group theory – Quanta Magazine

After 20 Years, Math Couple Solves Major Group Theory Problem

Leila Sloman — Wed, 19 Feb 2025 15:45:12 +0000

In 2003, a German graduate student named Britta Späth encountered the McKay conjecture, one of the biggest open problems in the mathematical realm known as group theory. At first her goals were relatively modest: She hoped to prove a theorem or two that would make incremental progress on the problem, as many other mathematicians had done before her. But over the years, she was drawn back to it…

Source

‘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…

Source

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.

Source

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…

Source

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. Hart’…

Source