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 ...

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.

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 ...

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 ...

Neuroscientists are exploring whether shapes like squares and rectangles — and our ability to recognize them — are part of what makes our species special. Credit...Video by Yoshi Sodeoka Supported by ...

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 ...