Proofs

Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.