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Of course, I am generalising here. It may have been a teacher, a theorem, self pursuit, discussions with family / friends / colleagues, etc. that opened your mind to the beauty of mathematics. But this question is specifically about which books inspired you.

For me, Euler, master of us all is right up there. I am interested in which books have inspired other people.

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For me, it was, long time ago, an old and (from my today's perspective) very boring book on calculus in slovak language (Kluvanec, Misik, Svec: Matematika 1,2 :-)) However, the proofs were done quite neatly and orderly. –  Peter Franek Jun 12 at 21:04
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Is there an English translation of this that you know of? –  martin Jun 12 at 21:05
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Mine is similar to Peter's; mine was Calculus by Stewart, which interested me because of the fact that it didn't contain all the proofs and forced me to do reading elsewhere. –  Hayden Jun 12 at 21:10
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@Peter Franek: FYI, on more than one occasion in sci.math Zdislav V. Kovarik mentioned textbooks by Vojtech Jarnik. See this 17 March 2000 sci.math post at Math Forum, for example. –  Dave L. Renfro Jun 12 at 21:13

49 Answers 49

A Mathematician's Apology by G. H. Hardy.

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To me, who I was a hater of mathematics before high school, this book changed my mind and spirit to make me a real lover of mathematics. It's Awesome <3 :)

It was the international best-seller that makes mathematics a thrilling exploration.

The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger, Rotraut Susanne Berner (Illustrator)

book cover

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The Trachtenberg Speed System of Basic Mathematics, in elementary school, was an eye-opener for me, indicating how striking improvements are possible in established methods, together with an inspiring back story about how Trachtenberg survived the concentration camps.

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The one that opened my mind to the beauty of mathematics was ¿Qué es la geometría no-euclídea? (What is non-euclidean geometry?) by P.S. Alexandrov. It introduced me to the beauty of all the possibilities that are offered in the mathematical world and how they usually match with each other.

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Apostol's Introduction to Analytic Number Theory. It's a beautifully written and self contained book. Even if you cannot solve all the problems, just reading the text will take you a long way. One of the best number theory books I've seen.

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Lots of good answers here. Mine is Hugo Steinhaus' Mathematical Snapshots, which someone gave me when I was a high school freshman. You can order a reprint of the Oxford University Press, New York, 1969 edition directly from Dover for a mere $20: http://store.doverpublications.com/0486409147.html. No need to use Amazon as an intermediary.

I still like my original 1950 hardbound edition better - for (my) old times' sake. I even have a copy of and early (first English?) edition printed in Poland (with red/blue 3d glasses.

Looking back over my published papers I can find the germs for lots of them in ideas I first encountered in Steinhaus - fair division, Appolonian circles, linkages, the normal distribution, coin weighing problems, zonohedra and the stellated dodecahedron (http://www.cs.umb.edu/~eb/stellateddodecahedron/).

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The books of S.L. Loney interested me a lot

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I suspect this topic will turn out to be simply a list of great books in mathematics - and that's a beautiful thing!

For me, the one that really did it was Raymond Smullyan's "What Is the Name of This Book?" which I was given when I was about ten years old. That's the book that really made me see the beauty and the sheer joy of mathematical logic, and I have no doubt that it led me, through winding paths, to many of the other titles already mentioned. (Including GEB, Proofs From the Book, Byrne's Euclid, and many, many others)

As a close second, I would nominate Gardner's "Aha!", which deals with intuition in solving mathematical puzzles. I had this book at a similar time, and I'm sure it affected my thinking deeply, just as Smullyan's did.

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Allen Hatcher! Title: "Algebraic Topology" the best I have read. Very beautifully explained concepts, pictures vividly drawn and some examples of applications, for instance, amazing(ly simple) and profound relation between division algebra structure on $\mathbb R^n$ and the cup product.

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The Elements Book I to VI by Euclid (trans. done by John Casey). Good book :)

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I liked Euclid, but the version I read had come out of the New York Public Library, and someone had written notes in the margin. I enjoyed the marginal notes at least as much as I enjoyed the Elements itself. –  MJD Jun 16 at 7:18

When I was on a family vacation right after the 5th grade, I was told I could buy one souvenir at Knott's Berry Farm. So I went into their bookstore and bought this: Mathematical Recreations and Essays by W. W. Rouse Ball and H. S. M. Coxeter

It became my constant companion.

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Earlier in life, One, Two, Three, Infinity by Gamow opened a world of mathematics beyond algebra. But more recently Prime Obsession by John Derbyshire

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Structure and Interpretation of Computer Programs

Not a math book per se, but it is quite math heavy.

This book showed me the connection between math and programming, not as a toolbox from which you take a formula when you write programs, but as a way to reason about programs mathematically; how the structure of programs can be made to resemble mathematical reasoning.

I also found extreme beauty in how a computer language could have arisen from a mathematical system (the Lambda Calculus).

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John D. Barrow, 'Pi in the Sky' http://www.goodreads.com/book/show/125076.PI_in_the_Sky

I happened to read this fresh outta high school and boy did I thirst for Math undergrad studies after this!

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I was interested in Maths early. My first Maths book (other than text books) was Logarithmic and Other Tables for Schools by Frank Castle, 1967, given to me by a student teacher in about grade 5, 1979ish.

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Discrete Mathematics with Applications, by Susanna S. Epp. For me, this is text is the doorway to higher mathematics. It's also the best text I've found for learning how to perform proofs.

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Mathematics by David Bergamini, part of the Life Science Library.

I read some portions of it when I was in elementary school, and some later, and other parts I still haven't read. From that book I found out that such a thing as mathematics exists.

On page 191 we see the back of a boy's head. The accompanying caption on page 190 says "As the youngster at right shows, most human heads have a fixed point, in the form of a whorl, from which all the hair radiates. Topologically, it would be impossible to cover a sphere with hair---or with radiating lines---without at least one such fixed point. For the same reason, the wind cannot blow everywhere over the earth's surface at once: there must be a point of calm." So it was asserting that that could be proved simply by abstract reasoning. When I was in elementary school, I found that amazing.

Then in 9th grade, I read C. Stanley Ogilvy's Excursions in Geometry. You'd be very callous if you didn't find that book beautiful.

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For me, it was Dunham's Journey Through Genius. My Calculus II class was split into groups and each group was assigned part of the book. My partner and I were assigned the two chapters on set theory. I was bored one weekend and decided to read the first chapter or two. It was easily the most influential text I've read my whole life. Prior to that I had considered going into physics (and did take many physics courses in undergrad) but I knew that my heart was won by mathematics. Dunham made mathematicians come alive and knew how to really hook a reader. I ended up reading the whole book that weekend. Most of the proofs I could understand without too much difficulty, sans Cantor's diagonalization argument. I think I had to read that four or five times to truly understand what he was doing and where the contradiction came from. Once I understood, I felt like the flood gates had been opened and I've never looked at the world the same since.

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Dungeons & Dragons, Basic edition player's manual.

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This answer is for people with a sense of humor... –  IntrinsicRandomEvent Jun 16 at 6:24
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As a D&D person myself, I get it, I just think that most people on this site will not think of summing up dice or calculating DCs really counts as mathematics. Perhaps too trivial. –  Alfred Yerger Jun 16 at 7:50

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