a list compiled by Alex Kasman (College of Charleston)
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An autistic boy finds comfort in Cantor's discovery that the set of fractions is greatly outnumbered by the set of irrationals. (See, for example, Cantor's Diagonal Argument.)
I did not much enjoy the representation of the autistic child, his wellmeaning but ineffective mother, and her abusive boyfriend. This is not so much because there is anything wrong with the writing, it was fine, but rather only because I feel that I have seen all of this before. On the other hand, the idea of applying Cantor's notion of cardinality to daily life, to the question of the relative "cardinality" of the good moments to the bad, is an intriguing and even inspiring one. The effect is enhanced by the inclusion of quotations from a nonfictional text on the way that time is (mis)perceived by the brain. Moreover, this story does an excellent job of teaching the underlying mathematics, so that even someone who did not already know it could really learn it without even having to consult an external source. It includes figures to demonstrate the correspondence between the rational and natural numbers, definitions of the transfinite cardinals "aleph sub zero" and "beth sub one", and even an appendix addressing a subtle point in the Cantor's diagonal proof (i.e the fact that rational numbers which can be written with a denominator that is a power of ten actually have two different decimal representations). The Countable was published in the December 2011 issue of Asimov's Science Fiction magazine. However, I am not putting it in the "science fiction" category in my database since the story does not portray any events which are beyond our current scientific understanding or technical abilities. Rather, it uses fiction as a way to explain some interesting real mathematics, and uses that mathematics to offer a new perspective on life...which makes it an example of great mathematical fiction. 
More information about this work can be found at www.asimovs.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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(Maintained by Alex Kasman, College of Charleston)