a list compiled by Alex Kasman (College of Charleston)
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A mathematician invents a machine that provides abstract mathematical objects ("vectors" and "tensors") a certain reality. His goal is to allow them not to solve equations but to create new ones. However, before he works out exactly the settings he wants to put in the machine, it is started inadvertently by a burglar and the lawyer guest he has staying at his house, with disastrous consequences (e.g. buildings move, or vanish filled with people who find themselves in a place without recognizable dimension, time scales change in different parts of the universe, land masses disappear and swallow oceans, etc.)
Reading this story reminds me of many other works of mathematical fiction. It presents the idea that true reality is mathematics while what we consider the physical universe is just an illusion (as do Mathenauts and Luminous). The story also suggests that mathematical discoveries can change reality (as do Unreasonable Effectiveness and Distress). However, it is remarkable that this story does all of that and was written in 1934! In 2009 (as I write this), the description of this machine that can do mathematics and what it can achieve seems quaintly oldfashioned, but for a story written before the invention of anything we today would call a computer, it is quite impressive. Originally published in Astounding Stories, September 1934. (Thanks to Fred Galvin for providing me with a readable copy of this old classic.)

More information about this work can be found at www.isfdb.org. 
(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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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in nonfictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.
(Maintained by Alex Kasman, College of Charleston)