Each chapter begins with a paragraph about a historical fad: mesmerism, coonskin caps, Rubik's cubes, etc. The statistician is trying to use mathematical techniques -- e.g. correlations and cluster analysis along with just a bit of modeling via differential equations -- to understand how they start. However, the hair bobbing fad among Flappers in the 1920s is proving to be impossible for her to explain. Due to a misdelivered package, she ends up meeting a fashion-impaired chaos theorist in another department at the same company. As a result, sparks fly...sparks of scientific inspiration as well as passion.

Of course, the fact that the plot hinges on the chance occurrence of a package being delivered to the wrong recipient is itself a reference to the "butterfly effect". But, chaos theory plays a much larger role here than just that. In fact, a discovery about the source of chaos is of vital importance. Unfortunately, although the book's remarks about chaos theory and self-organized criticality probably would sound mathematical and sensible to many readers who know no better, to me they seem non-sensical and have little or nothing to do with the actual field of chaos theory. For example:

This quote foreshadows a discovery that the two researchers make near the end of the book. Since the title essentially gives it away, I don't think it is much of a spoiler for me to summarize their "big discovery". (But if you really want to avoid it, feel free to skip the next paragraph.)

Towards the end of the book, the statistician and chaos theorist conclude that the true source of chaos in any chaotic dynamical system is one particularly influential individual, a trend-setter or bellwether. I'm afraid that this does not entirely make sense. I can see that a dynamical system made up of interacting individuals with one exerting a greater influence than the others would be an interesting thing to study. However, it does not seem likely to me that this would lead to sensitive dependence on initial conditions unless that bellwether's individual behavior was already chaotic, in which case that cannot be the source of the chaos. Moreover, it is absolutely clear that not all chaotic dynamical systems arise from this proposed mechanism. Still, since the conclusion that they are is presented as being a discovery in the book, I will tag it as an instance of "fictional mathematics". (Note: The novel's literary bona fides are boosted by an allusion tying this idea about bellwethers to Browning's poem Pippa Passes.)

Another interesting idea developed within the narration grows out of the famous anecdote about Poincaré's epiphany regarding Fuchsian functions while stepping onto a bus. In particular, the book emphasizes that great discoveries do not generally occur in ordered and peaceful environments, but rather require messy, noisy and confusing circumstances. As it turns out, the environment in the book fits those requirements.

Both the statistician and chaos theorist work for a company called HiTek at which the staff are particularly dysfunctional and bureaucracy rules. This is a good source of satire about life in the R&D division of a large corporation, but if you're too busy laughing at the jokes you may miss the clever way that it all fits together and builds to the climax.

The big ideas of the book which sound vaguely mathematical are described in such broad terms as to make them generic. Still, it tosses around some mathematical terminology as window dressing and the research of the two protagonists is explicitly described as being "mathematical". Consequently, I do consider this to be an example of "mathematical fiction". And, although taste is entirely subjective, I must say that I really like this book and would strongly recommend it to anyone who finds the description above appealing.

BTW: Although the author has won Hugo and Nebula awards and although the publisher has classified it as science fiction, this novel does not take place in the future and does not involve aliens or robots or monsters or any fantastical inventions. Many readers who normally avoid the genre would not really consider this to be "science fiction". It might be better instead to describe it as "fiction about scientists".