algebraic geometry – 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 What Are Sheaves? https://www.quantamagazine.org/what-are-sheaves-20240719/ https://www.quantamagazine.org/what-are-sheaves-20240719/#respond Fri, 19 Jul 2024 14:00:55 +0000 https://www.quantamagazine.org/?p=139212 The post What Are Sheaves? first appeared on Quanta Magazine

]]> In 1940, the French mathematician and artillery officer Jean Leray was taken prisoner by the Germans. He told his captors that he was a topologist, fearful that if they discovered his true area of expertise, hydrodynamics, they would force him to aid the German war effort. For the nearly five years of his imprisonment, Leray kept up this subterfuge by carrying out research in topology...

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]]> https://www.quantamagazine.org/what-are-sheaves-20240719/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 ‘The Rest of the World Disappears’: Claire Voisin on Mathematical Creativity https://www.quantamagazine.org/a-mathematician-on-creativity-art-logic-and-language-20240313/ https://www.quantamagazine.org/a-mathematician-on-creativity-art-logic-and-language-20240313/#respond Wed, 13 Mar 2024 14:10:51 +0000 https://www.quantamagazine.org/?p=136219 The post ‘The Rest of the World Disappears’: Claire Voisin on Mathematical Creativity first appeared on Quanta Magazine

]]> It took a long time for Claire Voisin to fall in love with mathematics. That’s not to say she ever disliked the subject. Growing up in France — the 10th of 12 children — she enjoyed spending hours solving math problems with her father, an engineer. By the time she turned 12, she had begun reading a high school algebra textbook on her own, fascinated by the definitions and proofs outlined in its...

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]]> https://www.quantamagazine.org/a-mathematician-on-creativity-art-logic-and-language-20240313/feed/ 0 What Makes for ‘Good’ Mathematics? https://www.quantamagazine.org/what-makes-for-good-mathematics-20240201/ https://www.quantamagazine.org/what-makes-for-good-mathematics-20240201/#respond Thu, 01 Feb 2024 14:03:12 +0000 https://www.quantamagazine.org/?p=134856 The post What Makes for ‘Good’ Mathematics? first appeared on Quanta Magazine

]]> We tend to think of mathematics as purely logical, but the teaching of math, its values, its usefulness and its workings are packed with nuance. So what is “good” mathematics? In 2007, the mathematician Terence Tao wrote an essay for the Bulletin of the American Mathematical Society that sought to answer this question. Today, as the recipient of a Fields Medal, a Breakthrough Prize in Mathematics...

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]]> https://www.quantamagazine.org/what-makes-for-good-mathematics-20240201/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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