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I'm looking to find more examples of books which bridge the gap between "story" and "mathematics" using narrative and all those other wonderful features we might find in Harry Potter or some other well known children's book.

So far, Knuth's Surreal Numbers is one of the few attempts I've seen from a professional mathematician to produce a work of fiction which is also a work of serious mathematics: http://www-cs-faculty.stanford.edu/~uno/sn.html

Any other similar books would be a good place to look when thinking about "how do I sell this mathematical idea to kids"?

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What age and/or level of emotional and/or mathematical maturity? – shoover Mar 3 at 23:44
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See the books by Lillian Rosanoff Lieber (1886-1986) that I posted in my answer to Dr Seuss style prose advanced mathematics text. – Dave L Renfro Mar 4 at 20:33

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Gödel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter is a book about Mathematics, Art, Music, Computer Science and Artificial Intelligence. It alternates story chapters and descriptive chapters.

In my opinion the most valuable parts of the book are:

  • a very understandable presentation of Gödel's incompleteness theorem.
  • a good discussion of the arguments around Artificial Intelligence.
  • a large number of reproduced art works, many from Escher, but also many others.

Others will undoubtedly find other things to like about it.

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Hofstadter said it was about consciousness (we are a self-referential 'strange-loop') but it's all really the same thing. – hownowbrowncow Mar 4 at 18:09

Flatland by Edwin Abbott Abbott

It's a story about a 2-dimensional being's encounter with a three-dimensional being. (Well, there's a class(?) allegory at the beginning, but you can skip that.)

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What mathematical results are clearly and exactly demonstrated by Flatland's narrative? – John Mar 3 at 23:08
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@JohnMeuser I'm not sure about "mathematical results" but it certainly presents the idea of dimensionality very creatively and effectively – celeriko Mar 3 at 23:14
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Flatland was listed as an optional textbook for the intro topology unit I took. – Oxinabox Mar 4 at 4:22

Math Girls! It gave me a small taste of generating functions, and I want more! Very challenging math.

Surreal Numbers might be the best way to learn about Conway's system. Math Girls does not have math that is as original. But it is high-level math, and it's fun. (The storyline is more engaging than that of Surreal Numbers. I love both books, in different ways. The Number Devil is great for inspiring younger students with the beauty of math, but the math is not as high level. Flatland never moved me, personally.)

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RE: "generating functions, and I want more!" I posted a question on MSE (1592140) that garnered some nice answers using generating functions. It also led to the reference: Wilf's (1994) generatingfunctionology. – Benjamin Dickman Mar 4 at 6:47

The Diamond Age, a science fiction novel by Neal Stephenson, includes a subplot that involves mechanical Turing machines that are described in great detail and that are used in solving key puzzles that move the subplot along. The subplot involving Turing machines is only one part of a complex and multilayered story, but I thought I'd bring it up in case you might find it useful.

Another Stephenson novel, Anathem includes a great deal of philosophical discussions about mathematics, as well as discussing directed acyclic graphs, configuration space, and other mathematical topics. It is a long and complex novel, but unusually detailed (even for a sci fi novel) discussions of mathematical topics play a significant role.

I haven't read Cryptonomicon (also by Stephenson), but this review in Notices of the AMS notes that it includes quite a bit of mathematics, particularly cryptography.

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However none of them are written for children, readable by children, or (given instances of rape, murder and various other unpleasantness) suitable for children. – Graham Mar 4 at 15:50

"The Number Devil" by Hans Magnus Enzensberger is right up your alley. It is written for and is 100% accessible for children and introduces many math concepts such as recursion, infinity, and symmetry.

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Can you tell me more about how one of these mathematical concepts results from the narrative. Specifically, how is the narrative used as a tool for producing a specific mathematical result in the book? – John Mar 3 at 23:30
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@JohnMeuser I think you should read it and see for yourself :) – celeriko Mar 4 at 1:28
    
This is a very good book for introducing these concepts to children. I would note that some of the concepts are introduced with a non-standard name (they are mapped in an appendix at the end of the book). However, I consider that undesirable for people that didn't previously know about them and thus won't realise the "official" name (OTOH that could be helpful for some students that "hate maths"). Just an introductory phrase before reading each chapter («In this Chapter the Devil will show Robert X») should fix it. – Ángel Mar 5 at 0:03

To follow up on David's recommendation of Flatland, how about Ian Stewart's Flatterland.


      
An amazon.com review says,

Along his fictional path, Stewart touches on Feynman diagrams, superstring theory, time travel, quantum mechanics, and black holes, among many other topics.

Another review mentions fractal geometry and cosmic strings.

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(I haven't yet read it myself; on my to-read list.) – Joseph O'Rourke Mar 4 at 0:51

The Phantom Tollbooth (1961) by Norton Juster is a children's fantasy story that mixes wordplay and mathplay somewhat in the style of Lewis Carroll. It's suitable for anyone, but resonates well with the 8-12 age group, according to the GoodReads reviews by children.

Milo travels to the fantastic land called Kingdom of Wisdom, where he is joined by the "watch dog" Tock, who has a giant alarm clock on his side. They meet the feuding wizard brothers Azaz, the letters wizard who is King of Dictionopolis, and the Mathemagician, the numbers wizard who rules Digitopolis. Milo solves math riddles, eats Subtraction Stew, and has other adventures in his quest to settle the brothers' feud.

There's not a particular math concept that is illustrated, but if you want to get the 8-12 age group interested in learning more about math (and words), this might be a good place.

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The Mathematical Fiction web site, maintained by Alex Kasman of the College of Charleston, has summaries of hundreds of stories and movies that in some way include or discuss mathematics. It is searchable by keyword and indexed by mathematical topic(s) discussed.

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Incandescence by Greg Egan describes how a technologically unsophisticated alien civilisation, under the right circumstances (in this case, closely orbiting a neutron star) might discover general relativity based on simple observations and experiments.

On Earth, where relativistic effects are too small to easily observe, an analogy might be drawn with Newton's discoveries (where the effects were "easily" observable to a civilisation that lacked advanced technology).

It has mixed reviews and is one of Egan's least popular books, but I think most of the negativity comes from people who wanted more of a work of fiction, and less hard science. Egan is known for his hard science, and this book is heavier on it than most of his. I greatly enjoyed reading it.

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Cover of To Mock a Mockingbird

You might want to consider the books of Raymond Smullyan. They often take the form of a sequence of puzzles tied together loosely by a narrative. The puzzles are typically intended to work towards deeply understanding some topic. For example, To Mock A Mockingbird disguises a course on Combinatory Logic (closely related to lambda calculus) as a tale about birds and their calls.

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Some scholars think that Alice in Wonderland is entirely an allegory on mathematical topics by the Oxford logician and mathematician Charles Lutwidge Dodgson (Lewis Carroll).

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A K Dewdney's Planiverse and Rudy Rucker's White Light

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It might be better to include some description (rather than links alone) for why/how you think these are like Knuth's book. – Benjamin Dickman Mar 5 at 3:45

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