symmetry – 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 ‘Groups’ Underpin Modern Math. Here’s How They Work. https://www.quantamagazine.org/groups-underpin-modern-math-heres-how-they-work-20240906/ https://www.quantamagazine.org/groups-underpin-modern-math-heres-how-they-work-20240906/#respond Fri, 06 Sep 2024 15:05:01 +0000 https://www.quantamagazine.org/?p=140376 The post ‘Groups’ Underpin Modern Math. Here’s How They Work. first appeared on Quanta Magazine

]]> Mathematics started with numbers — clear, concrete, intuitive. Over the last two centuries, however, it has become a far more abstract enterprise. One of the first major steps down this road was taken in the late 18th and early 19th centuries. It involved a field called group theory, and it changed math — theoretical and applied — as we know it. Groups generalize essential properties of the whole...

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]]> https://www.quantamagazine.org/groups-underpin-modern-math-heres-how-they-work-20240906/feed/ 0 What Can Tiling Patterns Teach Us? https://www.quantamagazine.org/what-can-tiling-patterns-teach-us-20240703/ https://www.quantamagazine.org/what-can-tiling-patterns-teach-us-20240703/#respond Wed, 03 Jul 2024 13:20:01 +0000 https://www.quantamagazine.org/?p=138915 The post What Can Tiling Patterns Teach Us? first appeared on Quanta Magazine

]]> In the tiling of wallpaper and bathroom floors, collective repeated patterns often emerge. Mathematicians have long tried to find a tiling shape that never repeats in this way. In 2023, they lauded an unexpected amateur victor. That discovery of the elusive aperiodic monotile propelled the field into new dimensions. The study of tessellation is much more than a fun thought exercise: Peculiar...

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]]> https://www.quantamagazine.org/what-can-tiling-patterns-teach-us-20240703/feed/ 0 Why Is This Shape So Terrible to Pack? https://www.quantamagazine.org/why-is-this-shape-so-terrible-to-pack-20240628/ https://www.quantamagazine.org/why-is-this-shape-so-terrible-to-pack-20240628/#respond Fri, 28 Jun 2024 14:42:22 +0000 https://www.quantamagazine.org/?p=138843 The post Why Is This Shape So Terrible to Pack? first appeared on Quanta Magazine

]]> For centuries, mathematicians suspected that hexagonal tiles are the best possible way to fill space. By this they mean that if you want to subdivide a large area into tiles of equal size while minimizing the perimeter of each tile, you can’t do any better than hexagons. In 1999, Thomas Hales of the University of Pittsburgh finally proved it. They’re better than squares, triangles...

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]]> https://www.quantamagazine.org/why-is-this-shape-so-terrible-to-pack-20240628/feed/ 0 What Is the Nature of Time? https://www.quantamagazine.org/what-is-the-nature-of-time-20240229/ https://www.quantamagazine.org/what-is-the-nature-of-time-20240229/#respond Thu, 29 Feb 2024 14:00:20 +0000 https://www.quantamagazine.org/?p=135842 The post What Is the Nature of Time? first appeared on Quanta Magazine

]]> Time seems linear to us: We remember the past, experience the present and predict the future, moving consecutively from one moment to the next. But why is it that way, and could time ultimately be a kind of illusion? In this episode, the Nobel Prize-winning physicist Frank Wilczek speaks with host Steven Strogatz about the many “arrows” of time and why most of them seem irreversible...

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]]> https://www.quantamagazine.org/what-is-the-nature-of-time-20240229/feed/ 0 The Mathematician Who Finds the Poetry in Math and the Math in Poetry https://www.quantamagazine.org/the-theorist-who-sees-math-in-art-music-and-writing-20240112/ https://www.quantamagazine.org/the-theorist-who-sees-math-in-art-music-and-writing-20240112/#respond Fri, 12 Jan 2024 15:40:11 +0000 https://www.quantamagazine.org/?p=134011 The post The Mathematician Who Finds the Poetry in Math and the Math in Poetry first appeared on Quanta Magazine

]]> Sarah Hart has always had an eye for the covert ways mathematics permeates other fields. As a child, she was struck by the ubiquity of the number 3 in her fairy tales. Hart’s mother, a math teacher, encouraged her pattern-seeking, giving her math puzzles to pass the time. Hart went on to earn a doctorate in group theory in 2000 and later became a professor at Birkbeck, University of London.

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