a list compiled by Alex Kasman (College of Charleston)
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This short story describes a bizarre experiment in which researchers are cloned (quantum cloning, not the genetic kind; these researchers aren't "fleshers") and sent into a black hole. Their goal is to attempt to achieve "infinite computation". Both the foundational mathematics of computability theory and mathematical physics play a role. There is also quite a lot of mathematical name dropping. The city in which they live and the vessel in which they will travel are both named "Cartan", and they even specify which Cartan they are named after:
You may have noticed in the quote above that the black hole they are visiting is named after Nobel laureate Subramaniam Chandrashekhar, author of "The Mathematical Theory of Black Holes". Although it is sometimes hard to delineate between mathematics and physics in science fiction, the description of the physics here is sufficiently mathematical that I believe it qualifies as "mathematical fiction". For instance:
Computability theory is full of limitations on what we can determine (and what we can know) due to the finiteness of our computations. However, the story mentions "Tiplerian theology", a clear reference to the theological writings of mathematician Frank J. Tipler. According to this (presumably fictional) philosophy, our goal should be to alter the universe to allow for infinite computation. This is at least one of the goals of the researchers in their "Planck Dive".
Originally published in Asimov's magazine, February 1998 and reprinted in the anthology "Luminous". 
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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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)