a list compiled by Alex Kasman (College of Charleston)
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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 notQ, Q implies notP, which is equivalent to saying either P or Q but not both. But if notP is not implied by notQ...") 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 middleaged) 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 setup 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. 
Buy this work of mathematical fiction and read reviews at amazon.com. 
(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.) 

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Your Help Needed: Some site visitors remember reading works of mathematical fiction that neither they nor I can identify. It is time to crowdsource this problem and ask for your help! You would help a neighbor find a missing pet...can't you also help a fellow site visitor find some missing works of mathematical fiction? Please take a look and let us know if you have seen these missing stories anywhere!.
(Maintained by Alex Kasman, College of Charleston)