Abstract:

This talk is divided into two parts. The first focuses on mathematics for AI: we will explore how mathematical tools are used to design, analyze, and improve neural network architectures, training algorithms, and more broadly, the foundations of machine learning systems. The second part looks at AI for mathematics. Recent progress in large language models (LLMs), which rely on generative networks to perform reasoning tasks, has placed mathematics at the center of today’s breakthroughs. Training and applying these models raises questions about how mathematics is expressed in natural (informal) language as well as how it can be formalized in structured systems such as Lean. This two-way interaction opens new possibilities for AI-assisted mathematical research, while also raising important questions about the future roles of teachers and researchers in mathematics.