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Geometry

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Father-Son Team Solves Geometry Problem With Infinite Folds

April 4, 2022

The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension.

An Ancient Geometry Problem Falls to New Mathematical Techniques

February 8, 2022

Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.

Why Triangles Are Easy and Tetrahedra Are Hard

January 31, 2022

The triangle angle sum theorem makes working with triangles easy. What happens when you can’t rely on it?

The Year in Math and Computer Science

December 23, 2021

Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

Mathematicians Transcend Geometric Theory of Motion

December 9, 2021

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.

Q&A

The Mathematician Who Delights in Building Bridges

November 17, 2021

Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

October 26, 2021

Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.

In Topology, When Are Two Shapes the Same?

September 28, 2021

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

The Journey to Define Dimension

September 13, 2021

The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.

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