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 ...

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American My first musical love was Beethoven. The 2nd ...

A new breakthrough that bridges number theory and geometry is just the latest triumph for a close-knit group of mathematicians. One of the first collaborations Xinyi Yuan and Wei Zhang ever undertook ...

A prime number theory equation by mathematics professor emeritus Carl Pomerance turned up on The Big Bang Theory, where it was scrawled on a white board in the background of the hit sitcom about a ...

Scientists have found what they say is a link between complex number theory and string theory. A mathematician and physicist working together found the connection, which they say is part of plotting ...

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 ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

One of the first collaborations Xinyi Yuan and Wei Zhang ever undertook was a trip to the Social Security office. It was the fall of 2004 and the two of them were promising young graduate students in ...

A basic feature of number theory, prime numbers are also a fundamental building block of computer science, from hashtables to cryptography. Everyone knows that a prime number is one that cannot be ...