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.

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 ...

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program. A group of nine mathematicians has proved the ...

Arun Ram receives funding from the Australian Research Council. MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000 ...

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