Number theory, the study of the properties of positive integers, is perhaps the purest form of mathematics. At first sight, it may seem far too abstract to apply to the natural world. In fact, the ...

It’s not often that a mathematics textbook is described as “gorgeous” or “a work of practical art.” But An Illustrated Theory of Numbers by Martin Weissman, associate professor of mathematics at UC ...

Melanie Matchett Wood is a professor of mathematics at Harvard University and a Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study. In October, she was awarded the MacArthur ...

It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question. Landmark results ...

After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in ...

The search for artistic truth and beauty has led Manjul Bhargava to some of the most profound recent discoveries in number theory. For Manjul Bhargava, the counting numbers don’t simply line ...

After the star-studded mystery thriller The Number 23 debuted in cinemas in 2007, many people became convinced that they were seeing the eponymous number everywhere. I was in school at that time, and ...

The original version of this story appeared in Quanta Magazine. A new proof has brought mathematicians one step closer to understanding the hidden order of those “atoms of arithmetic,” the prime ...

Number theory is the branch of mathematics that deals with the properties of whole numbers. Many number theorists are motivated purely by mathematical intrigue, and historically number theory had few ...

Number Theory is one of the oldest branches of modern mathematics. It is motivated by the study of properties of integers and solutions to equations in integers. Many of its problems can be stated ...