After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in ...

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

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 ...

Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a mathematician astray. Early evidence might not represent the bigger picture ...

During my time as an eager undergraduate mathematician, I’d often wonder what it would feel like to prove a truly new result and have my name immortalised in the mathematical history books. I thought ...

An attempt to fix problems with a controversial mathematical proof has itself become mired in controversy, in the latest twist in a saga that has been running for over a decade and has seen ...

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 ...

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 ...

When a top-tier mathematician announced in August that he had proved one of the greatest problems in mathematics, the claim was trumpeted in the New York Times, Nature, Science and the Boston Globe.