Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major ...

The reason we can gracefully glide on an ice-skating rink or clumsily slip on an icy sidewalk is that the surface of ice is ...

Large language models such as ChatGPT come with filters to keep certain info from getting out. A new mathematical argument ...

Is language core to thought, or a separate process? For 15 years, the neuroscientist Ev Fedorenko has gathered evidence of a ...

Researchers have used metamathematical techniques to show that certain theorems that look superficially distinct are in fact ...

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program. A group of nine mathematicians has proved the ...

What movie do these emojis describe? That prompt was one of 204 tasks chosen last year to test the ability of various large language models (LLMs) — the computational engines behind AI chatbots such ...

In mathematics, ubiquitous objects called groups display nearly magical powers. Though they’re defined by just a few rules, groups help illuminate an astonishing range of mysteries. They can tell you ...

In cellular automata, simple rules create elaborate structures. Now researchers can start with the structures and reverse-engineer the rules. Alexander Mordvintsev showed me two clumps of pixels on ...

For three decades, researchers hunted in vain for new elementary particles that would have explained why nature looks the way it does. As physicists confront that failure, they’re reexamining a ...

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise. In October 2018, David Asperó was on holiday in Italy, gazing out a car ...