dynamical systems – Quanta Magazine

How America’s Fastest Swimmers Use Math to Win Gold

Jordana Cepelewicz — Wed, 10 Jul 2024 14:45:34 +0000

In the fall of 2014, Andrew Wilson took a front-row seat in Ken Ono’s number theory class at Emory University in Atlanta. Wilson was not only double majoring in applied math and physics, he was a walk-on member of Emory’s swim team. Ono took an interest in Wilson’s ambitions. “We thought that together, maybe we could use our interest in mathematics to help him improve as a swimmer,” Ono said. Ono...

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‘Entropy Bagels’ and Other Complex Structures Emerge From Simple Rules

Jordana Cepelewicz — Tue, 27 Feb 2024 15:49:38 +0000

Repetition doesn’t always have to be humdrum. In mathematics, it is a powerful force, capable of generating bewildering complexity. Even after decades of study, mathematicians find themselves unable to answer questions about the repeated execution of very simple rules — the most basic “dynamical systems.” But in trying to do so, they have uncovered deep connections between those rules and other...

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Unfolding the Mysteries of Polygonal Billiards

David S. Richeson — Thu, 15 Feb 2024 16:05:41 +0000

In Disney’s 1959 film Donald in Mathmagic Land, Donald Duck, inspired by the narrator’s descriptions of the geometry of billiards, energetically strikes the cue ball, sending it ricocheting around the table before it finally hits the intended balls. Donald asks, “How do you like that for mathematics?” Because rectangular billiard tables have four walls meeting at right angles...

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The Quest to Decode the Mandelbrot Set, Math’s Famed Fractal

Jordana Cepelewicz — Fri, 26 Jan 2024 16:46:49 +0000

In the mid-1980s, like Walkman cassette players and tie-dyed shirts, the buglike silhouette of the Mandelbrot set was everywhere. Students plastered it to dorm room walls around the world. Mathematicians received hundreds of letters, eager requests for printouts of the set. (In response, some of them produced catalogs, complete with price lists; others compiled its most striking features into...

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Flow Proof Helps Mathematicians Find Stability in Chaos

Jordana Cepelewicz — Thu, 15 Jun 2023 14:46:40 +0000

As with so much in mathematics, the proof started with coffee. In September 2019, Kathryn Mann of Cornell University visited Kingston, Ontario, to give a guest lecture at Queen’s University. Afterward, she sat down with her host, Thomas Barthelmé, for what was supposed to be a quick cup of coffee. He wanted to get her opinion on a problem he was working on involving mathematical models called...

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