proofs – Quanta Magazine

With Fifth Busy Beaver, Researchers Approach Computation’s Limits

Ben Brubaker — Tue, 02 Jul 2024 14:00:00 +0000

Once upon a time, over 40 years ago, a horde of computer scientists descended on the West German city of Dortmund. They were competing to catch an elusive quarry — only four of its kind had ever been captured. Over 100 competitors dragged in the strangest creatures they could find, but they still fell short. The fifth busy beaver had escaped their clutches. Of course, that slippery beast and its...

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How Is Science Even Possible?

Steven Strogatz — Thu, 20 Jun 2024 13:20:11 +0000

The universe seems like it should be unfathomably complex. How then is science able to crack fundamental questions about nature and life? Scientists and philosophers alike have often commented on the “unreasonable” success of mathematics at describing the universe. That success has helped science probe some profound mysteries — but as the physicist Nigel Goldenfeld points out, it also helps that...

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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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‘A-Team’ of Math Proves a Critical Link Between Addition and Sets

Leila Sloman — Wed, 06 Dec 2023 15:40:14 +0000

In a randomly chosen set of numbers, addition can go wild. Add together every pair from such a set, and you’ll end up with a new list that’s likely to have a lot more numbers than what you started with. Start with 10 random numbers, and this new list (called the sumset) will have about 50 elements. Start with 100 and the sumset will probably have around 5,000; 1,000 random initial numbers will...

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The Deep Link Equating Math Proofs and Computer Programs

Sheon Han — Wed, 11 Oct 2023 14:30:52 +0000

Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because they show that two old concepts, once thought distinct, are in fact the same. Take James Clerk Maxwell’s equations showing that electricity and magnetism are two aspects of a single phenomenon...

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