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 ...

Call a complex polynomial f(x,y) _expanding_ if there is e>0 such that for all sufficiently large finite sets A and B of complex numbers with |B| >= |A|, we have |f(A,B)| > |A|^{1+e}. A result of ...

In mathematics, ubiquitous objects called groups display nearly magical powers. Though they’re defined by just a few rules, groups help illuminate an astonishing range of mysteries. They can tell you ...