mathematics – 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

Perplexing the Web, One Probability Puzzle at a Time

Erica Klarreich — Thu, 29 Aug 2024 14:00:56 +0000

In late January, Daniel Litt posed an innocent probability puzzle on the social media platform X (formerly known as Twitter) — and set a corner of the Twitterverse on fire. Imagine, he wrote, that you have an urn filled with 100 balls, some red and some green. You can’t see inside; all you know is that someone determined the number of red balls by picking a number between zero and 100 from a hat.

Source

Mathematicians Prove Hawking Wrong About the Most Extreme Black Holes

Steve Nadis — Wed, 21 Aug 2024 14:31:25 +0000

To understand the universe, scientists look to its outliers. “You always want to know about the extreme cases — the special cases that lie at the edge,” said Carsten Gundlach, a mathematical physicist at the University of Southampton. Black holes are the enigmatic extremes of the cosmos. Within them, matter is packed so tightly that, according to Einstein’s general theory of relativity...

Source

The Geometric Tool That Solved Einstein’s Relativity Problem

Joseph Howlett — Mon, 12 Aug 2024 14:49:08 +0000

After Albert Einstein published his special theory of relativity in 1905, he spent the next decade trying to come up with a theory of gravity. But for years, he kept running up against a problem. He wanted to show that gravity is really a warping of the geometry of space-time caused by the presence of matter. But he also knew that time and distance are counterintuitively relative: They change...

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