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Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being
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Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being

4.02 of 5 stars 4.02  ·  rating details  ·  211 ratings  ·  23 reviews
This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arit ...more
Paperback, 512 pages
Published August 16th 2001 by Basic Books (first published 2000)
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I consider this book to be essential reading for anyone attempting to seriously understand Mathematics. In fact this book or should probably be required for anyone teaching Mathematics!

I've long believed that there was no way to break down thought into discernible mechanistic-like chunks and analyze the thought process in a non-hand-waving manner. I am delighted to discover I was wrong about this. It turns out cognitive scientists have developed what seems to be a very solid method and vocabular
Recently completed reading this challenging journey through Lakoff's embodied mind theory with our Philosophy of Math study group at Saint Martin's University. The group, made up of math, philosophy, and computer science professors, struggled with Lakoff's approach to how fundamentals of number, arithmetic, algebra, and infinitesimals are grounded in bodily metaphor and permutations of such metaphors through conceptual blending (for a more detailed look at conceptual blending see Fouconnier/Turn ...more
Peter D. McLoughlin
Although I am a Mathematical Platonist. I couldn't help but be fascinated by Lakoff account of how concrete metaphors from the body and everyday experience inform our mathematical abstractions of the most aetherial and least earthy types. My only answer to Lakoff repudiation of platonism for a cognitive origin of mathematics is where does the regularity of the world (that cognitive patterns are built on) originate. An excellent Book.
Hamed Zakerzadeh
It is the worst rating I have ever given to a book! Simply speaking, the whole book is trying to convince you that it has a more realistic explanation of the nature of mathematics, and believe me, it cannot even fake it! The most obvious examples are infinite series and Taylor expansion.

In former, the authors propose a (loosely defined) "metaphor" to show how the infinite series work, which cannot even show the convergence or divergence of the series! It actually gets help from math and is faki
Jared Leonard
Very educational even if you don't have a strong background in math. If you are a fan of Lakoff's previous works (like "Metaphors We Live By" or "Philosophy in the Flesh") this is definitely a must read. The primary argument is that traditional conceptions of mathematics are incorrect because they make the fundamental mistake of presuming that axioms "just are" and have no subjective context. The authors do a great job of laying down the groundwork for showing that the mind has an innate ability ...more
An utter disappointment but not devoid of value. I doubt i'll bother to continue reading, so here are my initial thoughts.

I'm far too dim to understand Lakoff + Núñez's ideas.
Or maybe they're not saying anything other than people have to use language to express and explain mathematical ideas and language is entirely metaphorical.
Or maybe they're saying that mathematics is entirely metaphorical and language is fundamental.
There's a philosophical chicken-and-egg problem with this entire book.
Or ma
Stan Murai
George Lakoff, a cognitive linguist, and Rafael E. Núñez, a published their work "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being" in 2000 as a 'cognitive science' study of how mathematics is 'embodied' and based on 'conceptual methaphors'. Cognitive science in an interdisciplinary approach towards studying how the mind works and the processes which characterize it, namely thinking. In this book, mathematics is regarded as embodied or shaped by aspects of the bo ...more
I find some of the arguments in this book tautological, thought it is difficult to articulate why. The section on an Embodied Philosophy of Mathematics is one of the most interesting in the book. The authors argue against "The Romance of Mathematics" (Platonism, plus some cultural effects) and against Postmodernism as a philosophy of mathematics. Their solution to "what is mathematics" lies somewhere in the middle: every human has certain basic cognitive capabilities. Based on these capabilities ...more
I read Lakoff's earlier book, Metaphors we live by, and loved it. This is way more in depth. It starts strong with an introduction to what are best thought of as "hard wired" cognitive faculties like "subitizing" (instantaneous number recognition, this is also seen in other animals to a lesser extent). The authurs then build on visual schema to lay the basis for useful metaphors to comprehend higher math, at least through arithmetic and elementary logic. After that, the book goes off the rails. ...more
James Ashby
I was hoping for so much more from this book based upon the way it was described. At the time of reading this book, I was searching for a research-supported narrative delineating the cognitive development of mathematics as a complex web of neural networks. This book fragments the web into a series of mathematical topics and argues how the mind processes the algorithm(s) associated with that topic. There are times when pre-requisite thinking is discussed, but there is no information on how these ...more
Alex Lee
Cognitive linguistics has at its underlying aesthetic the very literal understanding that how we think of things is what they are. This follows post-structural rhetoricians like Paul Ricoeur who argue that the connective tissue of language is metaphor -- where metaphor is the substantiation of the naked copula form is through content. We forget the form of the copula in metaphors and thus experience the content as a variation of the copula form instead of being the actual connection. In other wo ...more
Carlos Burga
Reading this book seemed like watching a picture come in and out of focus constantly. The authors start the book with the great promise to explicitly present the underlying metaphors of all of mathematics and they begin quite well. They explain arithmetic from innate counting abilities in humans and clarifying the metaphors by which those innate abilities are extended to all of what we know as arithmetic. Unfortunately, the book starts to see-saw on the following chapter on algebra. The authors ...more
Like language, simple arithmetic has an instinctual basis. People can immediately see whether there is one object in front of them, two, or three, and expect that one object and one more object make two. What of more complicated mathematics? The authors argue that it is built up from simple arithmetic using metaphors, the mechanism that, as Lakoff has argued in another book, is central for cognition. For example, the conceptual jump from real to complex numbers is akin to the conceptual jump in ...more
Lakoff and Nunez are cognitive scientists with a deep interest in mathematics and in this book, they try to explain mathematics from a cognitive perspective. The result is fascinating. I am a mathematical realist and, as such, I have some philosophical disagreements with the authors of this book, but their explanation of the metaphors involved in some mathematical concepts I found fascinating. Furthermore, I think their ideas of embodied mathematics is fully reconcilable with an Aristotelian hyl ...more
Lakoff never ceases to amaze me. Mind-blowing. Intelligent. Beautiful.
A superbly written mathematics book for geeks and non-geeks alike. OK it's better if you're a little geeky. The author is a linquist, and provides compelling metaphorical explanations for difficult concepts. The Appendix contains a lucid explanation of the famous Euler 'Magic equation'. That alone is worth the price of the book. I honestly haven't read this book in its entirety, it's not that kind of book. I just keep going back to it again and again, based on my interest of the moment.
Quite the wonderful blending of my two favorite areas -- mental science and mathematics. Lakoff discusses the mental models/metaphors underlying much of modern mathematics, with special implications for how mathematics should be taught. As a special treat, he ends by describing the meaning (metaphorically, of course) of the equation e^(i*pi)=-1.
Perhaps this book was way above my way of thinking about certain math concepts, but I found the reading to be too dry. Especially coming from a cognitive science major. Although I may change my rating once I've re-read it outside of a term paper kind of setting, it might be a while before I would want to takle this book again.
Aleks Veselovsky
I found that this book was too cognitive for mathematicians and too mathematical for cognitive psychologists. Some of the metaphors were useful, but mostly I felt that they were just one way of looking at things and not universal, like the authors claim. Overall, I thought the book needed more pedagogical applications.
Stella Pollard
This book was wonderful. I would reccomend it to anyone who is majoring in mathematics education, mathetmatics, or just enjoys the world of numbers.
Oct 17, 2010 Hollis marked it as to-read
This wasn't as 'dense' reading as I'd anticipated, but I need to read it when I have more time to focus - abandoned it for the moment
Aug 19, 2007 Sherwin added it
Shelves: cognition
Really provoking and intereasting. An evolutionary and Psychobiological essay on emergence of Mathematical basic entities.
A great read for anyone with a love for math, or with an interest in how human ideas come to be.
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Nov 23, 2015
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There are no discussion topics on this book yet. Be the first to start one »
  • What Is Mathematics, Really?
  • PI in the Sky: Counting, Thinking, and Being
  • The Embodied Mind: Cognitive Science and Human Experience
  • Infinity and the Mind: The Science and Philosophy of the Infinite
  • The Principles of Mathematics
  • Fluid Concepts and Creative Analogies
  • The Mathematical Experience
  • Mathematics: The Loss of Certainty
  • The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip
  • Proofs and Refutations: The Logic of Mathematical Discovery
  • I Want to Be a Mathematician: An Automathography
  • The Universal History of Numbers: From Prehistory to the Invention of the Computer
  • Mathematics and Its History
  • The Colossal Book of Mathematics
  • Tree of Knowledge
  • Euclid in the Rainforest: Discovering Universal Truth in Logic and Math
  • Mathematical Mysteries: The Beauty and Magic of Numbers
  • The Way We Think: Conceptual Blending and The Mind's Hidden Complexities

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George Lakoff is Richard and Rhoda Goldman Distinguished Professor of Cognitive Science and Linguistics at UC Berkeley and is one of the founders of the field of cognitive science.

He is author of The New York Times bestseller Don't Think of an Elephant!, as well as Moral Politics: How Liberals and Conservatives Think, Whose Freedom?, and many other books and articles on cognitive science and ling
More about George Lakoff...

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