Applied Mathematics (IPAM) from March 10 to June 13, 2025. It also briefly explores some of the current open questions and future […]