Where Mathematics Comes From

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1. exprofmaddyNov 2024
   Some very nice related works that dispel widespread math myths: (1) What Is Mathematics, Really? Hersh, 1997. https://books.google.com/books/about/What_is_Mathematics_Rea... (2) Where Mathematics Comes From. Lakoff and Nunez, 2000. https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
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2. wirthjasonSep 2024
   How could someone write a post like this and leave off the great book “Metaphors We Live By” by Lakoff and Johnson?

   Is particularly found the part about how metaphors “hide and highlight” information. In other words the metaphor we use necessitates how we think. We often frame arguments using the metaphor of war and that frames how we think. The other party is an enemy that must be defeated, its bloody, and there is a loser. However we could frame it as a dance, in which case they are a partner, and for the outcome to succeed they must move together in harmony.

   Lakoff has written other fascinating books like how metaphors are used in politics as well as math (“Where Mathematics Comes From”).

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3. bmitcOct 2022
   I'm sorry, but I just disagree that that's how mathematics is defined and that it doesn't depend on our biology and perception, because we are making those definitions.

   A book I might recommend and that I'm going through at the moment is Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez. The origin and meaning of mathematics is strongly influenced by cognitive sciene, and thus biology. I've been downvoted, but this is not a totally novel or off the rails idea. It is basically accepted in robotics that embodied cognition is how you get a robot to understand and perceive its environment. Where do you think that idea came from?

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4. davOct 2022
   Paul Graham needs to read this and get back to us.

   Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being by George Lakoff

   https://www.goodreads.com/book/show/53337

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5. bmitcSep 2022
   Some interesting entries I know about:

   * Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez

   * The Mathematician's Mind by Jacques Hadamard

   * Mathematics Form and Function by Saunders MacLane

   * On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics by Agustin Rayo

   The preface and chapter 1 of A Book of Abstract Algebra by Charles C. Pinter has an excellent discussion of a certain perspective of mathematics. Hermann Weyl wrote a lot about this stuff too.

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6. verylittlemeatApr 2018
   George Lakoff wrote a great book on this called "Where Mathematics Comes From."

   He is critical of how mathematics is currently taught from "first principles" and proofs rather than from a more intuitive body/metaphor perspective. He believes proofs are in many ways academic gatekeeping. His final chapter explains Euler's identity using only the intuitive metaphors he built up in previous chapters.

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