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 ...

There are three kinds of prime numbers. The first is a solitary outlier: 2, the only even prime. After that, half the primes leave a remainder of 1 when divided by 4. The other half leave a remainder ...

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 ...

The University of Colorado Center for Number Theory has interests spanning number theory, from analytic to algebraic. There is a focus on arithmetic geometry, including arithmetic dynamics, elliptic ...