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 ...

Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems. It’s one thing to turn a cartwheel in an open field. It’s ...