Mathematics and Artificial Intelligence

This volume explores the enduring and increasingly vital relationship between mathematics and artificial intelligence (AI), highlighting how mathematical ideas continue to provide the foundation for advances across the AI landscape. Bringing together leading perspectives from diverse disciplines, the book examines recent developments in areas such as computational geometry, combinatorial optimization, mathematical logic, automated reasoning, probability theory, game theory, and data analysis. The contributions demonstrate how rigorous mathematical methods not only underpin intelligent systems but also drive innovation in emerging AI applications. Based on the latest research and survey presentations, the book offers a timely overview of both established principles and new directions at the interface of mathematics and artificial intelligence. Serving as a sequel to earlier landmark works on AI and mathematics, this collection reflects more than three decades of scholarly exchange fostered through the Annals of Mathematics and Artificial Intelligence journal and the International Symposium on Artificial Intelligence and Mathematics biennial conference. The chapters showcase a broad spectrum of theoretical and applied research, including topics presented at the 2025 anniversary session on AI and Mathematics at the Joint Mathematical Meetings . Dedicated to the memory of Peter L. Hammer, whose visionary contributions helped shape the field, the book celebrates the continuing power of interdisciplinary collaboration and points toward future opportunities for discovery at the intersection of mathematical sciences and artificial intelligence.