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The Math Instinct: Why You're a Mathematical Genius

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There are two kinds of the hard kind and the easy kind. The easy kind, practiced by ants, shrimp, Welsh corgis—and us—is innate.

What innate calculating skills do we humans have? Leaving aside built-in mathematics, such as the visual system, ordinary people do just fine when faced with mathematical tasks in the course of the day. Yet when they are confronted with the same tasks presented as “math,” their accuracy often drops.

But if we have innate mathematical ability, why do we have to teach math and why do most of us find it so hard to learn? Are there tricks or strategies that the ordinary person can do to improve mathematical ability? Can we improve our math skills by learning from dogs, cats, and other creatures that “do math”? The answer to each of these questions is a qualified yes. All these examples of animal math suggest that if we want to do better in the formal kind of math, we should see how it arises from natural mathematics.

From NPR’s “Math Guy”— The Math Instinct will provide even the most number-phobic among us with confidence in our own mathematical abilities.

272 pages, Hardcover

First published March 15, 2005

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About the author

Keith Devlin

85 books164 followers
Dr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a Consulting Professor in the Department of Mathematics, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 26 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is "the Math Guy" on National Public Radio.

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Displaying 1 - 30 of 37 reviews
1,840 reviews44 followers
January 15, 2015
This book seems inspired by Steven Pinker’s “The Language Instinct”. The author explains his theory that humans and animals are endowed with a type of natural ability to “do math”, some level of understanding and skill that is ingrained and active before we obtain math instruction at school, and in some cases even despite that formal schooling. This is of course a fascinating and attractive idea to anyone who has ever struggled with differential equations.
Unfortunately, the book doesn’t quite deliver on this promise. It starts off with some fascinating observations that indicate that very young babies have a sense of “numerosity”. But then it veers into zoology and botany territory, with chapter after chapter of phenomena that can be summarized as “animal or plant behavior, that, if it were done by humans, would involve math skills”. So we learn about the waggle dance that bees do to indicate to their hive-mates where some pollen-rich flowers can be found. Or the way cats torque their bodies during a fall to land on their paws. Or about the impressive navigational capacities of birds, fish and insects. About echolocation by bats and the owl’s incredible hearing. About Fibonacci numbers in the numbers of seeds in sunflowers and petals on plants. All of this is grist to the author’s mill of “innate math capacity”, but I found it only moderately interesting. Things picked up again around page 163 or thereabouts, where the author explains some fascinating experiments explaining the difference beween “school maths” and “street maths”. He does a good job of explaining these psychological experiments. He also has an interesting theory that links mathematical ability with linguistics, explaining, for instance, that the fact that Japanese children appear to outperform American children in math at young ages may have more to do with the logical structure of their numbering nomenclature, than with innate ability or better school curricula. In the end, the book flags again. The author seems to want to turn all of this information into a hopeful message for people who struggle with (school) math, but can’t seem to come up with anything more inspiring than “keep on trying”. So overall I would place this book in the category of “animal behavior” rather than “math education”.
Profile Image for Fatima Al Shamasi.
31 reviews11 followers
June 12, 2018
When I picked up the book from the library, after reading the title of the book ‘The Math Instinct: Why You’re a Mathematical Genius’ my first reaction was to assume that the book would explain how we are hard wired to do math, or how we as humans have the ability to do complex or advanced (or even simple) math. Instead, the author expounded for what seemed to be around 80% of the book about how mathematical characteristics can be found in nature (mainly by using examples pertaining to animals) and the remaining 20% on how we have natural mathematical tendencies, the reason why we have difficulties doing ‘school’ mathematics and the difference between the aforementioned in contrast to ‘natural’ mathematics. By the end of the book (which didn’t really help me understand why I’m a mathematical genius at all) the author seemed to be using this book to promote his other book ‘The Math Gene’. Irregardless, the examples he used to illustrate how math can be found all throughout nature (which he tried to sell off as animals doing math) were interesting, but all in all the book was disappointing to say the least.
Profile Image for João Conrado.
62 reviews1 follower
March 13, 2025
Um livro fantástico para ampliar o entendimento de como os animais usam habitualmente recursos que só conseguimos utilizar usando termos matemáticos.
209 reviews
October 8, 2019
I felt like this book over-promised and under-delivered. There were some interesting examples of math in nature, but not an overly strong case supporting the (probably true) premise that humans are inherently good at numbers and math.
Profile Image for Tom.
151 reviews1 follower
July 22, 2025
Overall, The Math Instinct by Keith Devlin is an excellent book. He notes that there are two kinds of math — the abstract math taught in schools and the natural math that can be found in animal behavior, more generally in nature, and in people not oriented to the math that they were taught in school. In multiple chapters, the author notes that much of what he writes comes from other books and articles.To a certain extent, the book is a collection of already published information.

I have some observations about The Math Instinct.

In one case, the author describes how honeybees measure and communicate distance. However, he notes that the distance communicated is affected by the heights of the nest and the food source. What seems to be communicated is the perception of distance more than the actual distance.

Some of what is in the book seems strange to me. For example, the author says that when some people are asked to multiply 5 times 6 they often say 56 because the number 56 is in the multiplication tables whereas they don't say 37 when asked to multiply 3 times 7 because 37 is not in the multiplication tables. Perhaps this is how some people think, but I have never had this problem. I have never known anyone who has this problem.

Chapter 12 seems to be self-contradictory. The author says that Brazilian child street traders, described in an earlier chapter, were able to do all the computations necessary for their work because numbers to them had meaning. He then says that some kids have trouble with math in school because they're dealing with symbolic numbers that have no meaning. However, at the end of the chapter, he notes that once you learn addition, subtraction, multiplication, and division in school, you don't have to learn anything else. You just keep applying those procedures to whatever numbers you are given. And he says that street mathematics requires a whole bag of tricks and depends on finding ingenious, simplifications or groupings that depend on the actual numbers involved. So the end of the chapter seems to contradict the rest of the chapter. Although, I suppose that applying meaning to numbers makes it easier to learn the tricks, simplifications, and groupings that the author says allows child street traders in their stalls to do street mathematics.

With a copyright date of 2005, the book is somewhat out of date. For example, robotics are significantly more advanced than the author indicates in the chapter on motion.

The observations that I make above are just a very small part of the book. There is much more to learn than that. The Math Instinct is well worth reading. I had never thought about math being performed by animals and by nature in providing features to plants and animals. I have never thought about some people having problems learning mathematics and the difference between abstract math and natural math. The book provides a different perspective on mathematics.
Profile Image for Matthew.
207 reviews18 followers
August 27, 2020
Natural math, or the math that comes by instinct, is present in animals as well as humans. That is, the ability to recognize differences in number, size, etc. The first evidence of this presented in the book is babies a few days after being born. Devlin goes on to show how this is also the case with rats, chimpanzees, and a host of other animals. He also shows how animals operate according to mathematics, and plants emerge according to advantageous patterns -- relevant due to math being the science of patterns.

Extensive time is taken to explain what sets humans apart. It is their ability to practice abstract math, and he grounds this in both the neuroscience and linguistics behind mathematics -- the way our brains use numbers is similar to how our brains use words, because in fact they are words. Interesting details are presented alongside this demonstrating why the Hindu-Arabic numbers are superior, and why knowing Chinese puts children a year ahead in counting to 40 compared to their English-speaking Western peers.

One application of the book is that we can tap into our instinct and move through the stages of progressively difficult mathematics if we want to. The potential is there, but if no meaning is attached to the the math itself, we may never rise beyond a very basic understanding -- it's not our lack of ability that holds us back. We tend to be good at what we set our minds to, not to what we set our minds against.

As a teacher, I am inspired to learn more, as well as teach more, as a result of reading this book.
149 reviews9 followers
May 6, 2017
Devlin wrote a fine book. The writing was very accessible, the topics interesting. But for the most part, it didn't grab me. I suspect it had more to do with the fact that math is not an inherently fascinating topic to me, which is certainly not Devlin's fault. It's actually part of why I read the book, actually, to try to see math in a different way that might make it more interesting. The material was interesting, but it didn't "wow" me like I kind of hoped. The title seemed slightly deceiving. I thought what his content on the various animals showed was not so much their mathematical aptitude, especially when it came to things like the means by which nature gives animals spots and stripes, but rather that math is an innate building block of the universe. Still interesting to see how that is the case, but not exactly what the title seemed to suggest.

It became most intriguing to me from chapter 11 onwards, as it discussed the cognitive aspect of numbers, and how language plays a role in understanding numbers and math. Cognitive development and linguistics always fascinate me, so that piqued my interest a bit more.

Perhaps not as entrancing as some of the subjects I've read, but it still feels like it was worth my time.
Profile Image for dejah_thoris.
1,346 reviews23 followers
December 18, 2017
A great book that explains the difference between natural mathematical abilities and the mathematical tools we are taught in school. Ever wonder how the Common Core math techniques arose? They're based on a study of child street vendors studied in their work environment vs. formal testing in their homes. Sure, the mathematical skills we're taught make math easier once we understand them, but getting to that level of comprehension is difficult when we're taught to disassociate mathematical concepts and techniques from actual objects. Devlin also does a great job of explaining the mathematical techniques animals use, which is an interesting enough topic on its own. This book is very lay-person friendly, so check it out if the topic piques your curiosity.
Profile Image for John Hardin.
34 reviews1 follower
April 22, 2019
This book was a mix for me. Some of the chapters were more related to my current interests than others. Parts of the book were about things like how visual perception of depth is related to mathematics, and how animals have a certain level of mathematical ability. But the chapters that really caught my interrest were those related to how people are often able to do problems in practical mathematics in their heads, but then fail when the same problems are presented in the form of school-form math problems. I've been doing tutoring of 5th graders at a local school and was fascinated by how this might relate to the way I'd want to teach math.
Profile Image for Erica.
11 reviews1 follower
June 8, 2025
The opening chapters (babies and dogs) were very interesting and piqued my interest. The middle sections, although interesting, were a little slow for me. However, the last few chapters (starting with street math) were so interesting that I kept stopping to highlight sections and talked at length with people near me about it. I feel like there are some very interesting implications for how we ought to be teaching math. I highly recommend reading at least the beginning and middle chapters, although there’s nothing to be lost from spending some time in the middle.
Profile Image for Heather.
233 reviews
March 8, 2019
I loved every word, example, and Even the bibliography and references to other chapters. Everything about this book was perfect. Every single example was amazing. At the very end I was a bit, I shouldn’t say disappointed, of what the real answer was for becoming a mathematical genius. It really boils down to two things that we all already know I think. Constructing meaning and repetition. But perhaps I know this because of my fieldwork. I would give this book 100 stars.
Profile Image for Stacy.
451 reviews3 followers
April 30, 2019
I really liked this book. But yeah, I am a math geek. Since I started substitute teaching, I hear kids say 'I am bad at math'. This book shows how humans (and animals) do math instinctually and that it is how we represent it and teach it that is hard for some. Really interesting. Looking for more books like this.
Profile Image for M.Marie.S..
534 reviews1 follower
August 1, 2020
Accessibly written, with great examples from the animal kingdom. I'm a sucker for animal stories.
Profile Image for mono.
425 reviews3 followers
August 21, 2021
ftfy - "The Math Instinct: Patting Yourself of the Back With Questionable Cherry Picked Bad Research"
4 reviews
August 7, 2018
The title doesn’t really capture the content. It is probably better to call it “MATHEMATICAL INSTINCT: WHY BIRDS, LOBSTERS, AND ... ARE GENIUSES - AND YOU TOO!” The book spends vast amounts of time exploring natural mathematics within nature that are unseen to the layman, whereas I thought it was a book about mathematical genius of humans and animals.
Profile Image for نجلاء.
71 reviews
February 10, 2014

"أنتَ عبقري رياضيات. وكذلك السلطعونات، الطيور، القطط والكلاب"

هكذا يبدأ الكاتب كيث دلفن بشرح كتابه، لكن يزيد ويتطرق إلى النمل، الأسود، الفراشات وحتى النباتات! (وغيرهم). يدور الكتاب حول محورين: جميع ما في الطبيعة يستطيع تنفيذ حسابات رياضية شديدة في التعقيد في غضون أجزاء من الثانية بطريقة لا شعورية. والنظام التعليمي يقتل الكثير من هذه الحدسية الفطرية ويسلح الإنسان بمعلومات تغبش عليه المعنى الحقيقي لما يتعلمه.

في الحركة، التنقل، النمو، البناء، والإحساس، هناك أمثلة للبرمجة الطبيعية التي خُلق بها الخلق. أحصل وأن حملت صينية محملة بالكؤوس والصحون، وأتى أحد آخر ليخفف عنك عبء الحمل فأخذ من الصينية حملا ثقيلا بدون معرفتك فاختل توازنك بشدة؟ أو حاولت أن توقع بعلبة مياة فارغة في سلة المهملات؟ أو هممت بالركض على أرض غير مستوية ؟ أو تعرضت للكثير من المواقف غيرها الحركية؟ فدماغك يقوم بالشغل الدسم المعقد عنك، يحسب الملايين من الحسابات في ثواني معدودات وأقل، حسابات تأخذ من أساتذة الرياضيات جهد ذهني متين كي يحلوها على الورق. ويأخذ من الروبوتات الكثير من الموارد للحساب، هذا إن تمكن العلماء من الوصول إلى دقة في الحساب تقارب حساب الإنسان لبرمجة الروبوت.

السلطعون يستطيع تحديد مكانه من الأرض، ومكان وجهته من خلال حساباته لمجال الأرض المغناطيسي. وكذلك الطيور إن كانت السماء غائمة فلم تستطع رؤية النجوم للاستدلال على موقعها ووجهتها. وفي تجربة قام بها أحد علماء الحيوان على السلطعونات، أحاطها بمجال مغناطيسي مفبرك واستطاع التحكم بإحساسها بالموقع (مخللا بذلك سيرها الطبيعي، يجعلني أفكر في الأمور العديدة التي يفعلها الإنسان وقد تؤثر على حركة الطبيعة الطبيعية).والكتاب يشرح بين طياته العديد من الأمثلة، منها في تطور الخطوط الجمالية على جلد النمر (إذ لم يولد بها، بل تطورت والتفسير الرياضي في الكتاب)، وكذلك في نمو النباتات وتوزع فروعها على جذعها، وفي إحساس الفراشات باليوم من خلال أشعة الشمس، وفي العديد غيرها يطول الحديث فيها.

الجزء الأهم من الكتاب (في رأيي) يتحدث عن أخطاء وخطايا النظام التعليمي في حق تزويد الطلبة بالمعلومات المفيدة وإلهامهم بالحس السليم للرياضيات وتعزيز غريزتهم. بالعديد من الأدلة يستنتج الكاتب أن الرموز الاستدلالية (لغة الرياضيات المكتوبة) والرياضيات الحدسية لم ينجحا بالارتباط لدى الكثيرمن الطلبة. وأن لكي يفلح النظام التعليمي يجب أن تربط الرموز بالواقع وعلى المرء أن يتمرن مرارا وتكرارا كي تتطور قدراته الغريزية. فالإنسان سوف ينمي ما يحتاجه فقط من القدرات.
على الهامش، وفي ظل شرح الكاتب للفرق بين الرياضيات الرمزية والغريزية، يختلف الكثير من الكتاب في اختيارهم للمصطلحات للتفريق بين الأمرين. وهنا أقول يكثر الكلام وتظل المبادئ ثابتة.

الكتاب بشكل عام خفيف لا يتناول رياضيات معقدة. هو أقرب للخواطر منها إلى نظرية علمية مثبتة.
Profile Image for Jarrodtrainque.
62 reviews2 followers
Read
September 12, 2007
There are two kinds of math: the hard kind and the easy kind. The easy kind, practiced by ants, shrimp, Welsh corgis—and us—is innate./ What innate calculating skills do we humans have? Leaving aside built-in mathematics, such as the visual system, ordinary people do just fine when faced with mathematical tasks in the course of the day. Yet when they are confronted with the same tasks presented as "math," their accuracy often drops./ But if we have innate mathematical ability, why do we have to teach math and why do most of us find it so hard to learn? Are there tricks or strategies that the ordinary person can do to improve mathematical ability? Can we improve our math skills by learning from dogs, cats, and other creatures that "do math"? The answer to each of these questions is a qualified yes. All these examples of animal math suggest that if we want to do better in the formal kind of math, we should see how it arises from natural mathematics./ From NPR's "Math Guy"—The Math Instinct will provide even the most number-phobic among us with confidence in our own mathematical abilities./
Profile Image for Ensiform.
1,509 reviews147 followers
March 18, 2012
The author describes the truly amazing abilities of dogs, bees, ants, birds and other creatures when it comes to eye-mouth coordination, navigation, locomotion, and so on. He uses this data, along with some studies on how infants pay attention to certain sets of things up to three, and some other studies on poorly-educated street vendors who can do complicated math procedures in their heads but not on paper, to argue that people have an innate instinct for mathematics.

It’s an interesting book, but not a cohesive one, and ultimately unsatisfying. The animal studies are fascinating, but nearly completely irrelevant to the matter at hand; the animals, as Devlin himself says, aren’t “doing mathematics” any more than the world is “doing physics” as it spins. The studies on humans, especially the differences between school math and real-world math abilities, are germane, and Devlin has a good case to make that people can do math, but are turned off it through poorly-done formal study. Finally, the book concludes with an exhortation for people to practice the basics more through memorization. Gosh, thanks.
319 reviews10 followers
November 19, 2012
I like to think that I follow scientific literature pretty well, but this book had quite a few surprises in store for me, citing the results of numerous studies of how humans and animals use and comprehend numbers--even though it's six years old (a long time for such new and active fields). There was a lot to learn about how other animals engage with numeracy in the world, and about how humans learn and interact with it.

I was impressed enough to be interested in reading more from this author--The Math Gene, which he published six years prior to this, and perhaps, if available, something more recent. This book was a gift, and I wouldn't have picked it up otherwise, but I'm glad I did.

One thing I didn't appreciate in the book was the constant reminders that most people don't like math, or that the reader might be thinking s/he is afraid of certain areas of math--I like math! I think a lot of this book's audience likewise likes math, if they're afraid of math, having that word in the title will probably already dissuade them from reading it!
Profile Image for Krista.
Author 9 books95 followers
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January 11, 2025
There are two parts to this book; the first half or so contains examples of innate math in animals and humans and the second half contains historical evolution of mathematical symbols and some cognitive science concepts. I was hoping for a third part of the book that had real examples of how some teachers or charter schools are teaching math better or more intuitively, but there was very little if any of that. So the book was interesting, though not mind-blowing; a little like reading Psychology Today.
Profile Image for Houston.
4 reviews2 followers
March 2, 2009
I found this book interesting, although I do not agree with some of Devlin's claims. It is important to note that the common idea of practicing mathematics is not what he outlines (not the conscious application of mathematical skills)... instead it is the idea of 'innate' mathematics. Overall, the book was very fun to read, and it really does open one's eyes to the different ways mathematics can be applied to everyday life.
Profile Image for Sharon Cate.
104 reviews7 followers
September 9, 2012
I really enjoyed the chapters which tied mathematics and language. The book's message regarding the importance of mathematical relevancy is especially timely with the current emphasis of the common cores standards in education. I guess my biggest gripe with the book is the author's instance on attributing the marvels of vision and how animals and plants are "designed" to do complex mathematics to "Nature" instead of a Designer. This book was okay but it could have been so much more.
Profile Image for Paul The Uncommon Reader.
151 reviews
January 3, 2015
Interesting. Changed my perception of what maths is (innate and somehow present, like scientific data, in the universe, rather than somehow invented by people like e.g. languages are. Though "language" probably isn't).
Also never thought of mathematical ability as being influenced by linguistic norms before. Remain sceptical on that one though. Aren't you either good at maths or at languages, but rarely both?
Profile Image for Trent.
Author 10 books12 followers
November 29, 2016
Starts off strong showing the innate math abilities we all have, from object presence as an infant, to casual mathematics used in everyday thinking. Some neat stories about animals and how their actions and decisions show mathematical patterns. Then it got a little dry as it discussed testing and some case studies about math, but the end had some a-ha moments (the use of fractions to explain the difference between arithmetic and proportional reasoning). Decent read.
Profile Image for Elizabeth.
180 reviews5 followers
August 2, 2009
I truly enjoyed every aspect of this book. I loved the discussions about the different mathematical things animals and humans do everyday without even thinking about it. The part about street math was quite interesting.
Profile Image for Paul Berg.
44 reviews
January 19, 2011
I kept waiting for this book to get better, but it didn't -- I ended up skipping large swaths of it. There were a few interesting points, but it seemed like the author kept reitering uninteresting things.
Profile Image for Mirek Kukla.
156 reviews82 followers
September 18, 2010
Author argues that animals 'do math', by which he means 'do things that humans aren't be able to do (or understand) without math.' A couple of interesting facts - lobsters navigate using the earth's magnetic field, for instance - but the argument is mostly shallow
551 reviews
December 22, 2014
Lost interest after the guy said something about corgis not actually doing calculus. Bro, do you even corg?

Seriously, just got busy with school and didn't manage to finish by the time I was out of renewals with the library.
Profile Image for Heidi.
2 reviews
June 5, 2008
Interesting book for those who love math. I just started it so I am not quite ready to rate it just yet, but if my preliminary findings are accurate, I would give it a 4/5 star.
Displaying 1 - 30 of 37 reviews

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