Topic: Mathematical proofs

Mathematicians Sylvia Serfaty and Amaury Hayat discuss AI-assisted mathematical research with Alexandra Delbot. The conversation examines recent claims of difficult problem solving, how researchers assess and understand machine-generated proofs, and the implications for publication, mathematical practice and the responsibilities raised by the Leiden declaration.

Steven Strogatz and Harvard mathematician Melanie Matchett Wood explore what counts as evidence in number theory before a rigorous proof is available. Their discussion examines how probability and randomness guide conjectures about prime numbers and infinite collections, and how probabilistic patterns can lead mathematicians toward certainty.