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proofs

geometry

An Ancient Geometry Problem Falls to New Mathematical Techniques

By Steve Nadis
February 8, 2022
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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.

topology

How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

By Kevin Hartnett
October 26, 2021
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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.

topology

New Math Book Rescues Landmark Topology Proof

By Kevin Hartnett
September 9, 2021
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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.

Illustration of colorful flowchart using raised blocks against a black background
proofs

Proof Assistant Makes Jump to Big-League Math

By Kevin Hartnett
July 28, 2021
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Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

2020 in Review

The Year in Math and Computer Science

By Bill Andrews
December 23, 2020
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Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

Black and white historical photo of eight men in front of a building, including Henri Cartan, André Weil and Szolem Mandelbrojt.
Abstractions blog

Inside the Secret Math Society Known Simply as Nicolas Bourbaki

By Kevin Hartnett
November 9, 2020
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For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.

Illustration of researchers building and writing a digital library, which helps a humanoid robot do advanced math
foundations of mathematics

Building the Mathematical Library of the Future

By Kevin Hartnett
October 1, 2020
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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.

Photo of students sitting at desks competing in the International Mathematical Olympiad
Abstractions blog

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

By Kevin Hartnett
September 21, 2020
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Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

An abstract illustration showing broken tools, cubes, numbers and other abstract representations of impossible math
Quantized Columns

When Math Gets Impossibly Hard

By David S. Richeson
September 14, 2020
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Mathematicians have long grappled with the reality that some problems just don’t have solutions.


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