geometry – Quanta Magazine

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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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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The Year in Math

Jordana Cepelewicz — Mon, 16 Dec 2024 17:51:28 +0000

In May, a team of nine mathematicians announced a major breakthrough. They had proved what is called the geometric Langlands conjecture — a central component of a broader research program to build a “grand unified theory” of mathematics. The proof, which totaled more than 800 pages and marked the culmination of 30 years of work, was, in the words of one mathematician, a “crowning achievement.”…

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Physicists Reveal a Quantum Geometry That Exists Outside of Space and Time

Charlie Wood — Wed, 25 Sep 2024 16:07:38 +0000

In the fall of 2022, a Princeton University graduate student named Carolina Figueiredo stumbled onto a massive coincidence. She calculated that collisions involving three different types of subatomic particles would all produce the same wreckage. It was like laying a grid over maps of London, Tokyo and New York and seeing that all three cities had train stations at the same coordinates.

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If the Universe Is a Hologram, This Long-Forgotten Math Could Decode It

Charlie Wood — Wed, 25 Sep 2024 16:06:53 +0000

John von Neumann came about as close as humanly possible to embodying the Platonic ideal of a genius. Conversant in ancient Greek by age 6, the Hungarian made significant mathematical advances in his teens. Then, as an adult, he invented game theory and helped design the atomic bomb and the modern computer. Along the way, as a young man in 1932, von Neumann rewrote the rules of quantum mechanics…

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