linear algebra – Quanta Magazine

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...

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New Breakthrough Brings Matrix Multiplication Closer to Ideal

Steve Nadis — Thu, 07 Mar 2024 15:30:13 +0000

Computer scientists are a demanding bunch. For them, it’s not enough to get the right answer to a problem — the goal, almost always, is to get the answer as efficiently as possible. Take the act of multiplying matrices, or arrays of numbers. In 1812, the French mathematician Jacques Philippe Marie Binet came up with the basic set of rules we still teach students. It works perfectly well...

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What Makes for ‘Good’ Mathematics?

Steven Strogatz — Thu, 01 Feb 2024 14:03:12 +0000

We tend to think of mathematics as purely logical, but the teaching of math, its values, its usefulness and its workings are packed with nuance. So what is “good” mathematics? In 2007, the mathematician Terence Tao wrote an essay for the Bulletin of the American Mathematical Society that sought to answer this question. Today, as the recipient of a Fields Medal, a Breakthrough Prize in Mathematics...

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Researchers Approach New Speed Limit for Seminal Problem

Lakshmi Chandrasekaran — Mon, 29 Jan 2024 15:11:07 +0000

The traveling salesperson problem is one of the oldest known computational questions. It asks for the ideal route through a certain list of cities, minimizing mileage. Despite seeming simple, the problem is notoriously difficult. While you can use brute force to check all the possible routes until you find the shortest path, such a strategy becomes untenable after just a handful of cities. Instead...

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AI Reveals New Possibilities in Matrix Multiplication

Ben Brubaker — Wed, 23 Nov 2022 14:57:13 +0000

Mathematicians love a good puzzle. Even something as abstract as multiplying matrices (two-dimensional tables of numbers) can feel like a game when you try to find the most efficient way to do it. It’s a little like trying to solve a Rubik’s Cube in as few moves as possible — challenging, but alluring. Except that for a Rubik’s Cube, the number of possible moves at each step is 18...

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