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.

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 ...

Annals of Mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. Annals of Mathematics is published bimonthly with the cooperation of Princeton University ...

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers. On its surface, the Kakeya conjecture is a simple statement about rotating ...

Given a nonempty compact connected subset $X\subset {\Bbb S}^{2}$ with complement a simply-connected open subset $\Omega \subset {\Bbb S}^{2}$, let Dome(Ω) be the ...

Pierre Deligne netted the prize, one oft he most prestigious in mathematics and worth about $1 million, for proving a deep conjecture about algebraic geometry which has helped to transform number ...

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program. The grandest project in mathematics has ...