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17
Ten Must Read Books about Mathematics
By Antonio Cangiano. Filed under Essential Math, Suggested reading
I love books with the ability to inspire readers. Many non-mathematicians consider mathematics as something abstruse and complicated, suitable only for ‘nerds’. Often I highlight the unfounded nature of this prejudice, but nothing is more effective at disproving this stigma than a good book. I was in fact able to quickly change many of my friends’ views on the topic, by just giving them a good book which shows the beauty and fascinating nature of mathematics and science in general. The following is a list of great titles, most of which are fairly cheap. Not all of them are suitable for the mathematically illiterate though, and thus cannot simply be considered popular science. In the description I’ll give you fair warning if a particular title is better suited to those who are more advanced when it comes to math.
- The Man Who Loved Only Numbers: an original biography of the genius Paul Erdős, who was arguably the most prolific mathematician of the last century , renowned for being just as much of an eccentric as a math whiz. This book won its author a 1999 Aventis Prize for Science Books and you can watch a lecture that the author, Paul Hoffman, gave about the subject. As you can expect for such a unique mathematician, this book is filled with anecdotes and fascinating facts. If you are like me, you’ll buy a copy for yourself and will end up buying copies for your friends as a means of providing them with a light and interesting reading.
- An Imaginary Tale: The Story of “i” [the square root of minus one]: complex numbers are what puzzle many non-mathematicians the most. It’s intuitively easy to explain Rational and Real numbers to the layman, but complex numbers are often seen as something mysterious. In this book, Nahin goes the extra mile in his attempt to provide historical details as well as insight into the motivation behind complex analysis, offering a serious introduction to the topic that will also serve many mathematically inclined high schoolers and freshmen well.
- Dr. Euler’s Fabulous Formula: Cures Many Mathematical Ills: the author, Nahin, follows up his first book above with this gem - with a somewhat ridiculous title - about the most beautiful equation in the history of mathematics:
. It’s a delightful read, but beware that the author cuts to the chase in this one, and expects from the reader a solid understanding of complex numbers, as he exposes the application in various fields and covers advanced topics such as Fourier Series and Integrals (dedicating a chapter to each of them). Therefore I would consider the book “An Imaginary Tale” above, a prerequisite before approaching this book. - Godel, Escher, Bach: An Eternal Golden Braid: this book is one of the most famous bestsellers in the world, and should have a spot in any technically minded person’s library. I would argue that it is a particularly good read for programmers. It’s really hard to give justice to this tome in a few lines, so if you want you can read more about it through the reviews on Amazon or through its wikipedia entry.
- Mathematics for the Nonmathematician: history and methodologies of mathematics are well covered in this very inexpensive title. It combines two aspects which are difficult to match: it’s a page-turner like many math popular titles, while being instructional as well as an effective introductory text to basic mathematics for students and amateur mathematicians alike .
- God Created the Integers: The Mathematical Breakthroughs That Changed History: the historic introduction to some of the greatest mathematicians who’ve ever walked the face of the earth is worth the cover price alone. But this book is so much more than that, covering a wide range of mathematical topics which have been developed throughout history, in an accessible but rigorous way. It is admittedly more challenging than your average popular math title, but if you already have some mathematical basics mastered and are willing to work through it, you’ll gain a lot of insight about the nature of mathematics and the discoveries made by the giants of math from this excellent book.
- Fermat’s Last Theorem: if you are interested in learning more about the history and fascinating tales which surround one of the most well known theorems, this book will provide you with a marvelous and entertaining way to spend a Sunday afternoon. My wife who is not a mathematician, simply loved this book for its rich story telling and coverage of a topic with substantial historical significance.
- The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography: another intriguing title, by the same author of Fermat’s Last Theorem above. This book will get you excited about the topic of encryption and its history, from the time of Caesar right up to the future direction which encryption is taking in today’s technology based world. It currently has 5 stars on Amazon with 232 positive reviews out of 234.
- To Infinity and Beyond: What’s infinity? What it is its impact on mathematics and what are its cultural implications that it holds? These questions are clearly answered in this book which provides a beautiful exposition that is accessible to anyone. Read this book and chances are you’ll feel a sense of enlightenment as you soak up the words of this amazing writer. I would particularly recommend it as a gift for teenagers in high school, as a way of getting them interested in mathematics. This book will provide them with an essay on the reasons behind the study of Calculus and the practical implications within the areas of Art and Astronomy as well.
- Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics: unsolved number theory problems are a huge fascination for many mathematicians and hobbyists. It’s a fun field full of challenges and discoveries just waiting to spring forth. ‘Prime Obsession’ focuses on the Riemann’s Hypothesis, the most important unsolved problem in Mathematics. A reviewer on Amazon does an excellent job at describing the beauty of this book, quoting him: “Prime Obsession is a delight: a book about a hypothesis on the distribution of prime numbers that reads like a gripping mystery. Most fiction isn’t this vivid, moving, and well written, and this is no fiction. It is history, biography, philosophy, and, yes, mathematics brought to life with wit and wonder. You have to read this extraordinary book. This is the story of the Reimann Hypothesis, the greatest unsolved problem in mathematics today.“.
: an original biography of the genius 
: complex numbers are what puzzle many non-mathematicians the most. It’s intuitively easy to explain Rational and Real numbers to the layman, but complex numbers are often seen as something mysterious. In this book, Nahin goes the extra mile in his attempt to provide historical details as well as insight into the motivation behind complex analysis, offering a serious introduction to the topic that will also serve many mathematically inclined high schoolers and freshmen well.
: the author, Nahin, follows up his first book above with this gem - with a somewhat ridiculous title - about the most beautiful equation in the history of mathematics: 
: this book is one of the most famous bestsellers in the world, and should have a spot in any technically minded person’s library. I would argue that it is a particularly good read for programmers. It’s really hard to give justice to this tome in a few lines, so if you want you can read more about it through the reviews on Amazon or through its 
: the historic introduction to some of the greatest mathematicians who’ve ever walked the face of the earth is worth the cover price alone. But this book is so much more than that, covering a wide range of mathematical topics which have been developed throughout history, in an accessible but rigorous way. It is admittedly more challenging than your average popular math title, but if you already have some mathematical basics mastered and are willing to work through it, you’ll gain a lot of insight about the nature of mathematics and the discoveries made by the giants of math from this excellent book.
: if you are interested in learning more about the history and fascinating tales which surround one of the most well known theorems, this book will provide you with a marvelous and entertaining way to spend a Sunday afternoon. My wife who is not a mathematician, simply loved this book for its rich story telling and coverage of a topic with substantial historical significance.
: another intriguing title, by the same author of Fermat’s Last Theorem above. This book will get you excited about the topic of encryption and its history, from the time of Caesar right up to the future direction which encryption is taking in today’s technology based world. It currently has 5 stars on Amazon with 
: What’s infinity? What it is its impact on mathematics and what are its cultural implications that it holds? These questions are clearly answered in this book which provides a beautiful exposition that is accessible to anyone. Read this book and chances are you’ll feel a sense of enlightenment as you soak up the words of this amazing writer. I would particularly recommend it as a gift for teenagers in high school, as a way of getting them interested in mathematics. This book will provide them with an essay on the reasons behind the study of Calculus and the practical implications within the areas of Art and Astronomy as well.
: unsolved number theory problems are a huge fascination for many mathematicians and hobbyists. It’s a fun field full of challenges and discoveries just waiting to spring forth. ‘Prime Obsession’ focuses on the Riemann’s Hypothesis, the most important unsolved problem in Mathematics. A reviewer on Amazon does an excellent job at describing the beauty of this book, quoting him: “Prime Obsession is a delight: a book about a hypothesis on the distribution of prime numbers that reads like a gripping mystery. Most fiction isn’t this vivid, moving, and well written, and this is no fiction. It is history, biography, philosophy, and, yes, mathematics brought to life with wit and wonder. You have to read this extraordinary book. This is the story of the Reimann Hypothesis, the greatest unsolved problem in mathematics today.“.In the comments below feel free to share your thoughts on these books (if you have read any of them) and add other to the list which are near and dear to your own mathematical heart.
… No differential equations were harmed in the making of this post. 
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37 Responses to “Ten Must Read Books about Mathematics”
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I also liked Everything and More: A Compact History of Infinity
Well I’ve read exactly half the list, and on your suggestion, I’ll check out the rest. Although I would toss in Letters to a Young Mathematician by Ian Stewart in there, too.
You are allowed to harm those nonhomogeneous ones! (-:
I love maths.These are good books to read on.
I strongly believe that all aspects of live can be formulated as equation and resolved for best solution using maths.Even i considered Tennis and cricket as maths
I’ve read the two Simon Singh books - the code book and fermats last theorem.They’re both great, easy to read yet very informative and exciting! I’ll certainly look into the others. Thanks!
Your list is hugely useful - thank you for giving it to us - thst is - the people who love maths - but didn’t pick it up in school.
For people who are like me very scared of any but basic maths - can I offer this site -
http://betterexplained.com/
Brilliant young guy - giving his genius to others - hey - ln - e - I’m using those to evaluate options every day.
Good luck with pushing maths out - you must have basic math - eg calculate a percentage, use the rule of 72 only learnt that from the site above recently and I’m sixty, read history - but never by the winning side.
May I also suggest “The Lady Tasting Tea” by David Salsburg. Fantastic ‘non-mathy’ exploration into the history and importance of statistics.
Flatland and its sequel, Sphereland, didn’t make the list? They are wonderful books about geometry and are fun to read.
A History of Pi is a good read as well
http://www.amazon.com/History-Pi-Petr-Beckmann/dp/0312381859
I am not a mathematician, but I’ve come late to love math even if understanding it is still takes herculian effort. As a child I was convinved that basic math was unstable, and no one could prove to me that 2+2=4 other than to line up oragnes or pennies. I wanted PROOF! Naturally, I got really bad grades.
I found this book as enlightenment: Jerry P. King’s The Art of Mathematics. He showed me I am not crazy and while some of it remains above my math level, I still treasure this book.
Thank you for the recommendations! I’ll certainly be checking them out. Great post!
::::KBS
John Paulos has several good books. I especially loved “Beyond Innumeracy,” which was a series of short essays on mathematical topics.
His “A Mathematician Reads the Newspaper” had a cute spin. He takes typical stories in each section of the newspaper (scare stories, business articles, sports) and submits each to a mathematical analysis. Helps you understand how to filter articles for exaggerations and distortions and bring better perspective on many topics. Excellent book.
I am Brazilian and I have to mention this great book “The Man Who Counted” by Malba Tahan (pen name of Júlio César de Mello e Souza, “O Homem que Calculava” in the original in Portuguese).
The book tales the story of Beremiz Samir, a brilliant mathematician who uses his skill to surprisingly make success among the viziers.
It has a very nice storytelling and in each chapter the author introduce us to an intriguing problem in which Beremiz Samir encounter pleasure (and fame) by solving it.
It is available at amazon…
What happened to Flatland? or even Flatterland, two very important maths books there, and not just for the maths.
If you are a mathematics guy, you should check this one out
http://freevideolectures.com/mathematics.html
[...] like to read through book reviews and recommendations. I came across this list today, Ten Must Read Books About Mathematics. Looks like there may be some interesting reads in that list. (I said I was a nerd, right?) [...]
I second/thrid the question about Flatland. A great and required read.
Flatland was initially on the list, while drafting the article.
Readers can get it new from Amazon for $3.99.
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Here are my three of my favorites:
(1) A Mathematician’s Apology, G. H. Hardy; (2) The Man Who Knew Infinity: A Life of the Genius Ramanujan, Robert Kanigel;
(3) Men of Mathematics, E.T.Bell [don't like sexist title]
[...] Ten Must Read Books about Mathematics (tags: math-blog.com 2007 math lista_de_livros) [...]
thanks for putting this list together;
i’ve put a link to this page at my site.
there seems to be a bias for the recent.
my own list would include, first of all,
*something* by the great martin gardner
(or maybe just “the complete _mathematical_games_”).
one or both of clifton fadiman’s anthologies
(i think these are back in print).
william dunham’s _journey_through_genius_
would probably make it … hmm …
it’s gonna be hard to stop at ten.
_flatland_ wouldn’t make the top 100.
here’s the math fiction homepage.
Dear Fellowsoul,
The collection is quite GOOD! I have already gone thru the 4th book by Hoffsstadter. I would have been happier if I had written that book. Simply Marvellous!!!
I would like you to add the following titles also which are equally breathtaking:
1. J. Stillwell: Numbers and Geometry, Springer
2. J. stillwell: History of Mathematics, Springer
(Make your life a rose, that speaks silently in the language of fragrance).
With best aishes,
Ganesh
1) I second the recommendation for “A Mathematician’s Apology”.
2) your formatting is all messed up here; the story text starts below all the sidebar content. (Firefox 1.5, Mac OS X)
Here’s my list.
Mathematics
* Journey Through Genius, by William Dunham © 1990.
* The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities, by William Dunham © 1994.
* Proofs Without Words II: More Exercises in Visual Thinking, by Roger B. Nelsen © 2000.
* Proofs Without Words: Exercises in Visual Thinking, by Roger B. Nelsen © 1993.
* Fermat’s Last Theorem, by Simon Singh © 1997.
* The Universal Book of Mathematics: From Abracadabra to Zeno’s Paradoxes, by David Darling © 2004.
* The Mathematics of Ciphers: Number Theory and RSA Cryptography, by S. C. Coutinho © 1998.
I agree with FLT and I’ll look into his code book. My last book is a code and cypher book which is a great one.
Here are a few more interesting books:
I have read the 3 following books and found them enjoyable.
Unknown Quantity: A Real And Imaginary History of Algebra by John Derbyshire
e: The Story of a Number by Eli Maor
Trigonometric Delights by Eli Maor
I have not read the following, but they are all on my wish list:
The Equation That Couldn’t Be Solved: How Mathematical Genius Discovered the Language of Symmetry by Mario Livio
The Pythagorean Theorem: A 4,000-Year History by Eli Maor
When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible by Paul Nahin
Chases and Escapes: The Mathematics of Pursuit and Evasion by Paul J. Nahin
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i am a math learner too i am in grade 10.
hope we can be friends.
my math weblog : http://math.haiyanh.com/
I’ve read most of these and I commend your selection. I too would vote for adding to this list “Letters to a Young Mathematician” by Ian Stewart.
[...] (yet still interesting, of course) topics. Might be worth a browse if it’s in your library. Ten Must Read Books about Mathematics -otherwise, this blog post lists 10 highly readable popular math books. I’ve read most of them and [...]
I haven’t read a LOT of books about mathematics, but one that weaved lots of people and lots of topics into one book that I appreciated: The Music of the Primes.
That’s a fine list. I’ve read and enjoyed most of them. But you left off the book I consider the best of all; Rudy Rucker’s “Infinity and the Mind.” It provides by far the best introduction to transfinite numbers and the “paradise opened by Cantor” of any book I’ve read.
I love math too. I would say, a nice list of books.
However, when I get doubts in mathematics I refer to wikipedia and wolfram. There is lots of information on the web that refering to books seems too “old fashioned” to me.
I think that this list of books is pretty good. I would not recommend: “The equation that couldn’t be solved”, and “Unknown Quantity” because there is not much math, and too much history for a MATH book. I love history, but not in a math book. In “Unknown Quantity”, you could read a dozen pages without a mention of math. I enjoyed “Zero” by Charles Seife, William Dunham’s “The Calculus Gallery”. Also, Hardy’s “A Mathematicians Apology”. However, I disagree with Hardy’s conclusion: mathematics is for people under 30. There are far too many counterexamples to that statement.
In a previous career I was a physicist, and mathematics was simply a tool. I’ve ‘grown up’ since then and now consider Maths (the Pure variety) to be an insight into ‘the Mind of God’ - for want of a better concept. Two really good books I’d recommend is ‘Mathematic: The Golden Age’ by Keith Devlin, and ‘Symmetry and the Monster - One of the Greatest Quests of Mathematics’ by Mark Ronan. Both bring one closer to the ultimate truth, revealing Maths to be both beautiful and mind-expanding. Enjoy.
I would also recommend Chaos: Making a New Science by James Gleick. It’s a great book showing all the wonderful aspects of chaos theory.
The greatest math book I have ever read, though I took math up to Calculas 111, was a book I bought as an eigth grade student in 1967 from a revolving rack at a pharmacy. Yes, they actually sold paperbacks in small pharmacies in those days. But to the book, that was written by non-other than the great Isaac Asimov, Realm of Numbers. This little paperback book, numbering barely one hundred pages, if studied throughly will give the reader a deep understanding of basic math and therefore make all higher math easier. All math is really just arithmetic in disguise.