Ruth Angle is an employee at the SETI library on Earth's moon. A large part of their job is to establish communication with the artificial intelligences that are transmitted from distant and sometimes ancient civilizations for the purpose of establishing trade. What they are trading are not physical goods but ideas.

After a quote of Galileo on the fact that math is the "language" of the universe, the opening line of the story is:

So, it is clear from the start that math is going to play an important role in this story. One reason that math would be important here is familiar from other works of science fiction: math is a universal language with which we would be able to communicate with alien species.

In addition, mathematical theorems and their proofs are among the things that are traded in the intergalactic market place.

But, the most original idea presented in this story is that there is a sort of correspondence between math and music. In particular, by communicating with one particularly unusual alien AI, Ruth discovers a way to transform theorems into music (and vice versa). This leads to a concert on the moon at which "The Sigma Structure Symphony" of the title is performed. (The sections of the story are entitled "Andante", "Allegretto Misterioso", "Andante Moderato" and "Vivace". So, we are probably also supposed to think of the story itself as being a sort of symphony.)

Unfortunately, despite all of these interesting ideas, I never felt as if there was anything that tied them all together in the end. (If you notice something that I missed, let me know.)

Perhaps that is because of the unusual circumstances under which it was written. Like "The Woman Who Shook The World Tree", this story was written as part of a contest to write a story inspired by a particular painting of a woman in a long skirt holding a flower next to an odd looking tree. It is interesting that both of these authors ended up with stories that are mathematical, since there is nothing necessarily mathematical about the painting. Benford is able to create a scene in which Ruth would be dressed like that on the moon, but it did seem a bit forced. Anyway, one good thing about this is that the story is available for free online as part of the Palencar Project.