graph theory – Quanta Magazine

In Highly Connected Networks, There’s Always a Loop

Leila Sloman — Fri, 07 Jun 2024 14:20:26 +0000

As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They can be used to attack a wide variety of problems, from modeling neurons in the brain to routing delivery trucks on the roads. Within math, they can be used to categorize important algebraic objects...

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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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Topologists Tackle the Trouble With Poll Placement

Lyndie Chiou — Tue, 26 Mar 2024 13:50:38 +0000

In Georgia’s 2020 gubernatorial election, some voters in Atlanta waited over 10 hours to cast a ballot. One reason for the long lines was that almost 10% of Georgia’s polling sites had closed over the preceding seven years, despite an influx of about 2 million voters. These closures were disproportionately concentrated in predominantly Black areas that tended to vote Democratic.

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Maze Proof Establishes a ‘Backbone’ for Statistical Mechanics

Leila Sloman — Wed, 07 Feb 2024 16:12:53 +0000

Imagine that a grid of hexagons, honeycomb-like, stretches before you. Some hexagons are empty; others are filled by a 6-foot tall column of solid concrete. The result is a maze of sorts. For over half a century, mathematicians have posed questions about such randomly generated mazes. How big is the largest web of cleared paths? What are the chances that there is a path from one edge to the center...

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The Year in Math

Konstantin Kakaes — Sat, 23 Dec 2023 01:33:58 +0000

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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