An apparently schizophrenic, homeless woman sells her body to get herself and her infant off the street on a cold night. Only at the end of this extremely short story do we realize that the imaginary world of "crysalline beauty" that she sometimes loses herself in is not part of her delusions, but mathematics itself:
(quoted from Snow)
She took out the first envelope, and carefully spread it open. Her other world was very close, the world that she created out of herself. She knew that somewhere, somewhere out in the world there were other people who knew how to enter that other world. Sometimes she wondered if she had ever met any of them. but, she decided that really didn't matter. What mattered was that other world.
She checked once more that Christie was sleeping soundly, and then, writing in almost invisibly tiny script, she started.
"Theorem 431. Consider the set of nonsingular connections mapping an 8dimensional vector space onto a differentiable Hausdorff manifold..."

I really like this story. It is beautifully written. I'm sorry that I basically have to give away the punchline in this review, but I did not see a way to summarize it without mentioning this point since otherwise it is simply about a homeless woman. I'm also sorry that I have to complain about it.
Clearly, Landis knows a lot about math and science. I mean, he's actually a physicist when he's not writing fiction. But, there are a few things here that bug me. I am always bothered a bit when I see the stereotype of the insane mathematician in fiction since I think this distorts the public perception of what mathematicians are really like. Similarly, the stereotype of the isolated mathematician is utilized here. The former stereotype here is at least believable (though I do not believe there is a correlation between math and insanity, of course there must be simply by chance some people who are both), but the latter here is a bit ridiculous. This is not the sort of mathematics that one can do in complete isolation.
I suppose it is not a big deal, but her reference to a connection does not make sense as she writes it. (A connection should be a map between the tangent spaces, or some other fiber bundle, at two points on the manifold and not a map from a vector space to the manifold.) Another similarly unimportant point is this: why does he say that the vector field of the falling snow is divergencefree? I would expect the wind blowing between buildings to result in pressure changes from point to point.
Originally published in Starlight 2 (Tor, 1998) it was republished in the anthology Impact Parameter. Contributed by
Geoffrey A. Landis
Say, thanks for listing the story.
The velocity vector field of falling snow is divergencefree because pressure differences in a fluid (like air) equilibrate at the speed of sound. Consider a unit cube one meter on a side, and suppose the smallest velocity difference a human eye can detect is one cm/sec. If one face of the cube had a 1 cm/sec more incident air than the remaining faces, the pressure in the cube would increase by 1000 pascal per second. But the dynamic pressure of air moving at 1 cm/sec is only 0.06 mPa. So any divergence of this magnitude could only be sustained for 60 microseconds.
(this is why aerodynamics call airspeed ≪ speed of sound "incompressible flow". )
Over continentsized regions, you can sustain atmospheric pressure differences. But on a cityblock scale, flow can be modeled as divergenceless to a very very good level of approximation.
you're right about the word "connection," though. Mea culpa.

