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 ...

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 ...

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 ...

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, ...

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems. Joseph Silverman remembers when he began connecting ...

Several fields of mathematics have developed in total isolation, using their own "undecipherable" coded languages. In a new study published in Proceedings of the National Academy of Sciences, Tamás ...

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 ...