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topology

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topology

Mathematicians Eliminate Long-Standing Threat to Knot Conjecture

By Leila Sloman
February 2, 2023
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A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.

2022 in Review

The Year in Math

By Konstantin Kakaes
December 22, 2022
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Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

quantum computing

After a Quantum Clobbering, One Approach Survives Unscathed

By Allison Parshall
December 7, 2022
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A quantum approach to data analysis that relies on the study of shapes will likely remain an example of a quantum advantage — albeit for increasingly unlikely scenarios.

Quantized Columns

Why Mathematicians Study Knots

By David S. Richeson
October 31, 2022
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Far from being an abstract mathematical curiosity, knot theory has driven many findings in math and beyond.

geometry

The New Math of Wrinkling

By Stephen Ornes
September 22, 2022
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A comprehensive mathematical framework treats wrinkling patterns as elegant solutions to geometric problems.

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.


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