In this short story, an aging mathematician witnesses a woman with an umbrella jumping (falling?) off of the Golden Gate bridge. Mathematical terminology is tossed around reasonably well ("proofs by contradiction", "the method of infinite descent", "the flawless arc of a sinusoidal oscillation") and the character of the mathematician is perhaps too close to the stereotype of the quiet, antisocial mathematician who is only happy when he finds a mathematical solution to the mysteries around him. Of course, the mathematics is not the main focus of the story. The mysteries of the woman, who she was and what happened to her are of central importance, as are how they affect the mathematician. I suspect the author selected the profession of mathematician for the man precisely because this stereotype is the perfect medium for this particular sort of art (because he is a mathematician, he needs the woman as his connection to the "real world") rather than that she wants to say anything in particular about math.
Still, since we're looking at math in fiction on this Website, I'll dwell on this point perhaps more than it deserves. For instance, let's consider the following passage:
(quoted from Falling Umbrella)
[His daughter] has taken his realm, mathematics, and embraced one of its corrupt cousins, economics. If theoretical mathematics is the pure and perhaps divine spirit of the universe, then economics is the whore, working only for money and the salacious desires of its clients. He believes he once told her this, long ago, back in her college days. If anything, it seemed to attract her more to the field.

I think it probably is true that some mathematicians prefer "pure mathematics", completely free of application. So, even if the word "whore" is a bit strong, the general sentiment is something that a relatively large minority of mathematicians might identify with. But, its purpose here is to reinforce the stereotype of a mathematician as being unconnected to the real world (both applied mathematics and his daughter). I'm a bit tired of this stereotype (can you tell?) and also tire of repeating that it is largely untrue.
So, instead, let me just say that when she uses mathematical terms, Whitty does a pretty good job of using them correctly (with "number plane" instead of "complex plane" being perhaps the only awkward phrase). And the story is well written, presenting a contrived scenario as a work of art to be studied for emotional potency and hidden symmetry. But, if you seek a story that gets somewhere or some insight into the world of mathematics, this is not the place to look.
BTW Visitors to this site might also be interested in "Darwin in Heaven", another (nonmathematical) story in the same collection in which Charles Darwin and Richard Feynman discuss evolution and theology in the afterlife.
