Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

To be on this list the book must satisfy the following conditions:

  1. It doesn't require an enormous amount of background material to understand.
  2. It must be a fun book, either in recreational math (or something close to) or in philosophy of math.

Here are my two contributions to the list:

  1. What is Mathematics? Courant and Robbins.
  2. Proofs that Really Count. Benjamin and Quinn.
share|cite|improve this question
I'm not a big fan of big lists. Not that it matters. – lhf Jul 7 '12 at 22:25
I find well-written textbooks more fun than "recreational math" books. – William Jul 7 '12 at 22:26
Yeah, you're probally right. However, many textbooks require a lot of background material, which is why I decided to restrict the books to the above categories. – Chris Dugale Jul 7 '12 at 22:27
@BlueRaja-DannyPflughoeft Math.SE has accepted big-lists, especially as comm-wiki, and this is a different question to the one you suggested: I wouldn't have even thought of my answer for that question. – Mark Hurd Jul 9 '12 at 1:56

26 Answers 26

Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter. Very interesting read - details Gödel's Incompleteness Theorem, and manages to touch on a wide variety of topics, including genetics, reductionism/holism, programming, art, music, brains, zen, language, etc. The central idea is that a special kind of self-reference (which Hofstadter calls a strange loop) seems to pop up everywhere, and is perhaps at the heart of intelligence and the appearance of meaning in a structure made up of meaningless parts.

share|cite|improve this answer
+1 I love this book very much~~~ For the amazing coincidence among the three masters~~ And the unify of math, logic, art and music! – Yuchen Liu Jul 8 '12 at 11:28
  • Flatland, by E. A. Abbott, and its sequel Sphereland by Dionys Burger.
share|cite|improve this answer

A whole lot of books by Raymond Smullyan, but To Mock a Mockingbird, which presents combinatory logic is definitely on the list, as is one of the several books in which he presents Gödel's first incompleteness theorem as a knights-and-knaves puzzle.

share|cite|improve this answer
To Mock A Mockingbird is my favorite of Smullyan's books by far (which is saying a lot), probably because it takes a different angle towards his usual topics. – Steven Stadnicki Jul 9 '12 at 1:31

I recommend Proofs from THE BOOK by Aigner and Ziegler. Here you can find a review.

share|cite|improve this answer

So, my favorite recreational math book growing up was Mathematical Mysteries, by Calvin Clawson. It's light on rigor, but it contains a lot of interesting mathematical concepts.

Also, I think it's important to list Herbert Robbins as an author when talking about What is Mathematics?, seeing how he was the one doing the actual writing.

share|cite|improve this answer
+1 for giving credit to Robbins - he is too often missed out. – Old John Jul 7 '12 at 23:03

I am quite prepared to be down-voted on this one, but here goes ...

I would have to include Andre Weil's book "Basic Number Theory", since:

  1. All the mathematicians I know regard basic number theory as fun and recreational.

  2. The author states in the preface: "No knowledge of number theory is pre-supposed in this book, except for the most elementary facts about rational integers".

share|cite|improve this answer
the end of the sentence should be added "; it is useful but not necessary to have some superficial acquaintance with the p-adic valuation of the field $\mathbb{Q}$ of rational numbers and with the completion $\mathbb{Q}_p$ of $\mathbb{Q}$ defined by these valuations." and the four pages of prerequisites following... :-) – Raymond Manzoni Jul 7 '12 at 22:52
Ah yes!! - I wish I had know about those sentences before I actually parted with my money and bought this book :-) – Old John Jul 7 '12 at 22:54
Very funny answer! +1 – Jonas Meyer Aug 1 '12 at 4:10
  • One, Two, Three… Infinity by George Gamow
share|cite|improve this answer

This is a topic that has been hit pretty well at MO in a few ways.

The most related question would be favorite popular math book, which has 60 answers and many (more than 60) books mentioned, along with their author(s) and a short description.

The question how to write popular mathematics well has some related bits, too. And on a not-so-recreational-level, there is the question Examples of great mathematical writing, which includes everything by Serre and the analysis series by Stein and Shakarchi.

share|cite|improve this answer

I'd like to add "A Budget of Trisectors" by Underwood Dudley. It's the author's experiences with false constructions of an angle trisection with compass and straightedge, and has some very interesting debates about what proofs are and how to explain them to the layperson.

share|cite|improve this answer

To my opinion Polya, G. "Mathematics and Plausible Reasoning" would go here as philosophy of math and a recreational book as well with many problems and examples, illustrating some well-known mathematical discoveries of past.

share|cite|improve this answer

Most introductory Dover books are pretty cheap and don't require too much background.

For example, Pinter's A Book of Modern Algebra is, in my opinion, quite well written and rich with exercises. (it lacks answers to all but a few questions, though).

The Number Devil: A Mathematical Adventure by Hans Enzensberger is a fun survey of elementary number theory. It's structured similarly to the series of children's books 'Diary of a Wimpy Kid.'

share|cite|improve this answer

I really enjoyed Fermat's Enigma by Simon Singh. This definitely falls more under the heading "philosophy of math", but it's great in conveying to laypersons (like me) what an interesting and thrilling field mathematics is.

share|cite|improve this answer

Unfortunately, they are priced quite expensively, but the four volumes of Winning Ways for your Mathematical Plays are simply wonderful. It can be fairly heavy reading (I've only skimmed parts of the various volumes), but it provides directly accessible mathematics without any prerequisite requirements.

share|cite|improve this answer
+1 : this is the book I was going to mention when I had a few minutes to answer. A delight from start to finish. – Steven Stadnicki Jul 9 '12 at 2:32

Thomas Ferguson's Game Theory is a really fun read (and it's available for free here)

share|cite|improve this answer

The book that inspired me to change majors from chemistry to mathematics and kept me going through the dark times during my father's cancer: I Want To Be A Mathematician by Paul Halmos. It is an addicting read with so much that is wise about mathematics, mathematicians and the entire culture surrounding them.It should be required reading for any new mathematics student.

share|cite|improve this answer

The Penguin Dictionary of Curious and Interesting Numbers by David Wells is a good read.

share|cite|improve this answer

One Minute Mysteries: 65 Short Mysteries You Solve With Math!

simply for the sheer whimsy of reading a book written by a 9-year-old.

Also because you can e-borrow it for free:

share|cite|improve this answer

Mathematics and the Imagination, by Edward Kasner and James R. Newman.

share|cite|improve this answer

The Man Who Counted, Malba Tahan

share|cite|improve this answer

Both of the following books are really interesting and very accessible.

Stewart, Ian - Math Hysteria This book covers the math behind many famous games and puzzles and requires very little math to be able to grasp. Very light hearted and fun.

Bellos, Ales - Alex's Adventures in Numberland This book is about maths in society and everyday life, from monkeys doing arithmetics to odds in Las Vegas.

share|cite|improve this answer
G.E.B. would also have been a nice choice but it's already listed and to be fair, while it doesn't require specific math knowledge per se, I think it does require a certain knowledge of mathematical thinking. – Zeta Two Jul 9 '12 at 13:36

Does God Play Dice? The New Mathematics of Chaos by Ian Stewart

This book explains very nicely about a very complicated topic. I liked simple calculator example which shows chaos with a basic equation like $x^2$

How to Cut a Cake: And Other Mathematical Conundrums by Ian Stewart

This one is pure fun.

share|cite|improve this answer

The Prime Number Theorem by G. J. O. Jameson is a delightful read.

share|cite|improve this answer

protected by Zev Chonoles Jul 8 '12 at 6:33

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.