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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

3.97  ·  Rating details ·  335 ratings  ·  37 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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Linguistic Overreach?

Get ready; here’s the headline news: MATHEMATICS IS A HUMAN CONSTRUCTION JUST LIKE LANGUAGE. In fact mathematics is a language and employs the same parts of the human brain and nervous system as any other language. It’s arguably the most precise language we have. But there is no truth to the rumour, first formulated by Plato, that the central elements of mathematics - numbers - have any existence beyond our use of them.

That’s it, ladies and gentlemen. We can rest easy in our
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
Mar 08, 2015 rated it did not like it
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
Peter D. McLoughlin
Apr 20, 2008 rated it it was amazing
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. ...more
Alex Lee
Jan 29, 2015 rated it it was amazing
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
Paige McLoughlin
A really good book on how people build from concrete to the abstract in the field where abstraction is most recondite Mathematics. I think that human abilities like mathematical reasoning start like all things human from quotidian day to day aspects of our lives, walking, talking, eating, drinking, socializing, tieing out shoes, and we abstract away via metaphorical thinking into loftier and more ethereal realms of thought. We are social animals, not gods so that is how human reason builds itsel ...more
Apr 13, 2015 rated it it was ok
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
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
Feb 14, 2013 rated it really liked it
Shelves: math, owned, sts
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
Oct 29, 2018 rated it it was amazing
Shelves: philosophy
A really really excellent book. Okay, yes, I’m weird, I’ve been interested off and on in philosophy of mathematics for probably almost a decade and a half. Partly to inject some “soul” into the lonely, mechanical, and austere world I had to inhabit as a software engineer, and partly because it’s just irresistible to me the way that the prevailing intuitions and beliefs that we have as to what math is, what numbers are, etc - are so superstitious and absurdly wrong, yet so difficult to explain aw ...more
Stan Murai
Jan 22, 2012 rated it really liked it
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
Jun 12, 2011 rated it did not like it  ·  review of another edition
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
May 03, 2009 rated it liked it
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
Jared Leonard
Apr 17, 2008 rated it it was amazing
Shelves: philosophy
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
Paul Gazis
Apr 07, 2017 rated it it was amazing
Thsi book could be regarded as a sequel to 'Philosophy in the Flesh', by Lakoff and Johnson. It presents a connectionist view of how the human brain might emulate logic to perform mathematics. I happen to agree with much of what the authors' thesis, so this may bias me in favor of their presentation, but even if you disagree, this book has much to recommend it. If you've been wondering why some mathematical concept seem to come so naturally ("I saw three lions. Now I only see two. This means one ...more
Sep 07, 2019 rated it did not like it
Engaging but full of errors and inaccuracies.
So, what is going on that gives the human brain the power to concoct mathematics or any abstract logical system? The purpose of this book is to explore this question. The authors start with innate perception, basic schemas (as defined by Piaget in his conception of cognitive development), relations expressed linguistically, and ordinary manipulation of objects (gathering things together, parceling them out, cutting them into pieces). They identify a set of 'grounding metaphors' that show the con ...more
Feb 02, 2012 rated it liked it
Shelves: linguistics
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
Diana Sandberg
Jun 20, 2020 rated it it was ok
Shelves: science-and-math
Started off pretty well; I liked the info on how they've determined that infants have a grasp of basic addition and subtractions, and I learned a cool new word: subitization, which means the action of instantly knowing how many objects are present in a group. These guys say we all have an inherent ability to do this for a number of objects up to three or four. I recall Glenn Doman claiming one could train a baby to be able to do it for much larger numbers, but my younger child wasn't interested ...more
Daniel Solomon
Jun 06, 2020 rated it really liked it
The book offers an attempt at a cognitive science theory of mathematical knowledge.
It can be seen as a form of psychologism, in which more sophisticated mathematics/logic concepts are derived from innate mental concepts that are based in genes/evolution (parts of language of thought in a sense) and that happen to be useful in relatively accurate human models of reality.
I think the book caused a lot of controversy among actual mathematicians reading it, because of its opposition to the platonic p
Nov 30, 2013 rated it really liked it
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
James Ashby
Jul 31, 2014 rated it it was ok
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
Jul 30, 2012 rated it it was amazing
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. ...more
Jul 04, 2009 rated it it was amazing
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.
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.
May 29, 2012 rated it liked it
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. ...more
Jan 27, 2016 rated it liked it
Cute and sometimes neat ideas on metaphors driving our basic mathematical reasoning. I read an uncorrected proof, so not sure what's still in the published version. It didn't give insights into the problem-solving process, as I was hoping, instead focusing more on "what IS a logarithm" or "what metaphors do we use to conceptualize the infinite." ...more
Aug 19, 2007 added it
Shelves: cognition
Really provoking and intereasting. An evolutionary and Psychobiological essay on emergence of Mathematical basic entities.
Hollis Fishelson-holstine
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 ...more
Jan 06, 2012 rated it really liked it
Shelves: mathematics
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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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

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