combinatorics – 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 Merging Fields, Mathematicians Go the Distance on Old Problem https://www.quantamagazine.org/merging-fields-mathematicians-go-the-distance-on-old-problem-20240401/ https://www.quantamagazine.org/merging-fields-mathematicians-go-the-distance-on-old-problem-20240401/#respond Mon, 01 Apr 2024 13:50:22 +0000 https://www.quantamagazine.org/?p=136723 The post Merging Fields, Mathematicians Go the Distance on Old Problem first appeared on Quanta Magazine

]]> The change of plans came on a road trip. On a beautiful day last April, the mathematicians Rachel Greenfeld and Sarah Peluse set out from their home institution, the Institute for Advanced Study in Princeton, New Jersey, heading to Rochester, New York, where both were scheduled to give talks the next day. They had been struggling for nearly two years with an important conjecture in harmonic...

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]]> https://www.quantamagazine.org/merging-fields-mathematicians-go-the-distance-on-old-problem-20240401/feed/ 0 Math That Connects Where We’re Going to Where We’ve Been https://www.quantamagazine.org/math-that-connects-where-were-going-to-where-weve-been-20240322/ https://www.quantamagazine.org/math-that-connects-where-were-going-to-where-weve-been-20240322/#respond Fri, 22 Mar 2024 13:08:27 +0000 https://www.quantamagazine.org/?p=136450 The post Math That Connects Where We’re Going to Where We’ve Been first appeared on Quanta Magazine

]]> Say you’re at a party with nine other people and everyone shakes everyone else’s hand exactly once. How many handshakes take place? This is the “handshake problem,” and it’s one of my favorites. As a math teacher, I love it because there are so many different ways you can arrive at the solution, and the diversity and interconnectedness of those strategies beautifully illustrate the power of...

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]]> https://www.quantamagazine.org/math-that-connects-where-were-going-to-where-weve-been-20240322/feed/ 0 The Surprisingly Simple Math Behind Puzzling Matchups https://www.quantamagazine.org/the-surprisingly-simple-math-behind-puzzling-matchups-20240125/ https://www.quantamagazine.org/the-surprisingly-simple-math-behind-puzzling-matchups-20240125/#respond Thu, 25 Jan 2024 16:20:30 +0000 https://www.quantamagazine.org/?p=134281 The post The Surprisingly Simple Math Behind Puzzling Matchups first appeared on Quanta Magazine

]]> It’s the championship game of the Imaginary Math League, where the Atlanta Algebras will face the Carolina Cross Products. The two teams haven’t played each other this season, but earlier in the year Atlanta defeated the Brooklyn Bisectors by a score of 10 to 5, and Brooklyn defeated Carolina by a score of 7 to 3. Does that give us any insight into who will take the title? Well, here’s one line of...

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]]> https://www.quantamagazine.org/the-surprisingly-simple-math-behind-puzzling-matchups-20240125/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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