Every pure mathematician has experienced that awkward moment when asked, “So what’s your research good for?” There are standard responses: a proud “Nothing!”; an explanation that mathematical research ...

In pure mathematics, very occasionally, breakthroughs arrive like bolts from the blue – the result of such inspired feats of reasoning and creativity that they seem to push the very bounds of ...

Mathematics is full of weird number systems that most people have never heard of and would have trouble even conceptualizing. But rational numbers are familiar. They’re the counting numbers and the ...

One of the reasons artificial intelligence is such an interesting field is that pretty much no one knows what it might turn out to be good at. Two papers by leading labs published in the journal ...

They had to throw away most of what it produced but there was gold among the garbage. Google DeepMind has used a large language model to crack a famous unsolved problem in pure mathematics. In a paper ...

THIS is a thoroughly good book which deserves to run through many editions. It is not (as its title might suggest) a book on mathematical logic or philosophy: it deals not with the nature of ...