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knot theory

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
Read Later

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
Read Later

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.

knot theory

Graduate Student Solves Decades-Old Conway Knot Problem

By Erica Klarreich
May 19, 2020
Read Later

It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.

Black and white photo of John Conway against a black background
Abstractions blog

John Conway Solved Mathematical Problems With His Bare Hands

By Kevin Hartnett
April 20, 2020
Read Later

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.


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