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topology

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

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.

Abstractions blog

Math After COVID-19

April 28, 2020

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

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.

Animation showing two sets of tangrams cycling between identical squares and different shapes.
geometry

Mathematicians Cut Apart Shapes to Find Pieces of Equations

October 31, 2019

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

foundations of mathematics

With Category Theory, Mathematics Escapes From Equality

October 10, 2019

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