Konstantin Kakaes – 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...

Source

]]> https://www.quantamagazine.org/what-are-sheaves-20240719/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...

Source

]]> https://www.quantamagazine.org/the-biggest-discoveries-in-math-in-2023-20231222/feed/ 0 A Triplet Tree Forms One of the Most Beautiful Structures in Math https://www.quantamagazine.org/a-triplet-tree-forms-one-of-the-most-beautiful-structures-in-math-20231212/ https://www.quantamagazine.org/a-triplet-tree-forms-one-of-the-most-beautiful-structures-in-math-20231212/#respond Tue, 12 Dec 2023 15:10:55 +0000 https://www.quantamagazine.org/?p=133151 The post A Triplet Tree Forms One of the Most Beautiful Structures in Math first appeared on Quanta Magazine

]]> Most people are only familiar with a handful of numbers that can’t be written as fractions, like $latex sqrt{2}$ or $latex pi$. But such numbers, called irrational numbers, are far more plentiful than fractions or rational numbers. How easy are they to approximate with fractions? If you use a fraction with an arbitrarily large denominator, you can get arbitrarily close. (As is well known, 22/7...

Source

]]> https://www.quantamagazine.org/a-triplet-tree-forms-one-of-the-most-beautiful-structures-in-math-20231212/feed/ 0 The Year in Math https://www.quantamagazine.org/the-biggest-math-breakthroughs-in-2022-20221222/ https://www.quantamagazine.org/the-biggest-math-breakthroughs-in-2022-20221222/#respond Thu, 22 Dec 2022 16:00:09 +0000 https://www.quantamagazine.org/?p=121400 The post The Year in Math first appeared on Quanta Magazine

]]> We can think of a mathematician as a kind of archaeologist, painstakingly brushing dust off the hidden structures of the world. But the structures mathematicians reveal are not only durable, but also inevitable. They could never have been any other way. They are also remarkably interconnected: Though each year the mathematical frontier continues to expand as new discoveries are made...

Source

]]> https://www.quantamagazine.org/the-biggest-math-breakthroughs-in-2022-20221222/feed/ 0