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 ...

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. Mountain climbing is a beloved metaphor for mathematical research.

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 amplituhedron, a shape at the heart of particle physics, appears to be deeply connected to the mathematics of paper ...

Can you imagine the imprint a four-dimensional hexagon might leave as it passes through your three-dimensional kitchen table? Probably not, but some people can. One such person was mathematician ...

The question seeks to find a maximum value for the area of a sofa that can slide around a 90-degree corner in a corridor of a given width. Mathematicians have long suspected that the answer lies with ...

A conjecture in geometric probability about the asymptotic normality of the r-content of the r-simplex, whose r + 1 vertices are independently uniformly distributed random points of which p are in the ...

A. Aizenbud, A partial analog of the integrability theorem for distributions on p-adic spaces and applications, Israel J. Math. 193 (2013), 233–262. MR 3038552. Zbl ...

The public’s view of the mathematician as a reclusive genius toiling away for years at an arcane problem is one that will not go away. The media have enthusiastically seized on this image since the ...