What do you think?
Rate this book
Language of Mathematics by Keith Devlin
Keith Devlin is trying to be the Carl Sagan of mathematics, and he is succeeding. He "Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent of a pair of ears. Mathematics can be seen only with the eyes of the mind." All of his books are attempts to get around this problem, to "try to communicate to others some sense of what it is we experience--some sense of the simplicity, the precision, the purity, and the elegance that give the patterns of mathematics their aesthetic value." Life by the Numbers, Devlin's companion book to the PBS series of the same name, is heavily illustrated and soothingly low on equations. But as he says, wanting mathematics without abstract notation "is rather like saying that Shakespeare would be much easier to understand if it were written in simpler language."The Language of Mathematics is Devlin's second iteration of the approach he used in The Science of Patterns. It covers all the same ground (and uses many of the same words) as the latter, but with fewer glossy pictures, sidebars, and references. Devlin has also added chapters on statistics and on mathematical patterns in nature. --Mary Ellen Curtin
Paperback
First published January 1, 1998
59 people are currently reading
1440 people want to read
About the author
Keith Devlin
85 books164 followersDr. 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.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 29 of 29 reviews
June 10, 2014
For some reason, mathematics has been thought simply as "science of numbers". Or more generally, "that certain art about dealing with numbers". This book, though, set out to give better definition.
Right off the bat the author says it. What is math? Math is, in a way, "A Science of Pattern".
Indeed, if you have to read only one paragraph of this book, you may well just read that. The following chapters then clarify all kind of patterns described in math. From number theory, statistics, even the more 'everyday' things like Newtonian Physics -- there are patterns in all of them. Therefore, can be described with math.
This is popular book, so pretty much all-prose. Recommended for readers not familiar with math but want to know more.
PS:
The quote above is really the essence of the book. The rest is details. I have to add, however, that they are *very* delicious details. :P
Right off the bat the author says it. What is math? Math is, in a way, "A Science of Pattern".
A particular study was classified as mathematics not so much because of what was studied but because of how it was studied—that is, the methodology used. It was only within the last thirty years or so that a definition of mathematics emerged on which most mathematicians now agree: mathematics is the science of patterns. What the mathematician does is examine abstract 'patterns'—numerical patterns, patterns of shape, patterns of motion, patterns of behavior, voting patterns in a population, patterns of repeating chance events, and so on. Those patterns can be either real or imagined, visual or mental, static or dynamic, qualitative or quantitative, purely utilitarian or of little more than recreational interest.
Indeed, if you have to read only one paragraph of this book, you may well just read that. The following chapters then clarify all kind of patterns described in math. From number theory, statistics, even the more 'everyday' things like Newtonian Physics -- there are patterns in all of them. Therefore, can be described with math.
This is popular book, so pretty much all-prose. Recommended for readers not familiar with math but want to know more.
PS:
The quote above is really the essence of the book. The rest is details. I have to add, however, that they are *very* delicious details. :P
July 22, 2020
I picked this up as a remedy to my mathematics education. Focusing on the spirit of mathematics is a concept that is foreign to me. My experience with Mathematics is more akin to a competitive sport, where pupils race to memorize the series of steps needed to score highly on a test. This book is refreshing.
Devlin's writing may be simple, but he treats the reader like an adult. The math is presented confidently in its own language, with diagrams and equations. This makes for a dense (yet rewarding) book. I would sit down for an hour of focus and get through 10 pages.
The core idea of the book is that mathematics is about patterns. Devlin explores patterns of geometry, symmetry, calculus or topology and finds the following structure: "There is an initial simplification, in which the key concepts are identified and isolated. Then those key concepts are analyzed in greater and greater depth, as relevant patterns are discovered and investigated. There are attempts at axiomatization. The level of abstraction increases. Theorems are formulated and proved. Connections to other parts of mathematics are uncovered or suspected. The theory is generalized, leading to the discovery of further similarities to—and connections with—other areas of mathematics. It is this overall structure of the field that I wanted to convey."
Removing one star since topics range too much in difficulty. Many of the passages in the physics or topology section were beyond my reach, yet the probability chapter barely covered my high school stats class.
Devlin's writing may be simple, but he treats the reader like an adult. The math is presented confidently in its own language, with diagrams and equations. This makes for a dense (yet rewarding) book. I would sit down for an hour of focus and get through 10 pages.
The core idea of the book is that mathematics is about patterns. Devlin explores patterns of geometry, symmetry, calculus or topology and finds the following structure: "There is an initial simplification, in which the key concepts are identified and isolated. Then those key concepts are analyzed in greater and greater depth, as relevant patterns are discovered and investigated. There are attempts at axiomatization. The level of abstraction increases. Theorems are formulated and proved. Connections to other parts of mathematics are uncovered or suspected. The theory is generalized, leading to the discovery of further similarities to—and connections with—other areas of mathematics. It is this overall structure of the field that I wanted to convey."
Removing one star since topics range too much in difficulty. Many of the passages in the physics or topology section were beyond my reach, yet the probability chapter barely covered my high school stats class.
October 20, 2019
Good book about mathematics that introduces lots of key topics and does a good job of explaining what mathematics is. I'm not sure what the target audience is - I imagine that those without much mathematical education might find parts of it difficult but it was a good reminder of previously understood concepts and introduction to new ones for someone who has done some maths but not for a long time.
November 30, 2021
I understood the first half pretty well. The second half mostly makes me want to learn more mathematics, mostly.
Especially liked reading about perspective. And regret giving up one calculus, algebra and geometry in second year University.
As Mathematics veers into more extreme abstraction, I become a bit lost. I can grasp vaguely why abstracted mathematics can work, and can work for practical purposes, but somewhere along the chain i get lost in the 'how'.
This book is not really a 'how' kind of book, but expects a high level of understanding already. It is more of a elevated overview, and this worked for me up to a point. Some useful connections.
Especially liked reading about perspective. And regret giving up one calculus, algebra and geometry in second year University.
As Mathematics veers into more extreme abstraction, I become a bit lost. I can grasp vaguely why abstracted mathematics can work, and can work for practical purposes, but somewhere along the chain i get lost in the 'how'.
This book is not really a 'how' kind of book, but expects a high level of understanding already. It is more of a elevated overview, and this worked for me up to a point. Some useful connections.
October 28, 2021
It's not something you read cover to cover but rather an encyclopedia. Found it useful when I had to help my son who had a question about a notation. You can also pick up a random topic and read it for fun.
July 31, 2025
Es un libro que hubiese agradecido haber tenido que leer nada mas empezar la secundaria, para poder entender unas matemáticas que tuve que aprender a base de repetir y repetir sin acabar de saber para qué eran.
August 30, 2021
Clearly written explanation of methods and results in modern mathematics, written for educatated laymen. Very good.
September 17, 2015
This is a fairly concise book. Devlin attempts to show us the construction of mathematics by its application and by demonstrating its conceptual genealogy. Of course, history of how a field grows is going to reveal its construction to us, although the language itself is at the highest level, hopelessly erudite.
Devlin's prose is concise, easy to read and yet sacrifices very little complexity for its clarity. The task he has undertaken however is a difficult one. In striving to show us applicability, Delvin allows us glimpses of what math can do for us in the daily routines of the world in which we live. Delvin doesn't strive to make a philosophical statement about math, yet it seems that he wants to posit mathematic's reality as being on par with the one in which we live. To do this would require a more concise approach, directed by principles. The chapters in this book suggest that Devlin wishes to pursue such an endeavor and yet at times, he seems unable to present us little more than examples and applications. In fact, his last chapter, about the 'Hidden Patterns of the Universe' seems to attempt to encapsulate an argument that Mathematics is as real as the universe is; although Delvin never makes this remark.
I don't have a problem with his content, or how he talks about it. I do have an issue with his organization. If anything, he seems to want to make his argument without making it; to throw at us a barrage of ideas so that we submit. Unfortunately, in his presentation of this massive amount of data, he lacks any kind of metaphysical or over arching ideal by which we can grasp that mathematics is real. Isn't it his point that inductive examples, examples by experience there may be plenty of, but a real proof is one that rationally equates two values so that their identity of relation is assured?
If we were to take mathematics as being as real as the universe, we would have to see a mathematical proof of it somehow. And so to that end, Devlin does not make this statement, although he seems to suggest it with many vague chapter titles and ruminations on how various patterns in the universe are at least explainable in mathematics. Devlin does not, however, explore that all patterns are explainable in mathematics, just that math is so applicable. Such an undertaking would be, in a sense, near impossible without a cogent understanding of exactly what a pattern is in the first place.
Still, I did enjoy reading this book, and learned a few things in the process. If you think this is an interesting topic, you may also enjoy reading this book.
Devlin's prose is concise, easy to read and yet sacrifices very little complexity for its clarity. The task he has undertaken however is a difficult one. In striving to show us applicability, Delvin allows us glimpses of what math can do for us in the daily routines of the world in which we live. Delvin doesn't strive to make a philosophical statement about math, yet it seems that he wants to posit mathematic's reality as being on par with the one in which we live. To do this would require a more concise approach, directed by principles. The chapters in this book suggest that Devlin wishes to pursue such an endeavor and yet at times, he seems unable to present us little more than examples and applications. In fact, his last chapter, about the 'Hidden Patterns of the Universe' seems to attempt to encapsulate an argument that Mathematics is as real as the universe is; although Delvin never makes this remark.
I don't have a problem with his content, or how he talks about it. I do have an issue with his organization. If anything, he seems to want to make his argument without making it; to throw at us a barrage of ideas so that we submit. Unfortunately, in his presentation of this massive amount of data, he lacks any kind of metaphysical or over arching ideal by which we can grasp that mathematics is real. Isn't it his point that inductive examples, examples by experience there may be plenty of, but a real proof is one that rationally equates two values so that their identity of relation is assured?
If we were to take mathematics as being as real as the universe, we would have to see a mathematical proof of it somehow. And so to that end, Devlin does not make this statement, although he seems to suggest it with many vague chapter titles and ruminations on how various patterns in the universe are at least explainable in mathematics. Devlin does not, however, explore that all patterns are explainable in mathematics, just that math is so applicable. Such an undertaking would be, in a sense, near impossible without a cogent understanding of exactly what a pattern is in the first place.
Still, I did enjoy reading this book, and learned a few things in the process. If you think this is an interesting topic, you may also enjoy reading this book.
July 1, 2024
Back in high school, my Precalculus teacher said the following, “math is all about patterns”. I had always heavily disagreed with that, even after completing my bioengineering degree. I believed math was all about rigorous calculation and modeling. This book proved me wrong. For that, I am grateful to the author.
As a support specialist working in the medical device industry, I most certainly agree with the following. “Mathematics, making the invisible visible”. A powerful statement and one of my favorites. This book has managed to spark a fascination in regards to mathematics far deeper than when before I read the book. Since then, I have read similar but more specialized books on the subject. Books such as The Number Zero, The Imaginary Tale, and In Pursuit of the Unknown-17 Equations that changed the world. Hence, this book served as a prudent introduction to mathematics.
Math has always been my favorite subject. Hence, I wanted a book that could organically provide me with how exactly the subject was devised. Little did I know that very question is quite difficult and maybe even impossible to answer. I posses several college mathematics textbooks and was in need for no more. Furthermore, I wanted to continue to grow in mathematical maturity. I wanted a book that would allow me to appreciate the mathematics I had already been intimately familiar with (Calculus, Differential Equations, Fourier Analysis, etc. This book did the job.
As a support specialist working in the medical device industry, I most certainly agree with the following. “Mathematics, making the invisible visible”. A powerful statement and one of my favorites. This book has managed to spark a fascination in regards to mathematics far deeper than when before I read the book. Since then, I have read similar but more specialized books on the subject. Books such as The Number Zero, The Imaginary Tale, and In Pursuit of the Unknown-17 Equations that changed the world. Hence, this book served as a prudent introduction to mathematics.
Math has always been my favorite subject. Hence, I wanted a book that could organically provide me with how exactly the subject was devised. Little did I know that very question is quite difficult and maybe even impossible to answer. I posses several college mathematics textbooks and was in need for no more. Furthermore, I wanted to continue to grow in mathematical maturity. I wanted a book that would allow me to appreciate the mathematics I had already been intimately familiar with (Calculus, Differential Equations, Fourier Analysis, etc. This book did the job.
November 15, 2010
Divulgare la matematica non è affatto semplice. Il problema è trovare il giusto equilibrio tra la complessità intrinseca dei temi trattati, che richiedono tutto un armamentario di notazioni e tecnicalità anche solo per essere comprese, e la famosa massima "ogni formula matematica in un libro ne dimezza le vendite". Devlin c'è riuscito in questo libro? Non troppo, direi. Non so se il guaio sia dovuto al fatto che il libro è la revisione "per non scientificamente alfabetizzati" di un volume uscito per la collana legata a Scientific American; sicuramente il problema non è nella traduzione che è buona, anche se nelle bozze sono sfuggiti un paio di errori. Però mentre ci sono capitoli oggettivamente venuti fuori molto bene, quello sulla logica e soprattutto quello sulla probabilità, la parte sui gruppi e sulla topologia sono poco comprensibili se non si sa già di che si parla... il che è ancora peggio, perché la posizione filosofica di Devlin è che la matematica è lo studio delle strutture, e quei due capitoli dovrebbero esserne la quintessenza. Diciamo ad esempio che io avrei evitato di "spiegare" la dimostrazione dell'ultimo teorema di Fermat, perché tanto non aggiunge nulla a quella che oggi definiscono pomposamente "l'esperienza matematica"... E comunque alla fine, con la metrica di Minkovskij, le formule le ha messe :-)
October 20, 2013
The book is an amazing journey through the history of mathematics that touches upon and connects discoveries and inventions in number theory, reasoning (logic), calculus, shape (geometries), position (topology), symmetry (groups), probability, and (finally) universe (atomic particles, quantum theory, etc.)
The historical view provides enough details of folks (quite of few of them we studied in school) and how they went about the inventions. The narrative connects various dots (folks and theories) across the space-time continuum.
Besides the great historical perspective and narrative, the exposition about the math is what makes the book special. If you have some training in math (say, calculus, groups, geometry, probability, and such as covered until 12th grade or Freshman year in college), then the exposition of advanced topics/concepts in focused areas is instantaneously accessible. Further, it is described in a way that one can connect the concepts to real world occurrences. In addition, the simplicity of exposition breaks down the concepts that I was constantly having "aha" moments (because either I remembered something I had learnt in 12th grade or I realized the essence of what I had learnt in 12th grade.)
IIRC, this is a book I bought 6 years ago and only got to reading it now. And, I'm glad that I read it :)
The historical view provides enough details of folks (quite of few of them we studied in school) and how they went about the inventions. The narrative connects various dots (folks and theories) across the space-time continuum.
Besides the great historical perspective and narrative, the exposition about the math is what makes the book special. If you have some training in math (say, calculus, groups, geometry, probability, and such as covered until 12th grade or Freshman year in college), then the exposition of advanced topics/concepts in focused areas is instantaneously accessible. Further, it is described in a way that one can connect the concepts to real world occurrences. In addition, the simplicity of exposition breaks down the concepts that I was constantly having "aha" moments (because either I remembered something I had learnt in 12th grade or I realized the essence of what I had learnt in 12th grade.)
IIRC, this is a book I bought 6 years ago and only got to reading it now. And, I'm glad that I read it :)
October 21, 2013
Kniha, jejímž hlavním rysem "nevyrovnanost". Nevyrovnanost ve zpracování témat, v obtížnosti kapitol a ve způsobu vedení výkladu.
Počáteční kapitoly jsou napsány poměrně slušně, i když výklad výrokové a predikátové logiky mi přišel dost odfláknutý a pro nezasvěcené nepřístupný. Problémem dalších kapitol je, že nechápu, kdo by měl být jejich čtenář. Pokud o problematice něco málo víte, nedovíte se nic nového, pokud nic nevíte, pochybuju, že vám někdy zbytečně komprimovaný výklad něco dá. Poslední dvě kapitoly knihy jsou spíš do počtu, aby autor mohl v rychlém sledu enumerovat odborné oblasti, kde matematika skutečně "z neviditelného činí viditelné" a dostál tak na poslední chvíli podtitulu knihy.
Počáteční kapitoly jsou napsány poměrně slušně, i když výklad výrokové a predikátové logiky mi přišel dost odfláknutý a pro nezasvěcené nepřístupný. Problémem dalších kapitol je, že nechápu, kdo by měl být jejich čtenář. Pokud o problematice něco málo víte, nedovíte se nic nového, pokud nic nevíte, pochybuju, že vám někdy zbytečně komprimovaný výklad něco dá. Poslední dvě kapitoly knihy jsou spíš do počtu, aby autor mohl v rychlém sledu enumerovat odborné oblasti, kde matematika skutečně "z neviditelného činí viditelné" a dostál tak na poslední chvíli podtitulu knihy.
October 2, 2015
I thought this was a good book but it was rather 'hit and miss' with me...probably more of issue with me than the book. The author does a fairly good job of sticking to concepts (I found his supposition that math is the study of patterns to be interesting) and shying away from equations. However, as a book on mathematics equations tend to be unavoidable and it is during the 'equation parts' of the book that I think it comes up short. With a background in engineering, I didn't have much trouble following the explanations but I'm not sure those without a reasonable math background would find it as accessible. Additionally, some of the subjects covered in the book were more interesting to me than others... but again, that's just me.
June 25, 2010
I liked this book. It was pretty much just what I was looking for when I picked it up. One of the reviews says it's "the perfect book for people who have questions about math they've always wanted to ask but were afraid they wouldn't understand the answers to" and I would definitely agree with this.
One of the things I liked best about this book was how well it showed the relationship between both the different fields of mathematics, and between mathematics and other fields. It seems like these relationships tend to be glossed over during a standard education, which is a shame, since the unity behind the different disciplines is one of the more interesting aspects of mathematics.
One of the things I liked best about this book was how well it showed the relationship between both the different fields of mathematics, and between mathematics and other fields. It seems like these relationships tend to be glossed over during a standard education, which is a shame, since the unity behind the different disciplines is one of the more interesting aspects of mathematics.
February 8, 2011
Not bad - sort of an introduction to the major themes of mathematics. It has some history but it doesn't get bogged down by trying to stay chronological or include every historical detail. It sort of "whets the appetite" for studying math beyond the textbook.
It's good. It was fun. It just didn't grab me. I think I wanted more detail. I felt like it was little too popularized or "dumbed down". And yet, I didn't feel it was "sparkly" enough to appeal to students.
Entertaining but not practical for classroom use.
It's good. It was fun. It just didn't grab me. I think I wanted more detail. I felt like it was little too popularized or "dumbed down". And yet, I didn't feel it was "sparkly" enough to appeal to students.
Entertaining but not practical for classroom use.
November 25, 2013
I really enjoyed this book. As a mathematician I was fairly familiar with many of the problems posed as classic milestones in mathematics achievement. It was cool to see that my undergraduate education was on the mark. He didn't over do the diagrams and they certainly added to the text.
After reading the prologue and first chapter of the book, I felt that Devlin was able to put into words many of the feeling I had about mathematics, why I found it intrinsically beautiful, and why I enjoyed doing it.
After reading the prologue and first chapter of the book, I felt that Devlin was able to put into words many of the feeling I had about mathematics, why I found it intrinsically beautiful, and why I enjoyed doing it.
January 17, 2015
The book takes the reader into a brief journey through the history of mathematics and goes through many of the important matematical methods and theories and their practical applications. Reader also gets to know a bit also about the renowned mathematicians behind them. Easily accessible low-overhead content fits perfectly just for casual reading especially if you're into mathematics but want to take a break from calculus, but still want to read something inspiring on mathematics.
July 27, 2011
For the curious on how the world "works" but not inclined to study Physical sciences, this is a great and enjoyable read. Full of light and simplified explanations of deep and purely scientific subjects as well as daily life "for granted" themes that most of us don't even think of for a second to see what's behind, conceptually.
March 11, 2014
Yes, I did feel real sad after reading this book. Reason: Why weren't we taught Mathematics the way the author teaches in this book?
Author's work on making users understand Calculus is simply amazing in this book. Highly recommended for anyone who wants to be in touch with and for those who're 'afraid' of Math.
Author's work on making users understand Calculus is simply amazing in this book. Highly recommended for anyone who wants to be in touch with and for those who're 'afraid' of Math.
December 17, 2012
It was wonderful probably up to the discussion of Probability Theory. After that the last few chapters felt somehow rushed through. But i enjoyed very much insights into the number theory, topology and the history of Math. Very interesting but i doubt someone totally without mathematical knowledge can fully appreciate it.
February 7, 2013
Very interesting, but not quite as accessible to the lay person as the various reviews suggest. Most of it is accessible to anyone with little or no math background, but there are highly technical sections. Just skip those!
November 12, 2013
So many books on History of Mathematics and philosophical approach but this is outstanding work by Keith. K.J.Devlin actually showed how one can see mathematics in real life and how mathematician thinks and come up with ideas. Most inspiring book of all times.
June 17, 2015
I thought this was a really well written book with helpful insight into the underlying principles of mathematics as well as its very interesting history. Defiantly made me appreciate my studies much more.
January 19, 2015
Really just...for a math book not only was this an incredibly enjoyable read, but it also taught me quite a bit about math theory in general.
October 17, 2014
An excellent reminder of how awesome math can be.
November 13, 2014
Extremely interesting and surprisingly easy to read! Thoroughly enjoyed this broad (and acknowledgedly brief) survey of the history of mathematics and some of the big ideas and current trends.
December 9, 2015
The beauty of mathematics , good
February 25, 2016
A perfectly competent overview, but it didn't grab me. Maybe it was the influence of the NyQuil haze, so perhaps that's not quite fair.
December 10, 2018
Was really cool to learn about how mathematics was developed, and how our way of teaching it hasn't really changed. Was an easy read.
Displaying 1 - 29 of 29 reviews