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

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

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 ...

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 ...

Sitting outside a Catholic church on the French Riviera, Carlo Rovelli jutted his head forward and backward, imitating a pigeon trotting by. Pigeons bob their heads, he told me, not only to stabilize ...

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 ...

Imagine that someone gives you a list of five numbers: 1, 6, 21, 107 and — wait for it — 47,176,870. Can you guess what comes next? If you’re stumped, you’re not alone. These are the first five busy ...

Physicists recently mapped the hidden shape that underlies the quantum behaviors of a crystal, using a new method that’s expected to become ubiquitous. Famously, at the quantum scale, particles can be ...