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 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 ...

All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...

The force we experience most intimately remains the most mysterious. Physicists understand how vast migrations of particles called photons light up our homes, and how swarms of “gluon” particles hold ...