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# geometry

## Latest Articles

### An Ancient Geometry Problem Falls to New Mathematical Techniques

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

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

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

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

### The Mathematician Who Delights in Building Bridges

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

### How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

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?

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

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

### New Math Book Rescues Landmark Topology Proof

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it.