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# Geometry

## Latest Articles

### Surfaces So Different Even a Fourth Dimension Can’t Make Them the Same

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

### Surfaces Beyond Imagination Are Discovered After Decades-Long Search

Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

### Father-Son Team Solves Geometry Problem With Infinite Folds

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

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.