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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.

As chemists tie the most complicated molecular knot yet, biophysicists create a “periodic table” that describes what kinds of knots are possible.

By investigating the central role played by knots in fluids and fields, physicists hope to unravel long-standing mysteries of turbulence.