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 ...

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 ...

A mathematical problem more than 300 years old gets a formal proof with the help of computer formal verification. A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler ...

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 ...

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 ...