Computer scientists often assume that the brain works by approximations, and therefore that computing hardware inspired by the brain won’t be as good at complex math as traditional hardware.

Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on ...

The tipping point came in the summer of 2025. That July, several artificial intelligence models solved five out of six problems at the International Mathematical Olympiad, an annual challenge for some ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...