Group theory serves as a fundamental language for describing symmetry in both mathematics and physics. Finite groups, defined by their limited number of elements, are central to modern algebra and ...

The original version of this story appeared in Quanta Magazine. In 2003, a German graduate student named Britta Späth encountered the McKay conjecture, one of the biggest open problems in the ...

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical ...

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 ...

In 1978, the mathematician John McKay noticed what seemed like an odd coincidence. He had been studying the different ways of representing the structure of a mysterious entity called the monster group ...