chaos theory – Quanta Magazine

The Year in Math

Konstantin Kakaes — Sat, 23 Dec 2023 01:33:58 +0000

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing impulses that disrupt those patterns. That tension came up repeatedly in our coverage this past year. We covered breakthroughs in graph theory, combinatorics, number theory and geometry — areas where...

Source

Chaos Researchers Can Now Predict Perilous Points of No Return

Ben Brubaker — Thu, 15 Sep 2022 14:17:38 +0000

Predicting complex systems like the weather is famously difficult. But at least the weather’s governing equations don’t change from one day to the next. In contrast, certain complex systems can undergo “tipping point” transitions, suddenly changing their behavior dramatically and perhaps irreversibly, with little warning and potentially catastrophic consequences. On long enough timescales...

Source

Hidden Chaos Found to Lurk in Ecosystems

Joanna Thompson — Wed, 27 Jul 2022 13:29:09 +0000

Physical scientists seem to find the phenomenon of chaos everywhere: in the orbits of planets, in weather systems, in a river’s swirling eddies. For nearly three decades, ecologists considered chaos in the living world to be surprisingly rare by comparison. A new analysis, however, reveals that chaos is far more prevalent in ecosystems than researchers thought. Tanya Rogers was looking back...

Source

Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize

Jordana Cepelewicz — Wed, 23 Mar 2022 11:53:50 +0000

Dennis Sullivan has always been driven by mathematical insights that are general and beautiful and have the power to amaze — “something that grabs you, like a piece of music,” he said. An encounter with one such theorem during his second year of college spurred him to switch his major from chemical engineering to mathematics; other encounters like it would later inspire him to spend years or even...

Source

How We Can Make Sense of Chaos

David S. Richeson — Wed, 02 Mar 2022 18:31:11 +0000

In 1885, King Oscar II of Sweden announced a public challenge consisting of four mathematical problems. The French polymath Henri Poincaré focused on one related to the motion of celestial bodies, the so-called n-body problem. Will our solar system continue its clocklike motion indefinitely, will the planets fly off into the void, or will they collapse into a fiery solar death?

Source