30 Great Math Books as Recommended by Our Readers

A couple of days ago we asked you to tell us about your favorite math book. Now that the results are in, we must say that while some titles were expected, there are quite a few surprises as well. Quite frankly we were blown away by the great list of math books we compiled with your input.

Listed in the order received, along with quotes from those who submitted them:

1. A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form by Paul Lockhart

Good light book — Folex

2. The Mathematical Experience by Phillip J. Davis, Reuben Hersh

When I was about to finish my degree in math, I had the opportunity to enjoy this new (to me) point of view. The historical and philosophical aspects make it really worth reading. — Jose Rodriguez

3. Winning Ways for Your Mathematical Plays: Volumes 1 and 2 by Elwyn R. Berlekamp, John H. Conway, Richard K. Guy

It expands on the concept of numbers tremendously. — Jerry Anning

4. Fourier Analysis by T. W. Körner

Lots of interesting math, lots of historical information and stories, some interesting applications. What’s not to like? — Peter

5. Tools of the Trade by Paul J. Sally, Jr.

Paul F***in Sally, nuff said QED, bitch. — John Rodgers

6. The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger, Rotraut Susanne Berner, and Michael Henry Heim

Great introduction to many mathematical topics for tweens. — Mark Bell

7. Logicomix: An Epic Search for Truth by Apostolos Doxiadis, Christos H. Papadimitriou, Alecos Papadatos, and Annie Di Donna

This comic is structured on the life of Bertrand Russel and his search for truth. It’s concise, easy to understand and most of all beautifully illustrated. It truly emerges you in one of the most important mathematical stories like no other normal book could. Certainly a must read for anyone with an interest in Mathematics and Logic. — Matthew Edwards

8. Geometry and the Imagination by David Hilbert and S. Cohn-Vossen

A book compiled by one of David Hilbert’s students covering a series of lectures about geometry. It is a great look into modern geometry and I think many undergraduates in math could follow along nicely. Very expansive. — Michael Music

9. Mathematics: Form and Function by Saunders MacLane

A beautiful and clear exposition of the branches of mathematics and their interconnections. — Nick Kirby

10. How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics by William Byers

I like the treatment/discussion of many foundational aspects of mathematics: logic, paradox, ambiguity, infinity, uncertainty, “truth,” that people too often take for granted or overlook. — Shecky R.

11. The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century by David Salsburg

This book introduces the history of statistics without getting too technical. Having studied statistics in school, it is amazing to hear the stories of the people who invented the statistical techniques. — Shigeru Sasao

12. Unknown Quantity: A Real and Imagined History of Algebra by John Derbyshire

Exposed me to whole areas of mathematics I’d never heard of, such as topology, abstract algebra, Reimann surfaces, and so on. — Scott McWilliams

13. Here’s Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math by Alex Bellos

I thought this was a great look into some origins of numbers and math concepts in a fascinating way. I didn’t use it in the classroom, but several of the examples and interesting facts easily made their way into my classroom discussions. — Dan Olexio

14. Real Analysis by N. L. Carothers

It’s a simple, intuitive, down to earth look at real analysis on metric space without losing on the rigour typically found in an upper year undergraduate course. — Nikolay Hristov

15. Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart

The book is fun to read and easy to understand. The mathematics is laid out beautifully within entertaining puzzles. — Danielle Stewart

16. The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth by Paul Hoffman

Very entertaining biography by Paul Hoffman. Erdos is portrayed as a very quirky yet endearing genius. — Janet Dee

It is a wonderful combination of biography and mathematics. It is a very well-written biography, intriguing and inspiring. In illustrating the life of the great mathematician Paul Erdos, Hoffman slips in snippets of interesting mathematical ideas and discoveries, allowing readers like me who are not yet familiar with more advanced mathematics to feel its magic. — Cissy Chan

17. The Visual Display of Quantitative Information, 2nd edition by Edward R. Tufte

It’s a wonderful book that can both function as a introductory textbook to visualization or a coffee table book. It is filled with fantastic diagrams and visuals both original and from a wide variety of sources, including international examples. It manages to have great breath and skim through topics without feeling deficient. — Joshua Niederriter

18. Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory by Carl M. Bender and Steven A. Orszag

Deeply insightful and utterly fascinating.

I had the privilege to explore this guide to the universe of asymptotics under Prof. Bender. I used to think, and still do (about 2 decades on), that this book is like the Rosetta Stone, and enables us to solve anything in applied mathematics.

A must have for anyone looking to understand the incredible universe we find ourselves in! — Monish Verma

19. Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter

The book is a marvel on many levels. — Hemanth Kapila

20. What Is Mathematics? An Elementary Approach to Ideas and Methods by Richard Courant, Herbert Robbins, and Ian Stewart

After reading this:

“It doesn’t matter what mathematical things are: it’s what they do that counts. Thus mathematics hovers uneasily between the real and the not real; its meaning does not reside in formal abstractions, but neither is it tangible. This may cause problems with philosophers who like tidy categories, but it is the great strength of mathematics — what I have elsewhere called its ‘unreal reality.’ Mathematics links the abstract world of mental concepts to the real world of physical things without being located completely in either.” – Ian Stewart, What is Mathematics?

…I was hooked and after reading it several times, I still can’t put it down! Great job to all who contributed to creating this masterpiece — Bill Zimmerly

21. A Mathematician’s Apology by G. H. Hardy

Wonderful description of why being a mathematician and mathematics matters which calls upon our higher selves rather than utilitarian notions. — Robert Janes

Beautiful stuff. — A.S.

22. The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele

Inspiring and beautiful proofs. — Sung guan Yun

23. Calculus Basic Concepts for High School by L.V. Tarasov, V Kisin, and A Zilberman

The entire book is written in the form of a dialogue between a teacher and a student. Calculus is introduced through sequences and inequalities. The discussion proceeds as naturally and intuitively as a first learner of the subject always wishes for. I was introduced to this book by a friend of mine when I was in high school. Today, as a teacher and a student of mathematics, I thank him wholeheartedly for that. This Soviet era mathematical gem is a must read for any one interested in pre-college mathematics. — Ashani Dasgupta

24. Visual Complex Analysis by Tristan Needham

Visual Complex Analysis is filled with deep insights about what’s going on in the complex plane. Tristan Needham writes in an informal style and it is difficult not to be drawn in by his enthusiasm and excitement. In addition to the traditional calculus topics, the book includes fascinating chapters on Mobius transformations, non-Euclidean geometry, and topology. Every chapter ends with several pages of clever and engaging problems, many of which will grab you like a good mystery novel and won’t let go until you solve them (well, at least if you’re the kind of person who reads math blogs). Who knew complex analysis could be so much fun? Needham did, and fortunately he’s shared his ideas and discoveries with the rest of us. — Joel Schwartz

25. Geometry: a High School Course by Serge Lang and G. Murrow

I was awful at geometry for years due to being taught it piecemeal, as a random assortment of processes and formulas to memorize without any unifying principle or foundation. As a result, I avoided or struggled though any bit of math that hinted at it – algebra because of the trigonometry, calculus because of the conic sections – until I finally decided to tackle it with everything I had. I pulled the first book off the shelf of the library’s geometry section and resolved that I would work through it cover to cover. Thank God it was Lang’s book. He starts off with the very basics, lines and the concept of distance, but in such a way as to revolutionize your conception of them and all other similar, presumably dull axioms. The book serves doubly as a text on problem-solving – after only a few chapters of thoughtfully constructing proofs my confidence in my mathematic ability was increased tenfold. What had previously seemed a veiled framework whose mysteries were penetrable only through mastery of abstruse tomes now seemed open and accessible to me through my inherent attribute of reason. I now know that this is the result of working through any systematic geometry text starting with Euclid, but Lang’s remains my favorite for the continually fascinating proofs and presentation. He had a wonderful gift for explaining things to the uninitiated without sacrificing rigor or intellectual strength. — Lauren Tubbs

26. The Princeton Companion to Mathematics by Timothy Gowers, June Barrow-Green, and Imre Leader

Coherent overview of all of pure mathematics. — Nicholas Urfe

27. Principles of Mathematical Analysis by Walter Rudin

The amount of mathematical rigor applied to the fundamental concepts of calculus. — Zachary Gilmartin

28. Mathematics for the Million by Lancelot Thomas Hogben

First read this book in 1946 when I was 14. It was, at the time, the most exciting book I’d ever read and created in me a lifelong interest in mathematics. As a result I ended up as an electrical engineer, one son as a professor of Physics, and another as a fixed income portfolio manager (heavy on Math). I ascribe all of this to to Lancelot Hogben’s book. It may be out-of-date now but I can think of no better introduction to the subject for the young mind. — Ronald Francis

29. Number Theory: An Elementary Introduction Through Diophantine Problems by Daniel Duverney

The exhibition of the beauty of the number theory, achieved on the basis of its own simplicity and clarity, is one of the best features of this book. The book is both well written and pragmatic, while its material is pedagogical and comprehensive. This book illustrates various elementary topics in number theory through very clear explanations, concise definitions, and plenty of exercises along with their solutions. — Ana B. Momidik-Reyna

30. Mathematical Thought from Ancient to Modern Times (Vol. 1) by Morris Kline

Traces the origin of mathematics all the way to Babylonian times. A very comprehensive book. — Matt Swass