knot theory

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

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.

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.