Favorite popular math book

Question

Christmas is almost here, so imagine you want to buy a good popular math book for your aunt (or whoever you want). Which book would you buy or recommend?

It would be nice if you could answer in the following way:

Title: The Poincaré Conjecture: In Search of the Shape of the Universe
Author: Donal O'Shea
Short description: The history of the Poincaré Conjecture.
(Perhaps something like "difficulty level": + (no prior knowledge of math, as the book mentioned above), ++ (some prior knowledge of math is helpful), +++ (Roger Penrose: Road to Reality (?))

I hope this is appropriate for MO, since I think is of interest to mathematicians (at least for those who want to buy a popular math book for some aunt :-) ).

score 63 · Answer 1 · answered Dec 11 '09 at 22:32

63

Title: Godel, Escher, Bach: an Eternal Golden Braid

Author: Douglas Hofstadter

Short Description: It's mildly debatable whether this is in fact a book about mathematics, but any mathematician who has read this book will understand why I recommend it and any who has not should. Probably best for those with either a philosophical or musical bent.

answered Dec 11 '09 at 22:32

Qiaochu Yuan

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I think Hofstadter would himself say that it is not about mathematics. And I'd say that he was wrong. – Dan Piponi Dec 11 '09 at 22:56
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I must be one of the few people who disrecommend the book. He draws some philosophical conclusions using arguments which have subtle philosophical gaps which are hard for a layman (to philosophy) reader to spot, and gives no hint there could be controversy. It is a legitimate argument that the gaps I mentioned are not actually gaps at all, but also a legitimate argument that they are. (Mathematical analogy for the kind of subtle error: confusing an abstract group with one of its faithful matrix representations.) – Alexander Woo Dec 12 '09 at 02:24
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Admittedly I'm no expert on philosophy. I just think GEB has a lot of interesting ideas in it, and Hofstadter presents them very artfully. – Qiaochu Yuan Dec 12 '09 at 03:57
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Indeed a very nice book. However, although I know many people who read it, I don't know a single one who doesn't have a degree in math (non of them had when they read it). Is your aunt up to it ? – David Lehavi Dec 13 '09 at 06:49
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@Woo Is there perhaps discussion somewhere on these issues that you could point me too. I am about a third of the way through and would like to hear some of these arguments, since I am as you say a "layman to philosophy". Thanks in advance. :) – B. Bischof Dec 14 '09 at 00:59
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I agree with @Woo that there are suspect philosophical arguments in GEB. Hofstadter would probably say that these arguments are more important than the mathematics. And yet I would still recommend GEB for the mathematics it contains. – Dan Piponi Feb 24 '10 at 22:22
Some chapters are better than others. I couldn't really get into the DNA typography stuff, but I loved a lot of other sections of the book. – Jim Conant Dec 04 '10 at 19:29
It's lovely, but many people complain about the formal logic stuff, which gets pretty heavy at times. Even mathematically inclined people. (Not me though, I've read it three times at least!) – Ketil Tveiten Dec 09 '10 at 08:54
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Math or no math, it's a fun and playful book to read. – Simon Rose Dec 10 '10 at 18:21
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V'Arnold would be very angry at calling "confusion of abstract groups with (faithful) matrix representations" a subtle mistake. If Euler could have understood the question, he would probably laugh a lot too. I wonder if those "subtle philosophical gaps" are similarly deep enough to destroy the conclusions of the book... – Feldmann Denis Jun 14 '12 at 15:51
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My mother, who is intelligent and very well-read but not comfortable with mathematics, found the book hard-going. – Todd Trimble Oct 09 '12 at 14:47

score 61 · Answer 2 · answered Dec 12 '09 at 00:06

61

Title: Flatland

Author: A. Square / Edwin A. Abbot

Short Description: Imagine how life would be in less than three dimensions.

answered Dec 12 '09 at 00:06

adamo

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Jean-Pierre Luminet's "The Wraparound Universe" is a relatively new publication that's kind of in the same direction. Only it's souped-up by general relativity, geometrization of 3-manifolds and some serious physical experiments. I just got it in the mail today but it looks promising. – Ryan Budney Dec 18 '09 at 06:24
Bundle it with "Flatland:The Movie", http://www.flatlandthemovie.com. Your aunt will not be disappointed! – Victor Protsak Jun 06 '10 at 23:28
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I first read Flatland when I was 11 or 12, and to me it was an invitation to imagine encounters with beings who live in more than three dimensions! It was a real eye-opener. – Todd Trimble Jun 07 '10 at 01:53
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It must be mentioned that at least some knowledge of Victorian society is needed to fully appreciate the satire, though. – Ketil Tveiten Dec 09 '10 at 08:51
Much more satisfying for a modern reader is The Planiverse, by Dewdney (see Wikipédia) – Feldmann Denis Jun 14 '12 at 15:58

score 61 · Answer 3 · answered Dec 12 '09 at 02:11

61

Title: Logicomix: An epic search for truth

Authors: Apostolos Doxiadis, Christos Papadimitriou

Artists: Alecos Papadatos, Annie Di Donna

Short description: A comic book biography of Bertrand Russell, focusing on his work on the foundation of mathematics. (About 345 pages. I just started reading it, so I haven't formed a firm opinion on it yet, but I like what I see so far.)

answered Dec 12 '09 at 02:11

Harald Hanche-Olsen

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This is a great book. They take some liberties with historical accuracy (as they explain in an appendix) but turn it into a compelling story. The characterization of the main players is excellent. – Konrad Swanepoel Dec 12 '09 at 10:32

score 52 · Answer 4 · answered Dec 12 '09 at 02:04

52

Title: Mathematics: A very short introduction

Author: Timothy Gowers

Short description: As the title says, very short. Gives the non-mathematical reader a good idea what mathematics is all about in just about 100 small pages.

answered Dec 12 '09 at 02:04

Harald Hanche-Olsen

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I've read it, and it is near perfect (there are just one or two paragraphs that I would have said otherwise). – Jose Brox Dec 12 '09 at 19:13

score 40 · Answer 5 · edited Dec 18 '13 at 19:03

40

Title: The Man Who Loved Only Numbers

Author: Paul Hoffman

Short Description: A biography of Paul Erdős. No previous knowledge of math.

edited Dec 18 '13 at 19:03

Rasmus

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answered Dec 11 '09 at 22:52

Guillermo Mantilla

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Although, those that knew him claimed he loved many things... – Micah Milinovich Dec 11 '10 at 17:23
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This is the most delightful biography I have read, of anyone in any field. – shreevatsa Aug 06 '12 at 14:08

score 38 · Answer 6 · answered Dec 16 '09 at 21:05

"classic"

Title: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (US)
Fermat's Last Theorem: The story of a riddle that confounded the world's greatest minds for 358 years (UK)

Author: Simon Singh

Short Description: The history of Fermat's Theorem, from the famous note "It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain." to the solution of the Taniyama-Shimura-Conjecture by Andrew Wiles.

By the way, the video Fermat's Last Theorem (1996) is based on the book.

I'd also recommend whatever else Simon Singh has written, it's all good. The most mathematical of his other works is The Code Book (aka. The Cracking Code Book, apparently the same book), which I suppose is mathematical enough. — Ketil Tveiten, Dec 09 '10 at 09:00

score 36 · Answer 7 · answered Dec 11 '09 at 22:16

36

Title: A Mathematician's Apology

Author: G. H. Hardy

Short Description: In the style of Plato and Xenophon, G. H. Hardy offers a justification for pure mathematics.

answered Dec 11 '09 at 22:16

Harry Gindi

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Really? I personally don't think this book has aged well. In particular his remarks about number theory being useless for warfare are completely off in light of WWII. – Qiaochu Yuan Dec 11 '09 at 22:23
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Let me instead counter-suggest Ian Stewart's "Letters to a Young Mathematician," which is in some sense a response to Mathematician's Apology (which is why I'm not putting it down as a separate answer). – Qiaochu Yuan Dec 11 '09 at 22:47
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I also didn't like the snobbery that Hardy displays prominently throughout the book. – Akhil Mathew Dec 11 '09 at 23:03
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There is no doubt about the snobbery, Akhil... Thing is Hardy was the most prominent English mathematician of the epoch. All in all, I kind of agree with t0rajir0u and would rather be given a copy of Littlewood's Miscellany or the Selected Expository Writing of P. R. Halmos. – José Hdz. Stgo. Dec 11 '09 at 23:12
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You know what a curious trait of the Apology is? Despite of its huge number of detractors, it is (easy) one of the most quoted texts throughout... – José Hdz. Stgo. Dec 11 '09 at 23:21
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Akhil Mathew, it's actually a really complicated book, and saying, "oh, snobbery!" is just nonsense. – Harry Gindi Dec 12 '09 at 00:08
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Qiaochu, Ian Stewart is a terrible author. His textbooks are really just trash of the worst kind, but I guess you've got to make a living. – Harry Gindi Dec 12 '09 at 00:09
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Hardy would be surprised by the central role number theory has in modern cryptography and electronic commerce. – lhf Dec 12 '09 at 01:20
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I don't know anything about Stewart's textbooks, but his popular writing is apparently widely recognized. I guess I should clarify my remark above - what I really mean is that I think it would be easy for a non-mathematician to get a slightly skewed impression of mathematics from the Apology. – Qiaochu Yuan Dec 12 '09 at 01:31
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Sure, but apology has a place in history as a great piece of writing, math-related or not. – Harry Gindi Dec 12 '09 at 02:28
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@fpqc: Yes, of course there's some good stuff in it. But I doubt it'd make a good present for the snobbery reason. – Akhil Mathew Dec 12 '09 at 04:35
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I think you're being somewhat unfair about the snobbery. Hardy is without doubt a fool in a number of respects, (as well as being a phenomenal mathematician) but this book was written quite obviously in despair, and that I think gives it a unique, touching quality most popular books about math fail to attain. – Kevin McGerty Dec 12 '09 at 05:15
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@KM: Agreed. The combination of lucid mathematical insight and unguarded description of personal darkness make it an absolutely unique and unforgettable book. I try to return to it once every few years as with Catcher In the Rye, Hamlet and other great literary works. (It is remarkable to me that some people simply repeat Hardy's gloomy pronouncements about old mathematicians as though they came out of a sober how-to guide.) – Pete L. Clark Dec 12 '09 at 16:41
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As Kevin McGerty and Pete Clark say, A Mathematician's Apology is an extremely personal and vivid essay by a phenomenal mathematician who was believed himself a has-been. I love it, but I wouldn't want to give it to a nonmathematician with the message "This is what math is about!" – David E Speyer Jan 11 '10 at 15:01
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Yes, a perfect Christmas gift -- a depressing book written by a person who appeared to have had no life outside mathematics and cricket, had a rather bizarre view of what mathematics was about, and was essentially suicidal at the time of writing. A far, far better book is Littlewood's "Mathematical Miscellany. – Igor Rivin Dec 09 '10 at 06:41
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@Igor: I don't think that the book itself is depressing, although the introduction (not written by Hardy) surely is. – Harry Gindi Dec 09 '10 at 08:09
Should we expect this question to get answers and comments every year in December? That's how it's working so far.
G. H. Hardy's opinion of the book titled Mathematics for the Million by the polymath Lancelot Hogben seems to be the exact opposite of David Mumford's opinion of that book. Where would those opining in this thread rank that book?
– Michael Hardy Dec 09 '10 at 21:40
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I upvoted this because of the discussion that follows. – Micah Milinovich Dec 11 '10 at 17:25
I'm not so sure Akhil is being unfair about the snobbery. I recall various somewhat sneering references to Hogben's book. It's also hard to tell how despairing the book is without having in one's head the back-story provided by Snow, which verges on Too Much Information. (Poor L. Hogben -- another guy who really dished it out to him was George Orwell in Politics and the English Language.) – Todd Trimble Oct 09 '12 at 18:19

Alison Miller · Answer 8 · 2009-12-12T03:16:44.933

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Title: The Book of Numbers.

Author: John Conway and Richard Guy.

Short Description: A beautifully illustrated book with all sorts of facts about all sorts of numbers. The difficulty is variable throughout the book: parts are written at a + level, while other parts are closer to +++.

edited Dec 12 '09 at 03:16

answered Dec 12 '09 at 01:13

Alison Miller

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score 30 · Answer 9 · edited Dec 18 '13 at 19:09

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Title: Journey Through Genius

Author: William Dunham

Short Description: A fencepost history of mathematics. For each highpoint it describes some fun history and then the actual math. Examples of topics covered are Heron's formula for triangular area, Euler's evaluation of $\zeta(2)$ and Cantor's set theory.

edited Dec 18 '13 at 19:09

Rasmus

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answered Dec 11 '09 at 23:09

Noah Snyder

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Dunham is a great writer. I also liked his book "Euler: The Master of us All" a lot. – Kevin H. Lin Dec 12 '09 at 15:46
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This book made me want to study mathematics! – Max Muller Jun 09 '10 at 17:31
I do not know of any better choice than this one. It is spellbinding. – Steven Landsburg Dec 09 '10 at 04:34
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I don't like the title - that genius cult in mathematics is a horrible thing in my opinion. – Peter Arndt Dec 09 '10 at 07:38
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Good point about the title, I still love the book though. – Noah Snyder Dec 09 '10 at 15:54

Nick Salter · Answer 10 · 2009-12-15T22:20:36.810

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Title: Fearless Symmetry

Authors: Avner Ash and Robert Gross

Short Description: Very much a +++ text, these guys actually got a pop-math account of Galois representation theory published! By far the most technically demanding pop-math book I've ever read, (and one that took me about three years to actually finish) it nonetheless makes for a compelling "non-technical" introduction to a beautiful subject.

edited Dec 15 '09 at 22:20

answered Dec 12 '09 at 02:17

Nick Salter

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The table of contents of this book is enough to make me want to read it! – Qiaochu Yuan Dec 13 '09 at 20:28
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This is a pop book? I just looked at the table of contents, and it looks like I could learn a lot from this...and now I'm off to add it to my wishlist on amazon... – Charles Siegel Dec 15 '09 at 13:56
I'm with Qiaochu on this. That is a captivating table of contents. – Simon Rose Dec 10 '10 at 18:28

score 29 · Answer 11 · answered Dec 12 '09 at 00:05

Title: Innumeracy: Mathematical Illiteracy and its Consequences

Author: John Allen Paulos, mathematician and well-known skeptic (in the good, modern sense of the word).

Short description: Paulos explains for the general public (and he does it fairly well) why it should understand a little more mathematics and know how to do Fermi calculations and educated probabilistic guesses. The dangers coming from pseudosciences are also highlighted, something very needed nowadays in my opinion.

Math level: +. Some chapters are not that easy to read without a mathematical background, more because of the great number of calculations and logic steps involved in the explanations than because of the math level of those per se.

Price: 9.89$ at Amazon.

+1 I enjoyed skimming this book, which I found lying around a nonmathematician's house, so it's also appropriate for this question. — Akhil Mathew, Dec 13 '09 at 00:19

score 26 · Answer 12 · answered Dec 12 '09 at 14:27

Title: The Lady or the Tiger?

Author: Raymond Smullyan

Short Description: If your aunt is young enough not to scorn the fairy-tales, this book is a charming collection of logic puzzles, presented under a guise of an entertaining story. The book presuppose no knowledge of mathematics (so difficulty is +), but it ends with a version of Godel's incompleteness theorem. Your aunt will be delighted!

Remark: Other books by Smullyan are also great, and will relieve you from wondering of what to give to your aunt for the next few Christmases.

Agreed, Smullyan is great. I also liked Chess Mysteries of Sherlock Holmes, although this isn't really a book about chess, but retrograde analysis. — Tony Huynh, Feb 24 '10 at 21:34

Christian Bjartli · Answer 13 · 2009-12-13T20:07:13.437

Title: Proofs and Refutations - The Logic of Mathematical Discovery

Author: Imre Lakatos

Short Description: A Plato-esque dialogue between a teacher and his students, aiming to discuss how mathematical discovery happens, how mathematical arguments take form and how mathematical knowledge arises. The discussion is based around the Euler-characteristic, starting off with a concrete conjecture about polyhedra, expanding into the result in full-blown generality through investigation, trial-and-error, the occasional side-track and creative injections as it happens in real life. The book is also sprinkled with mathematical in-jokes, and interesting historical facts about the result. This is a real gem that I keep on my bedside table. Probably at the higher end of the ++ spectrum.

I'm not sure if I'd get the book for my aunt. It takes mathematical reasoning skills to get though the argument and an understanding of why the questions above are worth answering in the first place. I might get it for a philosophically inclined friend instead.

That is indeed a very good book, but it is (a version of) a doctoral dissertation in philosophy. I don't think anybody can read it who do not have some experience with mathematical proof! — kjetil b halvorsen, Oct 09 '12 at 17:31

score 22 · Answer 14 · answered Jun 07 '10 at 01:01

Title: Letters to a Young Mathematician

Author: Ian Stewart

Description: A beautiful book in which Stewart tries to convey in the form of letters from a mathematician to his grand daughter what sort of things does the profession of mathematics involves. It is very interesting since the letters advance from the time in which the grand daughter is in high school up until she is a professional mathematician doing research. I would recommend it without a doubt.

From my own experience it has been really nice to come to this book at different times during the past years. I started college as an engineering student but on my third year I started taking courses from the mathematics program and I bought and read this book when I was just beginning. I had no real idea of what pure mathematics was all about (since I was used to the kind of calculus courses in which the emphasis is on computation rather than proving things) and this book gave me at least some perspective and a few hints of what may be ahead of me.

Just for the record, I ended up switching my major to mathematics.

score 20 · Answer 15 · answered Dec 29 '09 at 23:17

20

Title: Gamma : Exploring Euler's constant

Author : Julian Havil

Short description: Provides a fascinating history of a constant that doesn't get nearly as much attention as $e$ or $\pi$. Definitely has more math than most books intended for a general audience but I feel the book is accessible to those who persevere with it. And the reward is lots and lots of beautiful mathematics.

answered Dec 29 '09 at 23:17

Dinesh

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What a fantastic book! It's easily one of the main driving forces that got me into analytic number theory. – Alex R. Feb 25 '10 at 03:53

score 20 · Answer 16 · edited Jan 07 '10 at 14:19

20

Title: Prime Obsession

Author: John Derbyshire

Short Description: A book about the Riemann Hypothesis. Its been a while since I read this book, but I remember it being well-written and fun to read. It is very accessible, explaining everything. I think half of the chapters have no math (just facts about Riemann's personal life and such), while the rest is avery gentle introduction to math ideas (like infinite series).

http://www.amazon.com/Prime-Obsession-Bernhard-Greatest-Mathematics/dp/0452285259/ref=sr_1_2?ie=UTF8&s=books&qid=1260570418&sr=8-2

edited Jan 07 '10 at 14:19

Pete L. Clark

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answered Dec 11 '09 at 22:34

Rado

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I would rather read the account of a pro:
Marcus du Sautoy, The Music of the Primes.
– José Hdz. Stgo. Dec 11 '09 at 23:30
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The Music of the Primes and Prime Obsession are about essentially the same topic, but they're very different books. The Music of the Primes is a "+", but Prime Obsession is probably "++" (for difficulty level). I thought both were reasonably entertaining. – Darsh Ranjan Dec 15 '09 at 23:31

score 19 · Answer 17 · edited Dec 11 '09 at 22:58

19

Title: Uncle Petros and Goldbach's Conjecture

Author: Apostolos Doxiadis

Short Description: It is a very fun novel based on the life of a fictional character who spends most of his live trying to prove Goldbach's conjecture. It talks about some other famous problems in math. This novel is fun for mathematicians and non-mathematicians. No knowledge of math is required.

edited Dec 11 '09 at 22:58

Qiaochu Yuan

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answered Dec 11 '09 at 22:41

Guillermo Mantilla

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Indeed it is one of the best math-fiction story ever! – Yannic Jun 14 '12 at 18:19

score 18 · Answer 18 · answered Feb 24 '10 at 21:46

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Title: The Curious Incident of the Dog in the Night-Time.

Author: Mark Haddon.

Description: A mathematically gifted kid tries to solve the mystery of a dog murdered in the night-time.

Remark: Although this isn't a math book per se, it actually does contain a lot of interesting and non-trivial mathematics. Also, it's very well illustrated. As a final selling point, you have to respect any book whose chapters are indexed by the primes.

answered Feb 24 '10 at 21:46

Tony Huynh

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In my opinion, this looks more like a murder novel than an introductory or public mathematical book for an aunt to learn some math, any way, it is quite an enjoyment to read the book. – awllower Feb 17 '11 at 08:55

score 18 · Answer 19 · edited Jun 30 '15 at 13:15

Title: The Symmetries of Things

Authors: John Horton Conway, Heidi Burgiel, and Chaim Goodman-Strauss

Description: The authors begin by introducing the general concept of geometric symmetry / regular tiling, and then pose the problem of classifying all possible symmetries of the plane. They provide an elegant topological classification, and along the way introduce the notions of orbifold and classify the compact surfaces with boundary. It's then easy enough to also classify the discrete symmetries of the sphere. In part II, the authors introduce the notion abstract group, and classify the prime-order "color symmetries" of the plane, which are tiling patterns with different-colored tiles. Part III consists of a discussion of higher-dimensional tilings, including the four-dimensional Archimedean solids.

Part I is suitable for an interested amateur with no specific prior knowledge. Part II is at an advanced undergraduate level, although it does contain new results. Part III, which is about half the book, is research level. The book is printed in full-color.

score 16 · Answer 20 · answered Feb 24 '10 at 21:59

16

Title: The Code Book

Author: Simon Singh

Description: This is a popularized history of cryptography and cryptanalysis. It runs the range from shift-ciphers to modern public key cryptosystems and quantum key distribution. No prior knowledge of maths is necessary, but can be helpful.

It has been quite some time since I read this book, but I found it incredibly engaging at the time. I know it isn't strictly focused on mathematics, but I am surprised that no one else has mentioned it.

answered Feb 24 '10 at 21:59

Joe Fitzsimons

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In my opinion the greatest fragment of the book is explanation of reconstruction of linear letters of B ( or A, I do not remember) of Cretan people. – kakaz Mar 11 '10 at 15:25
This book also exists under the name The Cracking Code Book, apparently. – Ketil Tveiten Dec 09 '10 at 09:03

score 16 · Answer 21 · answered Dec 11 '09 at 23:17

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Title: Symmetry and the Monster

Author: Mark Ronan

Short Description: The history of the classification of finite simple groups. Reads like a good novel.

answered Dec 11 '09 at 23:17

Jorge Vitório Pereira

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A beautiful book. Though I'm biased, as an undergrad at Rutgers, I met a few of the major players in this story. One of my first recommendations to people when they ask me "You're an algebraist? What's that?" – Charles Siegel Dec 15 '09 at 13:58

score 16 · Answer 22 · answered Dec 12 '09 at 01:17

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Title: The Mathematical Experience

Authors: Davis and Hirsh

Short Description: A really accessible and funny introduction to the philosophy of mathematics. I think the description of the "ideal mathematician" is particularly hilarious.

answered Dec 12 '09 at 01:17

Anna Varvak

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score 16 · Answer 23 · edited Aug 25 '19 at 05:06

16

Title: Indiscrete Thoughts

Author: Gian-Carlo Rota

Description: General discussion on Mathematics, Princeton of the fiftees, lives of Artin, Feller and of Rota's intimate friend Stanislaw Ulam; fantastic bedtime reading. Also includes philosophical flavour like '10 things I had been taught' type.

edited Aug 25 '19 at 05:06

answered Dec 27 '09 at 07:57

Abhishek Parab

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This is one of my favorite books, but the philosophy section is a little too heavy to be called "popular" writing. – Qiaochu Yuan Dec 27 '09 at 08:04
Actually, I think some of the philosophy section would be of more interest to a general cultivated audience than most of the rest of the book, which might be interesting to mathematicians and academics but perhaps not to many others. – Todd Trimble Oct 09 '12 at 19:36

score 15 · Answer 24 · edited Oct 10 '12 at 03:07

Title: What is mathematics?

Author: Herbert Robbins and Richard Courant

This book is a very nice introduction to mathematics, it covers basic number theory, analysis, algebra, geometry and topology.

I'am very surprised that i couldn't find it on this list already.

(from a duplicate answer - feel free to edit) This would be for someone who has some mathematical ability, and really wants to understand what math is. Courant goes through essentially all of mathematics, starting at a very elementary level, but getting to some very deep and important stuff. He often does real proofs, and doesn't dumb it down, but does explain things conceptually very well, including sometimes giving just ideas or justifications for really difficult things, like the prime number theorem. I use this when I teach our senior proof seminar, just to force the math majors to own a copy.

I copy-pasted a description from a duplicate answer, since the previous description was a bit brief. Anyone who wants to clean it up should do so. — S. Carnahan, Oct 10 '12 at 03:08

score 14 · Answer 25 · answered Dec 12 '09 at 02:19

14

Title: The honors class: Hilbert's problems and their Solvers

Author: Ben Yandell

Short description: The title says it all. It gets dense at times, but it has an enormous range of topics and the biographies are very interesting. Probably a ++.

answered Dec 12 '09 at 02:19

Sam Lichtenstein

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This is really a great book! – Spinorbundle Dec 12 '09 at 10:32

score 14 · Answer 26 · answered Dec 14 '09 at 16:14

14

Title: Euler's Gem: The Polyhedron Formula and the Birth of Topology

Author: David S. Richeson

Short Description: V-E+F=2. Requires little (no?) preparation, but some willingness to think. I gave it to a few people who wanted to know more about what math really was (as opposed to adding longer and longer columns of numbers, as my mother believes), and those who made the investment of their time came away with a much better understanding.

answered Dec 14 '09 at 16:14

PeterR

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I finally got around to reading this! It is really, really fantastic. – Qiaochu Yuan Aug 26 '10 at 05:52
I agree fully with Qiaochu Yuan's comment above. It's a wonderful book, starting with polyhedra and ending with a touch of algebraic topology (and the Poincaré Conjecture in the epilogue). – J W Mar 28 '12 at 13:57

score 14 · Answer 27 · answered Dec 15 '09 at 13:16

Title: What is the name of this book?

Author: Raymond Smullyan

Short description: Lots and lots of logical puzzles (the kind with people always telling the truth, people always lying, people who sometimes tell the truth and sometimes lie, etc.) It is really entertaining, and it serves well as an introduction to the logic of propositions.

score 12 · Answer 28 · edited Dec 09 '10 at 07:42

12

Title: Men of Mathematics

Author: E. T. Bell

Short Description: Short biographies (~30?) of important mathematicians. Excellent relations of the death of Archimedes, Galois' temper, Newton's eccentricities, &c. Also try his (Edit: actually L. Hogben's) book Mathematics for the Millions.

edited Dec 09 '10 at 07:42

Gerhard Paseman

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answered Jan 07 '10 at 23:32

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A fun read, but not to be taken seriously as history. – Gerry Myerson Dec 09 '10 at 08:04
You are absolutely right, Gerry. Not that good history must always be literally true . . . – Dec 10 '10 at 07:44
Early editions of this book are not exactly politically correct by today's standards. – Micah Milinovich Dec 11 '10 at 17:30
Belated comment: good history should have regard for truth/accuracy – Yemon Choi Jun 15 '12 at 18:36
A couple of my friends chose mathematics as there career becuause of this book :) – Amir Asghari Dec 18 '13 at 13:58

score 12 · Answer 29 · answered Dec 11 '09 at 23:26

12

Title: King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry

Author: Siobhan Roberts

Short Description: Biography of Coxeter.

answered Dec 11 '09 at 23:26

Jorge Vitório Pereira

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score 12 · Answer 30 · answered Dec 12 '09 at 02:19

Title: Everything and More: A Compact History of Infinity

Author: David Foster Wallace

Short description: History of the idea of infinity, mostly leading up to Cantor's set theory ideas. It's been awhile since I've read this but I would say the mathematics is pretty decent for popular writing and the writing is really enjoyable if you like Wallace's style (and maddening if you can't stand him, I'm sure). This is the kind of math book you could get for someone who enjoys serious literature.

No prior knowledge is necessary, but the math-phobic could struggle.

Unfortunately Wallace didn't fully understand much of what he wrote about, and made some serious errors. — Michael Weiss, May 27 '17 at 18:32

Arturo Magidin · Answer 31 · 2010-12-09T22:12:55.593

Title: Mathematics and the Imagination

Authors: Edward Kasner and James Newman

Short Description: A number of chapters covering lots of subjects: counting numbers (including the coining of the word "googol"); $\pi$, $i$, and $e$; geometries, plane and "fancy" ("Lobachevsky's Eiffel Towers and Riemann's Holland Tunnels"); puzzles; paradoxes; chance and probability; topology ("rubber sheet geometry"); calculus. Very much in the spirit of Martin Gardner columns, but from before they existed (the book was originally published in 1940; Gardner began writing his columns in 1956). You can see a preview at Google books.

Which also leads me to

Author: Martin Gardner

Title: Various

Short Description: A joy to read.

score 11 · Answer 32 · edited Feb 17 '15 at 19:42

Ian Stewart is a very good mathematics popularizer and I understand why many of his books are in this list. But I really don't understand why none of Martin Gardner's books are listed here (at the time I'm writing this).

My favorite Martin Gardner book (actually, an updated collection of Scientific American Mathematical Games columns) is The Colossal Book of Mathematics. From the book's cover: "Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and other topics of recreational mathematics." I would say its difficulty level is "+".

score 10 · Answer 33 · answered Dec 11 '09 at 22:41

Title: Why Beauty is Truth: A History of Symmetry

Author: Ian Stewart

Brief Description: Stewart surveys the history of symmetry in mathematics (from ancient times to present day). There is particular emphasis on the insolvability of the quintic, the invention of Galois theory, and its impact on modern mathematics.

score 10 · Answer 34 · answered Jun 15 '12 at 16:46

10

Title: The I Hate Mathematics! Book

Author: Marilyn Burns

Short Description: The google.books description is well written. A book for nonbelievers. I had this as a kid, and i remember its questions and pictures having an effect on me. How many sides does a banana have and how can 4 colours colour this map.

answered Jun 15 '12 at 16:46

JHM

2,254

1

Upvoted because I loved this book as a kid (despite not hating math!) and haven't thought about it in thirty years. – JSE Jun 16 '12 at 01:30

score 9 · Answer 35 · answered Jun 07 '10 at 00:11

Title: The Man Who Counted (translated from Portuguese)

Author: Malba Tahan

Short description: A mixture of Arabian Nights and a classical puzzlebook. The stories follow a brilliant youth who solves mathematical problems. A highly enjoyable read for anyone who likes oriental tales, and just the right combination of adventures and mathematics for all aunts and nephews out there without a mathematics degree.

Malba Tahan is a pen name of the Brazilian mathematician and writer Júlio César de Mello e Souza. The book was first published as O homem que calculava in 1949.

score 9 · Answer 36 · answered Dec 11 '09 at 22:47

9

Title: An Imaginary Tale

Author: Paul Nahin

Short Description: This book is primarily about complex numbers. I can't remember it that well, but most of the book doesn't require calculus (though a fair part definitely does). Most of it is about the algebra and geometry of complex numbers and is thus accessible to the nonmathematician. The last chapter has a very fun introduction to complex analysis.

answered Dec 11 '09 at 22:47

Akhil Mathew

25,291

This book is/was riddled with errors. He released a second edition at the behest of R.B. Burckel, and from what he has told me, none of the corrections were made. I understand that this book is pop-math, and thus the reader may not be desiring of great precision. However, most of the errors contained therein could have been omitted without disruption of the colloquial style or prose. – B. Bischof Dec 14 '09 at 01:04
I read this one in high school and didn't like it. The errors were a serious problem, and the exposition felt dry to me. – Charles Siegel Dec 15 '09 at 13:57

José Hdz. Stgo. · Answer 37 · 2015-02-17T18:45:51.527

Wonder why it is that nobody has mentioned Lion-Hunting & Other Mathematical Pursuits? That book is one of my all-time favorites.

The book was edited by Gerald L. Alexanderson, the same individual behind the random walks of G. Pólya. Not only does the book contain the original article that launched the theory of big game hunting as a branch of mathematical research of its own, but also several of the subsequent contributions motivated by that 1938 groundbreaking paper of H. Pétard, e.g.:

If there is an even number of lions in the Sahara Desert we add a tame lion. Thus we may assume that the group of the Sahara lions is of odd order. This renders the situation capable of solution according to the work of Feit and Thompson.

Is this book one such that it contains a way to capture lions using inverse mappings?It seems to be pretty fun and may I ask what level does it require? — awllower, Feb 17 '11 at 09:05

score 8 · Answer 38 · edited Oct 10 '12 at 03:11

Title: Hilbert

Author: Constance Reid

Description: Biography of David Hilbert. Fascinating. Don't have to be D.H. to enjoy it. [the following is added from a duplicate answer - feel free to clean up -- ed.] A beautiful biography of a famous mathematician, showing the passion for knowledge represented by Hilbert and others at Goettingen around 1900. The book has a good description of Hilbert as a person, describes his family and coworkers and (sadly) the decay at the end of Hibert's life as the Nazis took over. I ask some of my undergraduate students to read this so that they can see the excitement of being in our profession. (The book is out of print, I think, but available via half.com or ebay.)

Second recommendation Also, Time-Life, ca. 1965, published one of it's picture books on math, titled of all things Mathematics (as I recall). Check it out if you can find it. Lots of cool pictures. Great for mathematically inclined high school kids.

Note added in edit: The aforementioned book from the Time-Life series also had great pictures of mathematicians. As I recall, there was one of Eilenberg lying on the couch of his Grenwich Village apartment, coat and tie still on. It was captioned with a quote which went, if I recall correctly, "Sometimes I like to think riding on the subway, but mostly I like to think lying down." Absolutely formative in my personal approach to math!

score 8 · Answer 39 · answered Dec 11 '10 at 22:21

What about the Princeton Companion to Mathematics?

It contains alot of introductory information on the spectrum of mathematics with historical note. When you need a quick perspective on branches of mathematics that are less familiar to you, it is a place to go. The book is divided into sections on famous mathematicians, theorems, and branches of mathematics all of which cannot be held by even the most well versed mathematician.

score 7 · Answer 40 · answered Dec 09 '10 at 05:00

Title: A tangled tale

Author: Lewis Carroll

Description: (by Carroll himself in the preface) The writer’s intention was to embody in each Knot (like medicine so dexterously, but ineffectually, concealed in the jam of our early childhood) one or more mathematical questions — in Arithmetic, Algebra, or Geometry, as the case might be — for the amusement, and possible edification, of the fair readers of that magazine.

Of course, this will work as a gift for a niece better than a gift for an aunt, but it is one of those few books (the only other ones I know are by Smullyan and they've been mentioned already) that have both an entertaining story line and some actual mathematical challenges for the reader in them and that require no special mathematical training to read and enjoy.

score 7 · Answer 41 · answered Dec 12 '09 at 01:51

7

Title: The Art of Mathematics

Author: B. Bollobas

Short Review: "The Author considers these problems to be the type that two mathematical friends would pose to each other and discuss over a cup of coffee in a lounge. I agree with that premise, they are not too hard and there is a proof that is relatively easy to discover and even easier to understand. These problems satisfy all of the requirements for a good problem..."

This is one of the most entertaining recreation-mathematical books I've ever read. It does require some mathematical knowledge to be fully appreciated though :)

answered Dec 12 '09 at 01:51

Gjergji Zaimi

85,056

2

I don't know about you, but this is a little too dense for my aunt! – Qiaochu Yuan Dec 12 '09 at 03:56
Haha, well I've gotten it as a present that's why it came to mind. I totally forgot about the aunt part. – Gjergji Zaimi Dec 12 '09 at 04:11
I'm reading this one now and rather like it. It should be noted that the problems in this book are some that mathematicians think about casually -- basically, Bollobas says he was looking for problems that Erdos or Littlewood, the two "great" mathematicians he says he's known, would have liked. So the level of difficulty is quite high for a "recreational" book. – Michael Lugo Dec 30 '09 at 02:13
Are this book and that by King, Jerry P. the same, thanks for any explanation. – awllower Feb 17 '11 at 09:11

score 6 · Answer 42 · answered Dec 09 '10 at 06:33

Title: Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century

Author: Masha Gessen

Short Description: Story of Grigory Perelman based on information from people who interacted with him. A lot of interesting stuff about life in general and mathematics education in particular in Soviet Union around 1980's. There is only one or two short chapters where the author tries to explain the mathematics but if you skip those you don't need any serious mathematical skills.

score 6 · Answer 43 · answered Dec 11 '10 at 14:42

Title: The Mathematician's Brain

Author: David Ruelle

Short description: (++) A book describing how Mathematics are founded, and tries to give a reasoning for the brain-work needed to do math.

From Amazon: The Mathematician's Brain poses a provocative question about the world's most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider's account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries.

score 5 · Answer 44 · answered Mar 11 '10 at 22:32

Title : The Parrot's Theorem (Le théorème du perroquet)

Author : Denis Guedj

Description : I read this while in high school, it's kind of a murder mystery, and it revolves around a family who has a mathematician friend who was trying to solve the Goldbach conjecture and Fermat's last theorem before he died. It includes many fun mathematics and is presented in a very light to read manner.

score 4 · Answer 45 · answered Jan 07 '10 at 13:54

4

Title: Recoltes et Semailles (Reapings and Sowings) Author: Alexander Grothendieck

Description: Grothendieck's autobiography and self-assessment as a mathematician and a person.

answered Jan 07 '10 at 13:54

Harry Gindi

19,374

11

I don't know if I'd call this "popular". – Michael Lugo Jan 07 '10 at 15:47
1

For sure this is an interesting book, first time I read first section then I was 18 I loved it. Second time I read it when I was 25-27 I hated it. Maybe it is time to read it again :) – Dmitri Panov Jan 19 '10 at 00:21

score 4 · Answer 46 · answered Jun 06 '10 at 22:30

4

I like Mario Livio's books:

The Golden Ratio: The Story of PHI, the World's Most Astonishing Number

and

The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

answered Jun 06 '10 at 22:30

Bart Snapp

519
3
14

score 4 · Answer 47 · answered Dec 09 '10 at 04:17

Title: The Magical Maze

Author: Ian Stewart

Short description: Various bits of counterintuitive, fundamental, and/or easily understood mathematics, to wit: modular arithmetic, Fibonacci numbers, depth-first search, the axiomatic method, the Monty Hall problem, the birthday paradoxes, wallpaper groups, cellular automata, dynamical systems, formalism, Godel incompleteness, Turing's halting problem, optimization problems (both continuous and discrete), algorithmic complexity, fractals, chaos, and Hausdorff dimension.

This book is, to a large extent, the reason I am in graduate school right now. I read it in the eighth grade, and now here I am.

Yannic · Answer 48 · 2012-06-14T19:12:31.957

4

Title: Satan, Cantor & Infinity

Author: Raymond M. Smullyan

Short Description: Another gem in the list of Smullyan's books. If you love "logical sorcery", this is a perfect gift for you.

edited Jun 14 '12 at 19:12

answered Jun 14 '12 at 18:25

Yannic

527

score 4 · Answer 49 · answered Jun 14 '12 at 19:45

Title One Two Three . . . Infinity: Facts and Speculations of Science

Author George Gamow

Short description While not limited to mathematics, this is a great book which presents some subtle mathematical ideas in an intuitive non-technical way. I especially like the presentation of Cantor's infinite cardinality theory, which can be followed by anyone. Unfortunately, there are some mistakes. I seem to recall his presentation implicitly assumes the continuum hypothesis, but maybe he did that for clarity. It doesn't really detract from the book.

score 4 · Answer 50 · answered Jun 15 '12 at 14:42

I see many favorites here, but this one should be mentioned too:

MR1710978 (2000h:00002) Hugo Steinhaus. Mathematical snapshots. Translated from the Polish. With a preface by Morris Kline. Reprint of the third (1983) English edition. Dover Publications, Inc., Mineola, NY, 1999. vi+311 pp. ISBN: 0-486-40914-7

It was first published in 1939 ("Kalejdoskop matematyczny" in Polish).

Here is the summary:

http://books.google.com/books?id=N63XpD1oJ6IC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

Things like fair division or platonic bodies made accessible for an aunt and a niece alike (I actually gave my copy to my niece a few years ago).

score 3 · Answer 51 · answered Oct 28 '10 at 05:27

I'd recomend "The Pea and the Sun, a mathematical paradox" which roughly explains the proof of Bannach-Tarski Theorem, which is a consequence of the axiom of choice and roughly says that you can break a pea in a finite number of pieces, tehn reassemble the pieces and get the sun

C.S. · Answer 52 · 2012-10-09T12:12:02.507

3

My favourite books are:

$\text{I want to be a Mathematician}$ by Paul Halmos.
Problems for Mathematicians, young and old, by the same author.
The Man who knew Infinity: : A Life of the Genius Ramanujan by Robert Kanigel. Fanastatic book. Covers almost all of Ramanujan's life and work. Certainly a must read.

edited Oct 09 '12 at 12:12

answered Jul 29 '11 at 15:54

C.S.

4,735

score 3 · Answer 53 · answered Dec 11 '09 at 22:46

3

Title: Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning

Author: Clifford A. Pickover

Short Description: A wonderful collection of historical anecdotes, mathematical trivia, and puzzles. I would especially recommend this if you were shopping for a younger relative.

answered Dec 11 '09 at 22:46

Qiaochu Yuan

114,941

I do like the books by Pickover very much. I think he is very over-looked. – Bart Snapp Jun 06 '10 at 22:30

Alison Miller · Answer 54 · 2009-12-12T03:13:53.147

Title: Another Fine Math You've Got Me Into

Author: Ian Stewart.

Short Description: Mathematical puzzle columns, (originally for the French version of Scientific American) some of which introduce interesting concepts from higher mathematics. Ian Stewart has written a lot in this vein (as have others, e.g. Martin Gardner), but this book is my favorite and is one of the mathematically meatiest of them (in my opinion).

I'd say this is a ++.

score 2 · Answer 55 · answered Jan 07 '10 at 12:05

Title: Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics

Author: Friedrich Waismann

Short Description: This book, first published in 1936, gives an introduction to the philosophy of mathematics and the foundations of analysis. It shows how to construct number systems, some very elementary set theory and how to make differential calculus precise. The focus is on concepts. It includes a discussion of things like continuuous, nowhere differentiable functions and discusses why R and R² are isomorphic as sets but not topologically. It even gives an very short and intuitive proof that R and R² are not homeomorphic.

The philosophical discussion is, naturally, a litlle bit dated. It discusses formalism, logicism and intuitivism. The philosophy still makes for exciting historical reading. It is clear that this discussion was very lively when this book was written.

The level should youalify as ++, the book is demanding but can certainly be read before going to college.

score 2 · Answer 56 · answered Jan 16 '10 at 17:20

I know this is a little late for Christmas, but nevertheless, I have a few (some of which have already been mentioned) books I've read that I've quite enjoyed. For the sake of brevity, I'll let you search the titles on Amazon for reviews and better descriptions.

Title: Everything & More: A Compact History of Infinity Author: David Foster Wallace

Title: The Mathematical Experience Author(s): Philip J Davis & Reuben Hersh

Title: One, Two, Three...Infinity Author: George Gamow

Title: Pi in the Sky Author: John D. Barrow

Title: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Author: John Derbyshire

Title: Strength in Numbers Author: Sherman Stein

Title: e: The Story of a Number Author: Eli Maor

Title: A History of Pi Author: Petr Beckmann

Title: Nature's Numbers Author: Ian Stewart

Title: Mathematics: The Science of Patterns Author: Keith Devlin

Title: Zero: The Biography of a Dangerous Idea Author: Charles Seife

Title: How to Enjoy Calculus Author: Eli S. Pine (Not really a "popular" book, per se', but still pretty good)

Title: How to Think About Weird Things Author(s): Theodore Schick & Lewis Vaughn (Not really about mathematics, but not so far out of the way that you wouldn't enjoy it if you also enjoy mathematics)

score 2 · Answer 57 · answered Dec 18 '13 at 15:05

Title: Prisoner's Dilemma

Author: William Poundstone

Short description (from New York Times Book Review): The real originality of PRISONER'S DILEMMA lies in its colorful synthesis of logical material and historical and biographical narration [which] takes us in parallel lines through cold war history, strategic games of the nuclear age and the life of von Neumann . . . Lively, open and multifaceted.

Indeed, the book can be read as a whole or just by following one of those "parallel lines". Depending of the line you choose, the level of difficulty would be + or ++!

score 2 · Answer 58 · answered Dec 11 '09 at 22:25

2

Title: Euclid's Window

Author: Leonard Mlodinow

Short Description: A history of geometry of sorts. It's very well-written and was one of my favorite math books growing up. But you should read the Table of Contents to actually get an idea of what the book is about.

answered Dec 11 '09 at 22:25

Qiaochu Yuan

114,941

1

It's perhaps worth noting that there are dissenting opinions on this book, e.g. the following review by Langlands: http://publications.ias.edu/rpl_works/L12/euclid/euclid-ps.pdf – TSG Dec 12 '09 at 12:08
Interesting. I read this book when I was very young and haven't since, so perhaps my opinion would change if I gave it another look. – Qiaochu Yuan Dec 12 '09 at 16:34

score 2 · Answer 59 · answered Jun 14 '12 at 17:34

Title: The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity

Author: Amir D. Aczel

Short Description: Another book about the development of ideas about infinity. The central character is Cantor, of course, but it also looks at people before, like Bolzano and Galileo, and afterwards, including Godel and Cohen for their work on CH.

I read this in high school, having just a little calculus background, and got a lot out of it. It does try to work in the themes of "contemplation of infinity leads to insanity" and "infinity as religious insight" a bit, which might be drawbacks. But when I read it for the first time, I remember laughing out loud at how amazing the ideas involving infinte cardinalites and AC were, so at least those are presented well.

score 1 · Answer 60 · answered Dec 18 '13 at 12:27

You should not miss this book about algebra.

Title: Unknown Quantity

Author: John Derbyshire

Not only it explains the rise of algebra since antiquity, it also helps the reader to gain an intuitive approach to think and apply algebra in suitable problems. Great reading experience.

score 1 · Answer 61 · answered Mar 11 '10 at 21:38

Title: Mathematics: A Very Short Introduction

Author: Timothy Gowers

Short description: "A marvellously lucid guide to the beauty and mystery of numbers"

This book is excellent for someone who wants to delve in to some basic, but interesting mathematics. It avoids very "popular mathematics" such as chaos theory and focuses in detail on "mundane" topics, such as dimension and estimation.

difficulty level: +

£4.73 on Amazon UK

This was already posted. – Jonas Meyer Mar 11 '10 at 21:42 — Jonas Meyer, Mar 11 '10 at 21:42

Favorite popular math book

61 Answers61

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