On June 23, 1993, the mathematician Andrew Wiles gave the last of three lectures detailing his solution to Fermat’s last theorem, a problem that had remained unsolved for three and a half centuries.

A marriage of formal methods and LLMs seeks to harness the strengths of both.

Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

Axiom says its AI found solutions to several long-standing math problems, a sign of the technology’s steadily advancing reasoning capabilities.

Take an outline map of the lower 48 U.S. states and four crayons. Can you shade in the map so that every state is a different color than each of its neighbors, without resorting to a fifth color? This ...

“You don’t have to believe in God, but you have to believe in The Book,” the Hungarian mathematician Paul Erdős once said. The Book, which only exists in theory, contains the most elegant proofs of ...

The field of theorem proving and higher‐order logic represents a confluence of computer science, mathematics and formal logic. It encompasses the automated and interactive approaches to establishing ...

Herbert Simon, the Nobel-prize winning economist, was a techno-enthusiast. In 1956 he predicted that, “within 10 years, computers would beat the world chess champion, compose ‘aesthetically satisfying ...

During my time as an eager undergraduate mathematician, I’d often wonder what it would feel like to prove a truly new result and have my name immortalised in the mathematical history books. I thought ...