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knot theory

An illustration of a knot that mathematicians might study using tools called invariants.
Abstractions blog

In a Single Measure, Invariants Capture the Essence of Math Objects

June 2, 2020

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

knot theory

Graduate Student Solves Decades-Old Conway Knot Problem

May 19, 2020

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.

Black and white photo of John Conway against a black background
Abstractions blog

John Conway Solved Mathematical Problems With His Bare Hands

April 20, 2020

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

Photo of two mathematicians drawing on a chalkboard
topology

Mathematics as a Team Sport

March 31, 2020

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

Multimedia

The Map of Mathematics

February 13, 2020

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

Photo of a complicated knot.
Abstractions blog

Color-Changing Material Unites the Math and Physics of Knots

February 10, 2020

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

Art for "Scientists Learn the Ropes on Tying Molecular Knots"
chemistry

Scientists Learn the Ropes on Tying Molecular Knots

October 29, 2018

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

Trefoil vortex knot.
fluid dynamics

Could Knots Unravel Mysteries of Fluid Flow?

December 9, 2013

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