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topology

Seifert surfaces formed from closed loops.
topology

Special Surfaces Remain Distinct in Four Dimensions

By Kevin Hartnett
June 16, 2022
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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.

An illustration of a person walking across a surface with many holes.
topology

Unimaginable Surfaces Discovered After Decades-Long Search

By Leila Sloman
June 2, 2022
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Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

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

The Joy of Why

Untangling Why Knots Are Important

By Steven Strogatz
April 6, 2022
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Steven Strogatz explores the mysteries of knots with the mathematicians Colin Adams and Lisa Piccirillo.

Abel Prize

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

By Jordana Cepelewicz
March 23, 2022
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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
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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
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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.


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