Mathematics often feels like a collection of isolated islands. Each one operates with its own rules, and building bridges ...

This year’s Abel prize, an annual mathematics lifetime-achievement award, bestowed by the Norwegian Academy of Science and Letters and modeled on the Nobel Prize, has been given to Gerd Faltings, a ...

Gerd Faltings proved a conjecture that had been unsolved for six decades, using connections between numbers and geometry.

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 Collatz Conjecture is a deceptively simple math problem. It has only two rules. First, pick any number. If it's even, divide it by two. If it's odd, multiply it by three and add one. This will ...

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, ...