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The Mathematics of Magic (1940)
L. Sprague de Camp / Fletcher Pratt
(click on names to see more mathematical fiction by the same author)

The "Enchanter Stories" by de Camp and Pratt are a very popular series of SF/fantasy stories whose protagonist, Harold Shea, is able to travel to other universes using symbolic logic. "The Mathematics of Magic" is actually the second story in the series. All of the stories contain a bit of math, but this one is a bit more explicit than the others, includes the word "mathematics" in the title, and happens to also be the title of a collection of these stories. So, I am planning to just include this one story in the list to represent the entire series, including a few written by other authors.

The premise is that all of the fantasies you know -- from ancient myths to recent novels -- are actually true descriptions of other universes that are just as real as ours but subject to different rules of logic. Thus, fiction authors are not really as creative as you might think. They simply can see into another universe, though they may not recognize this is what they are doing. Also, many people you might think are "crazy" actually have the ability to see these alternate realities. This is how the psychologists in the story (yes, they are not physicists or mathematicians!) initially discover the truth.

The psychologists in the story realize that it is possible to travel to these other universes by reciting the formal structure (e.g. "If P equals not-Q, Q implies not-P, which is equivalent to saying either P or Q but not both. But if not-P is not implied by not-Q...") In addition, in this story there is a brief discussion of the geometry which supposedly underlies all of this (extra dimensions, curved vectors, etc).

None of that makes too much sense, but it serves as an excuse for writing about people from our universe who are able to meet the ancient Norse gods and visit Dorothy Gale (now married and middle-aged) at her house in Oz. This has proved to be a winning formula that has been utilized by de Camp and Pratt and a few other authors who have been allowed to borrow the characters all the way into the 1990s.

The original "Harold Shea" story "The Roaring Trumpet" was published in Unknown, May 1940 and this sequel appeared in October 1940. (The title of the magazine in which they appeared can be a bit confusing, which may be why it is no longer around. It seems like a good set-up for a "who's on first?" routine. "What magazine was The Roaring Trumpet published in? " "Unknown." "Does anyone know the name of the magazine?" "Yes, I know!" "What is it?" "Unknown!"....)

For more information, check out the Wikipedia entry on Harold Shea.

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Works Similar to The Mathematics of Magic
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Imaginary Numbers : An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings by William Frucht (editor)
  2. A Logical Magician by Robert Weinberg
  3. Sine of the Magus [aka The Magicians] by James Gunn
  4. Mathemagics by Margaret Ball
  5. The Last Page by Anthony Huso
  6. Phantom by Terry Goodkind
  7. The Devil You Don't by Keith Laumer
  8. Pyramids by Terry Pratchett
  9. Numbercruncher by Si Spurrier (writer) / PJ Holden (artist)
  10. Through the Gates of the Silver Key by H.P. Lovecraft / E. Hoffmann Price
Ratings for The Mathematics of Magic:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
1.5/5 (2 votes)
Literary Quality:
4/5 (2 votes)

GenreHumorous, Science Fiction, Fantasy,
MotifHigher/Lower Dimensions,
TopicLogic/Set Theory,
MediumShort Stories, Collection,

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(Maintained by Alex Kasman, College of Charleston)