Ramsey theory – Quanta Magazine https://www.quantamagazine.org Illuminating science Mon, 16 Sep 2024 14:10:47 -0400 en-US hourly 1 https://wordpress.org/?v=6.2 Grad Students Find Inevitable Patterns in Big Sets of Numbers https://www.quantamagazine.org/grad-students-find-inevitable-patterns-in-big-sets-of-numbers-20240805/ https://www.quantamagazine.org/grad-students-find-inevitable-patterns-in-big-sets-of-numbers-20240805/#respond Mon, 05 Aug 2024 14:27:52 +0000 https://www.quantamagazine.org/?p=139566 The post Grad Students Find Inevitable Patterns in Big Sets of Numbers first appeared on Quanta Magazine

]]> In late 2017, Ashwin Sah and Mehtaab Sawhney met as undergraduates at the Massachusetts Institute of Technology. Since then, the pair have written a mind-boggling 57 math proofs together, many of them profound advances in various fields. In February, Sah and Sawhney announced yet another joint accomplishment. With James Leng, a graduate student at the University of California, Los Angeles...

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]]> https://www.quantamagazine.org/grad-students-find-inevitable-patterns-in-big-sets-of-numbers-20240805/feed/ 0 In Highly Connected Networks, There’s Always a Loop https://www.quantamagazine.org/in-highly-connected-networks-theres-always-a-loop-20240607/ https://www.quantamagazine.org/in-highly-connected-networks-theres-always-a-loop-20240607/#respond Fri, 07 Jun 2024 14:20:26 +0000 https://www.quantamagazine.org/?p=138387 The post In Highly Connected Networks, There’s Always a Loop first appeared on Quanta Magazine

]]> As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They can be used to attack a wide variety of problems, from modeling neurons in the brain to routing delivery trucks on the roads. Within math, they can be used to categorize important algebraic objects...

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]]> https://www.quantamagazine.org/in-highly-connected-networks-theres-always-a-loop-20240607/feed/ 0 The Year in Math https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/ https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/#respond Sat, 23 Dec 2023 01:33:58 +0000 https://www.quantamagazine.org/?p=132809 The post The Year in Math first appeared on Quanta Magazine

]]> 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...

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]]> https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/feed/ 0 The Lawlessness of Large Numbers https://www.quantamagazine.org/mathematical-tricks-for-taming-the-middle-distance-20230707/ https://www.quantamagazine.org/mathematical-tricks-for-taming-the-middle-distance-20230707/#respond Fri, 07 Jul 2023 13:20:38 +0000 https://www.quantamagazine.org/?p=127628 The post The Lawlessness of Large Numbers first appeared on Quanta Magazine

]]> So far this year, Quanta has chronicled three major advances in Ramsey theory, the study of how to avoid creating mathematical patterns. The first result put a new cap on how big a set of integers can be without containing three evenly spaced numbers, like {2, 4, 6} or {21, 31, 41}. The second and third similarly put new bounds on the size of networks without clusters of points that are either all...

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]]> https://www.quantamagazine.org/mathematical-tricks-for-taming-the-middle-distance-20230707/feed/ 0 Mathematicians Discover Novel Way to Predict Structure in Graphs https://www.quantamagazine.org/mathematicians-discover-new-way-to-predict-structure-in-graphs-20230622/ https://www.quantamagazine.org/mathematicians-discover-new-way-to-predict-structure-in-graphs-20230622/#respond Thu, 22 Jun 2023 14:35:33 +0000 https://www.quantamagazine.org/?p=127094 The post Mathematicians Discover Novel Way to Predict Structure in Graphs first appeared on Quanta Magazine

]]> It has been an exhilarating year in combinatorics research. In early 2023, mathematicians were stunned when two of the biggest problems in the field were solved in as many months. Now, a third major question has fallen with a 14-page proof “that has absolutely all the right ideas,” said Mehtaab Sawhney of the Massachusetts Institute of Technology, who added: “It’s completely shocking.

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