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.

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 ...

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 ...

Prince Rupert of the Rhine first asked this question in the 17th century, and he soon found out the answer is yes. Later, ...

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, ...

May 5 -- It's not often that the abstract mathematical discipline of topology is in the news, but a respected British mathematician announced last month that he has proved a nearly century-old puzzle, ...

In an old Indian parable, six blind men each touch a different part of an elephant. They disagree about what the elephant must look like: Is it smooth or rough? Is it like a snake (so thinks the man ...

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 ...