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 ...

Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a ...

Mathematicians have proved a key building block of the Langlands programme, sometimes referred to as a “grand unified theory” of maths due to the deep links it proposes between seemingly distant ...

In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate ...