logic – Quanta Magazine https://www.quantamagazine.org Illuminating science Mon, 16 Sep 2024 14:10:47 -0400 en-US hourly 1 https://wordpress.org/?v=6.2 What Makes for ‘Good’ Mathematics? https://www.quantamagazine.org/what-makes-for-good-mathematics-20240201/ https://www.quantamagazine.org/what-makes-for-good-mathematics-20240201/#respond Thu, 01 Feb 2024 14:03:12 +0000 https://www.quantamagazine.org/?p=134856 The post What Makes for ‘Good’ Mathematics? first appeared on Quanta Magazine

]]> 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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]]> https://www.quantamagazine.org/what-makes-for-good-mathematics-20240201/feed/ 0 How to Build an Origami Computer https://www.quantamagazine.org/how-to-build-an-origami-computer-20240130/ https://www.quantamagazine.org/how-to-build-an-origami-computer-20240130/#respond Tue, 30 Jan 2024 15:34:13 +0000 https://www.quantamagazine.org/?p=134768 The post How to Build an Origami Computer first appeared on Quanta Magazine

]]> In 1936, the British mathematician Alan Turing came up with an idea for a universal computer. It was a simple device: an infinite strip of tape covered in zeros and ones, together with a machine that could move back and forth along the tape, changing zeros to ones and vice versa according to some set of rules. He showed that such a device could be used to perform any computation.

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]]> https://www.quantamagazine.org/how-to-build-an-origami-computer-20240130/feed/ 0 The Deep Link Equating Math Proofs and Computer Programs https://www.quantamagazine.org/the-deep-link-equating-math-proofs-and-computer-programs-20231011/ https://www.quantamagazine.org/the-deep-link-equating-math-proofs-and-computer-programs-20231011/#respond Wed, 11 Oct 2023 14:30:52 +0000 https://www.quantamagazine.org/?p=131227 The post The Deep Link Equating Math Proofs and Computer Programs first appeared on Quanta Magazine

]]> 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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]]> https://www.quantamagazine.org/the-deep-link-equating-math-proofs-and-computer-programs-20231011/feed/ 0 Alan Turing and the Power of Negative Thinking https://www.quantamagazine.org/alan-turing-and-the-power-of-negative-thinking-20230905/ https://www.quantamagazine.org/alan-turing-and-the-power-of-negative-thinking-20230905/#respond Tue, 05 Sep 2023 14:44:25 +0000 https://www.quantamagazine.org/?p=129730 The post Alan Turing and the Power of Negative Thinking first appeared on Quanta Magazine

]]> Algorithms have become ubiquitous. They optimize our commutes, process payments and coordinate the flow of internet traffic. It seems that for every problem that can be articulated in precise mathematical terms, there’s an algorithm that can solve it, at least in principle. But that’s not the case — some seemingly simple problems can never be solved algorithmically.

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]]> https://www.quantamagazine.org/alan-turing-and-the-power-of-negative-thinking-20230905/feed/ 0 Why Mathematical Proof Is a Social Compact https://www.quantamagazine.org/why-mathematical-proof-is-a-social-compact-20230831/ https://www.quantamagazine.org/why-mathematical-proof-is-a-social-compact-20230831/#respond Thu, 31 Aug 2023 14:04:58 +0000 https://www.quantamagazine.org/?p=129663 The post Why Mathematical Proof Is a Social Compact first appeared on Quanta Magazine

]]> In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture, a major open question in number theory about the relationship between addition and multiplication. There was just one problem: His proof, which was more than 500 pages long, was completely impenetrable. It relied on a snarl of new definitions, notation, and theories that nearly all mathematicians found...

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