a list compiled by Alex Kasman (College of Charleston)
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Janelle, recently graduated from MIT with a degree in math, is pulled through the "branch cut" between two universes to an alternate Earth where two sword wielding brothers rule half the world. There, an old prophesy has predicted Janelle's arrival and states that the question of which of the brothers she marries will determine the fate of the empire. This story received much praise from the science fiction community, but I cannot say that I see why. The overall plot struck me as being a rather cliched fantasy. The mathematics that "dresses it up" so that it becomes science fiction was promising, but did not live up to that promise. As usual, I will focus below on the mathematics and explain more of what I mean about it not fulfilling its promise. For those interested in remarks about other aspects of the story, I will say that I personally agree with Mark Watson's review at bestsf.net. My biggest disappointment with the math in the story is that it never seems to amount to anything. There were clues in the story that something interesting and mathematical was going on. The alternate Earth seems mysteriously mathematical. I was waiting for some sort of explanation that tied it all together, but it never came. It would have been wonderful if the story had a resolution which explained the role of the math in the story, but as it was it seemed as if it was stuck in just because the author wanted to use some concepts she knew. If I'm mistaken (which could be the case if the story I read was not complete...it did not seem to really end...or if there is a sequel somewhere that I've not read) let me know. Onto some more specific mathematical details. The following exchange takes place shortly after a mysterious man has appeared and apparently taken Janelle through a portal to another universe:
The idea of making an analogy between the way branch cuts relate the different sheets of a Riemann surface and the common SF device of a "gateway between universes" is reasonable. Since this is a mathematical subject which is usually first introduced in standard graduate level complex analysis courses, most people (including undergraduate math majors) are not familiar with it. In that sense, it is an interesting thing to include in the story and to try to explain to the reader. However, to anyone who has learned about them already, the analogy is a bit obvious. Moreover, although the story tries to make it seem like something more than just an analogy, it must be seen as an analogy because the dimensions are not quite right. (A branch cut is a 1dimensional "gateway" between different 2dimensional "spaces". Worst of all, her later description of what branch cuts actually are is horrible. Considering that the author's Wikipedia page claims that she has a graduate degree in physics, teaches math and coaches students in math competitions, I would have thought that she could have done better. Historically, the concept arose first in the context of logarithmic functions of complex variables where one is tempted to say that the function is "multivalued", that it takes different output values for the same input value. I'll explain this in a box below for those of you who want to really see the details, but jumping to the point here, she gets it rather backwards by introducing two different exponential functions that take different values at the same input...which is not at all surprising (why would two different functions be expected to have the same value...they are different?) and would not lead you to the concept of Riemann surfaces. Another mathematical thread to the story has to do with frequent references to wave functions, harmonics, and Fourier analysis. She handles this a bit better than the Riemann surface stuff mentioned above, but doesn't do as much with it as I could have hoped:
A cute puzzle, the kind that would be encountered in a high school math competition, is squeezed into the story in a contrived way when Janelle convinces her captor that she is not good with math and so he can safely give her a clue to the numerical "key" that will help her escape. Originally published as a "novella" in Analog (2005). Having won a Nebula award, this long short story is now available in electronic format in various locations on the Internet, including this AnalogSF.com link.

More information about this work can be found at www.analogsf.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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Your Help Needed: Some site visitors remember reading works of mathematical fiction that neither they nor I can identify. It is time to crowdsource this problem and ask for your help! You would help a neighbor find a missing pet...can't you also help a fellow site visitor find some missing works of mathematical fiction? Please take a look and let us know if you have seen these missing stories anywhere!.
(Maintained by Alex Kasman, College of Charleston)