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 ...

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics. In mathematics, a simple problem is often not what it seems. Earlier this ...

After over three decades, five academic studies and one thousand pages, a team led by Yale Professor Sam Raskin has solved a part of what some consider math’s “Rosetta Stone.” Raskin led a nine-person ...

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.

The Latin root of the word conjecture, conicere, means to throw things together. Think of Jackson Pollock splashing different paints onto a canvas and hoping for some kind of coherent result. In ...

Mathematicians from New York University and the University of British Columbia have resolved a decades-old geometric problem, ...

In early 20th-century Paris, there was a boy so mesmerized by math that when his parents took his paper and pencil away, urging him to play, he found a rock and scribbled algebra equations on 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 ...