infinity – 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 How the Square Root of 2 Became a Number https://www.quantamagazine.org/how-the-square-root-of-2-became-a-number-20240621/ https://www.quantamagazine.org/how-the-square-root-of-2-became-a-number-20240621/#respond Fri, 21 Jun 2024 13:50:15 +0000 https://www.quantamagazine.org/?p=138611 The post How the Square Root of 2 Became a Number first appeared on Quanta Magazine

]]> The ancient Greeks wanted to believe that the universe could be described in its entirety using only whole numbers and the ratios between them — fractions, or what we now call rational numbers. But this aspiration was undermined when they considered a square with sides of length 1, only to find that the length of its diagonal couldn’t possibly be written as a fraction. The first proof of this...

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]]> https://www.quantamagazine.org/how-the-square-root-of-2-became-a-number-20240621/feed/ 0 How Math Achieved Transcendence https://www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/ https://www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/#respond Tue, 27 Jun 2023 14:45:42 +0000 https://www.quantamagazine.org/?p=127235 The post How Math Achieved Transcendence first appeared on Quanta Magazine

]]> In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides the ones used to count, and they have labored to understand their properties. Although each type of number has its own fascinating and complicated history, today they are all so familiar that they...

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]]> https://www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/feed/ 0 How Can Some Infinities Be Bigger Than Others? https://www.quantamagazine.org/how-can-some-infinities-be-bigger-than-others-20230419/ https://www.quantamagazine.org/how-can-some-infinities-be-bigger-than-others-20230419/#respond Wed, 19 Apr 2023 06:09:26 +0000 https://www.quantamagazine.org/?p=125081 The post How Can Some Infinities Be Bigger Than Others? first appeared on Quanta Magazine

]]> The idea of infinity is probably about as old as numbers themselves, going back to whenever people first realized that they could keep counting forever. But even though we have a sign for infinity and can refer to the concept in casual conversation, infinity remains profoundly mysterious, even to mathematicians. In this episode, Steven Strogatz chats with his fellow mathematician Justin Moore of...

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]]> https://www.quantamagazine.org/how-can-some-infinities-be-bigger-than-others-20230419/feed/ 0 How Big Is Infinity? https://www.quantamagazine.org/how-big-is-infinity-20220927/ https://www.quantamagazine.org/how-big-is-infinity-20220927/#respond Tue, 27 Sep 2022 15:48:51 +0000 https://www.quantamagazine.org/?p=119076 The post How Big Is Infinity? first appeared on Quanta Magazine

]]> At the end of the Marvel blockbuster Avengers: Endgame, a pre-recorded hologram of Tony Stark bids farewell to his young daughter by saying, “I love you 3,000.” The touching moment echoes an earlier scene in which the two are engaged in the playful bedtime ritual of quantifying their love for each other. According to Robert Downey Jr., the actor who plays Stark, the line was inspired by similar...

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]]> https://www.quantamagazine.org/how-big-is-infinity-20220927/feed/ 0 The Year in Math and Computer Science https://www.quantamagazine.org/the-year-in-math-and-computer-science-20211223/ https://www.quantamagazine.org/the-year-in-math-and-computer-science-20211223/#respond Thu, 23 Dec 2021 17:28:50 +0000 https://www.quantamagazine.org/?p=111258 The post The Year in Math and Computer Science first appeared on Quanta Magazine

]]> Mathematicians and computer scientists had an exciting year of breakthroughs in set theory, topology and artificial intelligence, in addition to preserving fading knowledge and revisiting old questions. They made new progress on fundamental questions in the field, celebrated connections spanning distant areas of mathematics, and saw the links between mathematics and other disciplines grow.

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