category theory – Quanta Magazine

The Year in Math

Konstantin Kakaes — Sat, 23 Dec 2023 01:33:58 +0000

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing impulses that disrupt those patterns. That tension came up repeatedly in our coverage this past year. We covered breakthroughs in graph theory, combinatorics, number theory and geometry — areas where...

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Is There Math Beyond the Equal Sign?

Steven Strogatz — Wed, 22 Mar 2023 06:53:03 +0000

Is there more to mathematics than the equal sign? A pair of shoes is different from a pair of gloves, yet we recognize a sameness in them because both meet our definition of a pair. Category theory is a branch of mathematics that examines how things can be essentially the same without being exactly equal. It’s what the mathematician Eugenia Cheng uses to make connections between abstract concepts...

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Conducting the Mathematical Orchestra From the Middle

Rachel Crowell — Wed, 02 Sep 2020 14:45:48 +0000

Emily Riehl sees similarities between the viola, which she grew up playing, and the mathematical field of higher category theory, in which she is currently a leading participant. She thinks of the two as the “glue” of their respective domains; just as the viola creates a richer orchestral sound, “there’s a sense in which category theory makes mathematics deeper,” she said.

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With Category Theory, Mathematics Escapes From Equality

Kevin Hartnett — Thu, 10 Oct 2019 14:00:01 +0000

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is a growing community of mathematicians who regard the equal sign as math’s original error. They see it as a veneer that hides important complexities in the way quantities are related — complexities that could unlock solutions to an...

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Will Computers Redefine the Roots of Math?

Kevin Hartnett — Tue, 19 May 2015 14:56:10 +0000

On a recent train trip from Lyon to Paris, Vladimir Voevodsky sat next to Steve Awodey and tried to convince him to change the way he does mathematics. Voevodsky, 48, is a permanent faculty member at the Institute for Advanced Study (IAS) in Princeton, N.J. He was born in Moscow but speaks nearly flawless English, and he has the confident bearing of someone who has no need to prove himself to...

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