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topology

Two red loops connected by a ghostly tube.
topology

How Complex Is a Knot? New Proof Reveals Ranking System That Works

By Leila Sloman
May 18, 2022
Read Later

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

Abel Prize

Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize

By Jordana Cepelewicz
March 23, 2022
Read Later

The American mathematician invented entire new ways to understand shapes and spaces.

2021 in Review

The Year in Math and Computer Science

By Bill Andrews
December 23, 2021
Read Later

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

geometry

Mathematicians Transcend Geometric Theory of Motion

By Kelsey Houston-Edwards
December 9, 2021
Read Later

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

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.

A video of masks swirling around.
quantum computing

Major Quantum Computing Strategy Suffers Serious Setbacks

By Philip Ball
September 29, 2021
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So-called topological quantum computing would avoid many of the problems that stand in the way of full-scale quantum computers. But high-profile missteps have led some experts to question whether the field is fooling itself.

Illustration showing yellow and green shapes over a blue background
topology

In Topology, When Are Two Shapes the Same?

By Kevin Hartnett
September 28, 2021
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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.

topology

New Math Book Rescues Landmark Topology Proof

By Kevin Hartnett
September 9, 2021
Read Later

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.

graph theory

How Big Data Carried Graph Theory Into New Dimensions

By Stephen Ornes
August 19, 2021
Read Later

Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.


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