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 ...

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 ...

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, ...

The study of arithmetic properties and digit restrictions in number theory explores the intricate relationships between classical arithmetic functions and the digital representation of numbers. This ...

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 ...

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 ...