Bilinear forms and character sums have emerged as pivotal tools in analytic number theory, offering robust frameworks for investigating sums wherein variables interact multiplicatively. Bilinear forms ...

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, ...

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 ...

Algebra and Number Theory are cornerstones of modern mathematics. At their heart, these fields study the underlying structures governing numbers and abstract entities, ranging from rings, fields, and ...

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 ...

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 ...