On August 26, 2026, I had the pleasure of giving a talk at the Mathematics for the Real World 2026 conference, jointly organized by the International Centre for Mathematics in Ukraine (ICMU) and the Centre for Quantum Mathematics (QM) at the University of Southern Denmark.
The talk was about artificial intelligence and math, and how both fields help and enable each other. I really enjoyed the conversations with mathematicians at the conference afterwards.
Artificial Intelligence and Math
Modern frontier AI systems are, at their core, large mathematical objects brought to life by engineering — and the mathematics behind them is readily accessible to a mathematical audience. This talk consists of two parts. In the first, I will give a high-level overview of the mathematics underlying today’s frontier AI systems: the linear algebra and probability at the heart of transformer architectures, the optimization theory behind training at scale, and the statistical ideas driving techniques such as reinforcement learning from human feedback and from verifiable rewards. In the second part, I will survey recent milestones of AI in mathematics — from performance on olympiad problems and formal proof assistants to first contributions to research-level questions — and discuss where these systems still fail and why. I will conclude with practical thoughts on how mathematicians can use AI productively today: as a collaborator for exploration, literature search, and formalization, while remaining fully in control.
My slides:
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