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 ...

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 ...

Goro Shimura, Princeton's Michael Henry Strater University Professor of Mathematics, Emeritus, died on Friday, May 3, in Princeton, New Jersey. He was 89. “Goro Shimura was a major research ...

Number theorist Peter Scholze, who became Germany’s youngest ever full professor aged 24, and geometrician Caucher Birkar—a Kurdish refugee—are among the winners of this year’s Fields Medals, the most ...