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# proofs

## 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.

### 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.

### 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.

### Proof Assistant Makes Jump to Big-League Math

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

### The Year in Math and Computer Science

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

### Inside the Secret Math Society Known Simply as Nicolas Bourbaki

For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.

### Building the Mathematical Library of the Future

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

### At the Math Olympiad, Computers Prepare to Go for the Gold

Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

### When Math Gets Impossibly Hard

Mathematicians have long grappled with the reality that some problems just don’t have solutions.