One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...

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.

When Hannah Cairo was 17 years old, she disproved the Mizohata-Takeuchi conjecture, a long-standing guess in the field of harmonic analysis about how waves behave on curved surfaces. The conjecture ...

The world may seem orderly, but randomness and chaos shape everything in the universe, from enormous galaxies all the way down to subatomic particles. Take a chilly window sheeting over with ice: even ...

Is it possible to deduce the shape of a drum from the sounds it makes? This is the kind of question that Iosif Polterovich, a professor in the Department of Mathematics and Statistics at Université de ...

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems. On September ...