Artificial intelligence

In this special live recording from the International Congress of Mathematicians in Philadelphia, July 2026, the central question discussed was what do mathematicians really value about doing mathematics in the first place?

Sarah Demers, chair of the physics department at Yale University, sees the potential for large language models to both help and harm her field.

Computer scientist Melanie Mitchell discusses why artificial intelligence doesn’t “think” or “reason” like humans, and how we can create better methods for measuring machine cognition.

AI’s greatest mathematical successes have come from answers to problems posed by a mid-20th century iconoclast. By examining what makes the Erdős problems unique, mathematicians are trying to understand how AI might change the rest of math.

The idea that artificial intelligence can “reason” is more intuitive than ever. But intuitions can be wrong, and the science is far from settled.

Our genetic heritage is not a blueprint or an algorithm, as many biologists have imagined, but something else entirely.

With automated proof-checkers, a problem can be broken up into small chunks, solved bit-by-bit, then reassembled with confidence that every piece is correct. For some, this heralds a new area in mathematical research.

AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.

Our tales of AI developing the will to survive, commandeer resources, and manipulate people say more about us than they do about language models.