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 ...

A new series of papers has settled a long-standing question related to the popular game in which players seek patterned sets of three cards. In a series of papers posted online in recent weeks, ...

Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us? A 125-page proof posted to arXiv may represent a huge breakthrough in geometric ...

If pure math can teach us anything, it’s this: occasionally, your special interest might just change the world. For Joshua Zahl and Hong Wang, that special interest was the Kakeya conjecture. “I read ...