A female mathematics professor undergoes a surgical procedure to enable her to live and communicate with aquatic aliens. Her goal is to learn to understand their mathematics well enough to reproduce their advanced technology (described in terms of "zero point energy"). There is not much mathematics (she says something about them only having two numbers  zero and one; that the sum of one and one is not two but a "bigger one"; and that their mathematics is based on some sort of harmonic analysis) but it is a nice enough little story.
Appeared first in Interzone #205, July/August 2006. And, for those who do not have access to that British SF magazine, it has been selected to appear in Dozois' The Year's Best Science Fiction TwentyFourth Annual Collection.
