sphere packing – Quanta Magazine

To Pack Spheres Tightly, Mathematicians Throw Them at Random

Kelsey Houston-Edwards — Tue, 30 Apr 2024 14:00:20 +0000

Mathematicians like to generalize concepts into higher dimensions. Sometimes this is easy. If you want to efficiently pack squares in two dimensions, you arrange them like a checkerboard. To squeeze together three-dimensional cubes, you stack them like moving boxes. Mathematicians can easily extend these arrangements, packing cubes in higher-dimensional space to perfectly fill it.

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In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math

Thomas Lin and Erica Klarreich — Tue, 05 Jul 2022 07:18:11 +0000

In late February, just weeks after Maryna Viazovska learned she had won a Fields Medal — the highest honor for a mathematician — Russian tanks and war planes began their assault on Ukraine, her homeland, and Kyiv, her hometown. Viazovska no longer lived in Ukraine, but her family was still there. Her two sisters, a 9-year-old niece and an 8-year-old nephew set out for Switzerland...

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The Math of Social Distancing Is a Lesson in Geometry

Patrick Honner — Mon, 13 Jul 2020 14:40:20 +0000

Sphere packing might seem like a topic only a mathematician could love. Who else could get excited about finding the most efficient way to arrange circles in the plane, or spheres in space? But right now, millions of people all over the world are thinking about this very problem. Determining how to safely reopen buildings and public spaces under social distancing is in part an exercise in...

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John Conway Solved Mathematical Problems With His Bare Hands

Kevin Hartnett — Mon, 20 Apr 2020 15:50:14 +0000

In modern mathematics, many of the biggest advances are great elaborations of theory. Mathematicians move mountains, but their strength comes from tools, highly sophisticated abstractions that can act like a robotic glove, enhancing the wearer’s strength. John Conway was a throwback, a natural problem-solver whose unassisted feats often left his colleagues stunned. “Every top mathematician was in...

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Out of a Magic Math Function, One Solution to Rule Them All

Erica Klarreich — Mon, 13 May 2019 15:20:26 +0000

Three years ago, Maryna Viazovska, of the Swiss Federal Institute of Technology in Lausanne, dazzled mathematicians by identifying the densest way to pack equal-sized spheres in eight- and 24-dimensional space (the second of these in collaboration with four co-authors). Now, she and her co-authors have proved something even more remarkable: The configurations that solve the sphere-packing problem...

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