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 ...

In Chasing (a) Conjecture, Khare has done more than narrate a personal triumph. He has rendered the abstract palpably human, ...

(Phys.org)—A group of mathematicians specializing in arithmetic geometry met for five days earlier this month in an attempt to understand a proof constructed by Shinichi Mochizuki, of Kyoto University ...

Yesterday I was doing some literature review for an article I’m writing about my inverted transition-to-proof class, and I got around to reading a paper by Guershon Harel and Larry Sowder¹ about ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

The Collatz conjecture is also known as the “3n + 1” problem. It’s an easy problem to explain and check, and has been tested up into the nineteen figure range. But it’s only now that anyone has come ...

What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide ...

A Russian mathematician may have finally cracked one of the most famous problems in mathematics: the Poincaré conjecture, a question about the shapes of three-dimensional spaces. If his work is ...

New computer tools have the potential to revolutionize the practice of mathematics by providing more-reliable proofs of mathematical results than have ever been possible in the history of humankind.