Mathematics – 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…

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The Largest Sofa You Can Move Around a Corner

Richard Green — Fri, 14 Feb 2025 14:35:53 +0000

If you’ve ever moved into a new home, then you know how difficult it can be to steer bulky furniture through narrow hallways or around awkward corners. Mathematicians have been trying to solve this problem, too, ever since 1966, when Leo Moser framed it in quantitative terms. Say you want to move a two-dimensional shape — your sofa (disregarding its height) — through an L-shaped hallway.

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New Proofs Probe the Limits of Mathematical Truth

Joseph Howlett — Mon, 03 Feb 2025 15:31:40 +0000

The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the eminent mathematician David Hilbert announced a list of 23 key problems to guide the next century of mathematical research. His problems not only provided a road map for the field but reflected a more ambitious vision — to build a firm foundation from which all…

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The Jagged, Monstrous Function That Broke Calculus

Solomon Adams — Thu, 23 Jan 2025 15:42:09 +0000

Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky foundation. Its core concepts were rooted in intuition and informal arguments, rather than precise, formal definitions. Two schools of thought emerged in response, according to Michael Barany, a historian of math and science at the University of Edinburgh.

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Mathematicians Discover New Way for Spheres to ‘Kiss’

Gregory Barber — Wed, 15 Jan 2025 15:37:55 +0000

In May of 1694, in a lecture hall at the University of Cambridge, Isaac Newton and the astronomer David Gregory started to contemplate the nature of the stars, only to end up with a math puzzle that would persist for centuries. The details of their conversation were poorly recorded and are possibly apocryphal — it had something to do with how stars of varying sizes would orbit a central sun.

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