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 ...

On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries. Number theorists, however, ...

Their ambitions were always high. When Will Sawin and Melanie Matchett Wood first started working together in the summer of 2020, they set out to rethink the key components of some of the most ...

Imagine you're walking down a path, minding your own business, when suddenly you find yourself trapped in a net thrown on you by an evil troll. He poses a challenge to you: he will give you a sequence ...

One of the first collaborations Xinyi Yuan and Wei Zhang ever undertook was a trip to the Social Security office. It was the fall of 2004 and the two of them were promising young graduate students in ...

After the star-studded mystery thriller The Number 23 debuted in cinemas in 2007, many people became convinced that they were seeing the eponymous number everywhere. I was in school at that time, and ...

According to computational complexity theory, mathematical problems have different levels of difficulty in the context of their solvability. While a classical computer can solve some problems (P) in ...

Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...