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In everyday life, you don't encounter many people who express that they feel a connection between mathematics and fun. Not where I live, in any case. This is true, despite that fact that many people who have achieved some math knowledge relish making use of that knowledge (and find joy in new mathematical realizations).

I wonder whether it is possible for someone who is an avid recreational reader to pick up a book, become engaged in it, and learn something about mathematics despite not seeing him or herself as a lover of mathematics.

The book(s) would need to be engaging, obviously. They may or may not ostensibly be about mathematics. Possibly one of more "big ideas" or important concepts would be covered in a way that:

  • The reader gains a new understanding of what math, itself, is. Perhaps they only encountered math as arithmetic and calculation in school and never clicked with algebra beyond some symbol manipulation. Through this book they encounter math as a way to see aspects of the world that otherwise remain unseen.
  • OR: The reader revisits some aspect of school math and sees it in a different light. They never imagined it would actually be useful or interesting somewhere.
  • OR: The reader actually learns some mathematics they can use.

My questions to you are:

  1. Do you think it's possible or probable to recommend a book of this type to a non math-lover and have them later tell you "I really enjoyed that book. And it turned out a good portion of it was about math."
  2. What specific math content or aspect of math do you think would make a good subject for a book of this type?
  3. Do you know of any books that already exist which have been or could become popular, and are as I described above?

Feel free to answer any or all of the questions.

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I was starting to write and answer, Elegant Universe by Brian Greene, Hyperspace by Michio Kaku or Love and Math by Edward Frenkel. But, the applicability aspect of your question killed my answer :) –  James S. Cook Jul 21 at 13:55
    
@James S. Cook I meant those criteria to be each sufficient on their own. I think asking for all of them would be a lot. –  JPBurke Jul 21 at 15:39
    
You might find some answers (to 3) or ideas in the related thread: matheducators.stackexchange.com/q/294/262 (My own answer, matheducators.stackexchange.com/a/3837/262, has two books; the former = Ellenberg's How Not To Be Wrong might fit the bill.) –  Benjamin Dickman Jul 21 at 17:00
    
@JamesS.Cook - Edited the question to clarify that it was intended to be interpreted more broadly (i.e. I added in the "or"s). –  JPBurke Jul 21 at 18:35
    
My neighbor has math books on the shelves in his living room.....but, then again, he's an actuary and she's a math teacher, so that might not prove anything about "anyone" ;) –  Tutor Jul 27 at 5:03

3 Answers 3

A couple books spring to my mind that fit the criteria:

Alice's Adventures in Wonderland by Lewis Carroll is a striking example in that although it might be weak in heavily structured mathematics, it uses modular arithmetic, non-euclidean geometry, and logic amongst other fields of math to tell the story.

Godel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter is a clearly mathematical book covering many topic in math, but I could see that it is daunting to many readers: not just in length, but sometimes needing to spend a minute to think about each passage.

One of my favorites is Flatland: A Romance of Many Dimensions by Edwin A. Abbott. He discusses math of several dimensions along with a critique of Victorian society.

Other particular example that I know of but have not looked over is Group Theory in the Bedroom, and Other Mathematical Diversions by Brian Hayes.

As probably noted by these examples, it seems that geometry and logic lends itself nicely to popular books. Character arguments can be framed in a logical sense which is frequently used in the above books, while geometry is pretty clear in that when writing, you can place your mind in a non-euclidean space quite nicely.

I think that many people, unless they already like math, might not be as appreciative of the mathematics as you might expect. They might read it for the story and not realize the mathematical concepts that it is using, critiquing, or explaining.

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I originally envisioned this question as being about learning about mathematics in surprising places, but I wanted to craft it more specifically to apply to education. You're quite right, though -- people may not appreciate what is mathematical about what they are reading. –  JPBurke Jul 21 at 18:38

This doesn't completely satisfy the criteria, but the book Super Crunchers: Why Thinking-by-numbers is the New Way to be Smart by Ian Ayers argues for why standard deviation should be a more widely used concept in everyday life. Therefore, this book could be thought of as a book that both motivates the learning of standard deviation as a concept (through the case it makes of what it can be used for in--for example--news reporting) and gives an informative introduction to the concept.

However, this book is essentially all about quantitative analysis of data (obviously mathy!). So a person would need to already be interested in that, or in the specific applications discussed (such as wine vintage pricing).

While there may be better examples, I like how this book identifies a mathematical concept and tries to make it relevant to the reader. The author may not have specifically intended it this way, but it could be seen as "here's why you're going to like knowing about standard deviation, and you'll wish people used it more."

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A book that may satisfy your conditions is The Cartoon Guide to Calculus by Larry Gonick, well at least I have heard that some people that have love it. In fact, it is an introductory book on calculus which treats the topics of functions, limits, derivatives, and integrals.

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