Leila Sloman – Quanta Magazine

‘Groups’ Underpin Modern Math. Here’s How They Work.

Leila Sloman — Fri, 06 Sep 2024 15:05:01 +0000

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...

Source

Grad Students Find Inevitable Patterns in Big Sets of Numbers

Leila Sloman — Mon, 05 Aug 2024 14:27:52 +0000

In late 2017, Ashwin Sah and Mehtaab Sawhney met as undergraduates at the Massachusetts Institute of Technology. Since then, the pair have written a mind-boggling 57 math proofs together, many of them profound advances in various fields. In February, Sah and Sawhney announced yet another joint accomplishment. With James Leng, a graduate student at the University of California, Los Angeles...

Source

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...

Source

Geometers Engineer New Tools to Wrangle Spacecraft Orbits

Leila Sloman — Mon, 15 Apr 2024 14:15:34 +0000

In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral in Florida, carrying NASA’s Europa Clipper mission. The $5 billion mission is designed to find out if Europa, Jupiter’s fourth-largest moon, can support life. But because Europa is constantly bombarded by intense radiation created by Jupiter’s magnetic field, the Clipper spacecraft can’t orbit the moon itself. Instead...

Source

Number of Distances Separating Points Has a New Bound

Leila Sloman — Tue, 09 Apr 2024 15:28:12 +0000

Scatter three points in a plane, then measure the distances between every pair of them. In all likelihood, you’ll find three different distances. But if you arrange the points in an equilateral triangle, then every distance is the same. In a plane, this is impossible to do with four points. The smallest number of distances you can engineer is 2 — the edges and diagonals of a square.

Source