The Poincaré conjecture can be understood by analogy with the case in two dimensions. A two-dimensional space, or surface, is like a bubble made from an infinitely thin film of soap. If the bubble is ...

Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.

This year’s Abel Prize, an annual lifetime achievement award for mathematics that is bestowed by the Norwegian Academy of ...

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 Rochester Institute of Technology doctoral student was part of a team of researchers that settled a 90-year-old math problem called Keller’s conjecture. David Narváez, who studies computing and ...

Since the conjecture was already known to be true in one and two dimensions, they sought to prove it in three: to show that if you can shift copies of one shape to tile all of three-dimensional space, ...

The Collatz conjecture is also known as the “3n + 1” problem. It’s an easy problem to explain and check, and has been tested up into the nineteen figure range. But it’s only now that anyone has come ...