Iwasawa theory investigates the variation of arithmetic invariants—such as class groups and Selmer groups—along infinite towers of number fields, most classically the cyclotomic Z p-extension of the ...

Partition theory studies the ways in which a positive integer can be expressed as a sum of positive integers, without regard to order. Originating in the work of Euler, it has evolved through 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 ...

“There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, ...