topology

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.

It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.

Modern mathematics relies on collaboration and travel. COVID-19 is making it increasingly difficult.

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

When 50 mathematicians spend a week in the woods, there’s no telling what will happen. And that’s the point.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Mathematicians have studied knots for centuries, but a new material is showing why some knots are better than others.

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.