group theory – Quanta Magazine

‘Groups’ Underpin Modern Math. Here’s How They Work.

Leila Sloman — Fri, 06 Sep 2024 15:05:01 +0000

Mathematics started with numbers — clear, concrete, intuitive. Over the last two centuries, however, it has become a far more abstract enterprise. One of the first major steps down this road was taken in the late 18th and early 19th centuries. It involved a field called group theory, and it changed math — theoretical and applied — as we know it. Groups generalize essential properties of the whole...

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Monumental Proof Settles Geometric Langlands Conjecture

Erica Klarreich — Fri, 19 Jul 2024 14:02:17 +0000

A group of nine mathematicians has proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof represents the culmination of three decades of effort, said Peter Scholze, a prominent mathematician at the Max Planck Institute for Mathematics who was not involved in the proof. “It’s wonderful to see it resolved.

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Mathematicians Marvel at ‘Crazy’ Cuts Through Four Dimensions

Jordana Cepelewicz — Mon, 22 Apr 2024 15:22:13 +0000

The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists understand such two-dimensional manifolds very well. And they have developed tools that let them make sense of three-dimensional manifolds and those with five or more dimensions. But in four dimensions...

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The Mathematician Who Finds the Poetry in Math and the Math in Poetry

Leila Sloman — Fri, 12 Jan 2024 15:40:11 +0000

Sarah Hart has always had an eye for the covert ways mathematics permeates other fields. As a child, she was struck by the ubiquity of the number 3 in her fairy tales. Hart’s mother, a math teacher, encouraged her pattern-seeking, giving her math puzzles to pass the time. Hart went on to earn a doctorate in group theory in 2000 and later became a professor at Birkbeck, University of London.

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A Close-Up View Reveals the ‘Melting’ Point of an Infinite Graph

Kelsey Houston-Edwards — Mon, 18 Dec 2023 16:10:24 +0000

In 2008, the mathematician Oded Schramm died in a hiking accident in the Cascade mountains some 50 miles east of Seattle. Though he was just 46 years old, he had constructed entirely new areas of mathematics. “He was a fantastic mathematician,” said Itai Benjamini, a mathematician at the Weizmann Institute of Science and Schramm’s friend and collaborator. “Extremely creative, extremely elegant...

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