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topology

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.

Art for "Möbius Strips Defy a Link With Infinity"
topology

Möbius Strips Defy a Link With Infinity

February 20, 2019

A new proof shows why an uncountably infinite number of Möbius strips will never fit into a three-dimensional space.

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.

Photo of Dr. Peter Scholze
2018 Fields Medal and Nevanlinna Prize

A Master of Numbers and Shapes Who Is Rewriting Arithmetic

August 1, 2018

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

520px illustration of classification of phases
condensed matter physics

Physicists Aim to Classify All Possible Phases of Matter

January 3, 2018

A complete classification could lead to a wealth of new materials and technologies. But some exotic phases continue to resist understanding.