a list compiled by Alex Kasman (College of Charleston)
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Highly Rated! 
These adventures of Max Jones, a boy who runs away from Ozark home and works his way up the ranks of a starship is a nice example of classical science fiction as well as being a bit mathematical.
The book explains that astrogators  the mathematicians who plot ships courses  are of tremendous importance in space travel. In fact, it explains that although officers can be mathematicians, physicists or businessmen, only the mathematicians stand a chance of becoming captains. Jones' mathematical connections play significant roles in the plot. It is because his uncle was a "great mathematician" that Jones is initially able to go into space at all. Then, it is because his own mathematical skill is recognized (from his success at 3D chess) that he is not punished when it is discovered that he broke some rules in getting onboard. Finally, when the aging captain makes a computational error in his own astronavigation, Jones catches the error and points it out. Unfortunately, nobody believes him and the ship winds up being "lost in space". The book has a nice discussion of geometry of the method of space travel that they use. A friend asks Jones about "space warps", to which he angrily replies that they do not use warps (as if he knows that this is an SF cliche and is tired of hearing about it.) Rather, he explains, they make use of the parts of space that are flat. He explains (which is quite in agreement with our modern view of the physics of spacetime) that near stars and planets, space has nontrivial curvature...but out in the emptiness it is almost flat.
Great story and nice mathematical references. Thanks to John Lange for suggesting its inclusion on this website! BTW, the entry on this book in Wikipedia suggests that it is intended as a response to Gulliver's Travels, another work of mathematical fiction (which presents a much less positive view of math)!

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)