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knot theory

Latest Articles

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.

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.

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.

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.

The Joy of Why

Deep Curiosity Inspires The Joy of Why Podcast

By Steven Strogatz
March 17, 2022
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The noted mathematician and author Steven Strogatz explains how the conversations with experts in his new Quanta Magazine podcast address his lifelong fascination with timeless mysteries.

machine learning

Machine Learning Becomes a Mathematical Collaborator

By Kelsey Houston-Edwards
February 15, 2022
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Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.

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.

An illustration of a knot that mathematicians might study using tools called invariants.
Abstractions blog

In a Single Measure, Invariants Capture the Essence of Math Objects

By Erica Klarreich
June 2, 2020
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To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.


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