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 ...

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 ...

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one results in a ...

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 ...

Monstrous moonshine, a quirky pattern of the monster group in theoretical math, has a shadow - umbral moonshine. Mathematicians have now proved this insight, known as the Umbral Moonshine Conjecture, ...

The grandest project in mathematics has received a rare gift, in the form of a mammoth 350-page paper posted in February that will change the way researchers around the world investigate some of the ...

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 ...