a list compiled by Alex Kasman (College of Charleston)
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Note: This work of mathematical fiction is recommended by Alex for hardcore fans of science fiction. 
What sort of mathematics would Vonnegut's Tralfamadorean's like to do? Or,
alternatively, what sort of worldview would a sentient species have if their idea of simple mathematics was the calculus of variations? Those are the mathematical questions addressed by this clever story. Of course, much more goes on here than just that. We meet an interesting character who is a linguist hired by the government to help us communicate with a new alien species. In addition to learning about her progress in this difficult task, we see how she is courted by, marries, and eventually divorces her partner in the project who is a physicist. In fact, the "your life" of the title is the life of the daughter from that marriage. At first, the physicists and linguists are both having trouble communicating with the aliens. The linguists are bothered by their nonlinear writing system which seems to require thinking of the sentence as a whole rather than as a string of words stretched out in time. The physicists start making headway when they try to talk to the aliens about the refraction of light. Somehow the aliens make it clear that they think about this phenomenon along the lines of Fermat's principle: that light takes the path from point A to point B which will get it there in the least time. Of course, this statement requires that you imagine the light knowing where it will be going before it gets there (sort of like the problem with the sentences, eh?) In fact, Fermat's principle is just an example of the application of variational mathematics to physics. If you've had some calculus you can probably get a vague idea of what the calculus of variations is. Remember how some points were "critical points" because the slope of the tangent line was zero there? The idea is the same but replace x (the variable) with a function itself and you get a sort of infinite dimensional generalization in which some FUNCTIONS are critical points because some sort of derivative of a function of the function is zero. Sounds weird, I know. In fact, we do not resort to using it too often because it does seem a bit too abstract. But the fact is, as this story relates, much of physics can be stated in these terms in a way that completely eliminates the notion of time passing or events causing other events. The idea of this story is to explore a different mindset in which the calculus of variations, rather than algebra, is the most elementary form of mathematics.
Added August 2016 I am excited to report that Story of Your Life is to appear as a major film release, and that the collection of stories in which it appears will soon be reissued in an affordable paperback format. Update 2017: Unsurprisingly, the film adaptation called Arrival, while an excellent film, cuts out nearly all of the math that got the short story listed on this Website. Oh, well... 
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)