This third novel in the "Dune" series (which was also made into a TV miniseries) contains a wonderful (but rather brief and not very significant) bit of fictional mathematics. The following quotation is presented as an excerpt from a lecture concerning the mathematical explanation of religious leader Paul Muad'Dib's ability to see possible futures:
(quoted from Children of Dune)
Only in the realm of mathematics can you understand Muad'Dib's precise view of the future. Thus: first we postulate any number of pointdimensions in space. This is the classic nfold extended aggregate of n dimensions. With this framework, time as commonly understood becomes an aggregate of one dimensional properties. Applying this to the Muad'Dib phenomenon, we find that we are either confronted by new properties of time or (by reduction through the infinity calculus) we are dealing with separate systems which contain n body properties. For Muad'Dib, we assume the latter. As demonstrated by the reduction, the point dimensions of the nfold can only have separate existence within different frameworks of time. Separate dimensions of time are thus demonstrated to coexist. This being the inescapable case, Muad'Dib's predictions required that he percieve the nfold not as extended aggregate but as an operation within a single framework. In effect, he froze his universe into that one framework which was his view of time.
Palimbasha:
Lectures at Sietch Tabr

The book also explains that Palimbasha is a mathematics professor sanctioned for his attempts to explain Muad'Dib's powers mathematically. Other than this, mathematics does not seem to play any significant role in the story. Furthermore, I cannot really make any sense out of the quote...it is just nonsense. But, interestingly, it is nonsense that really sounds like the sorts of things mathematicians say!
Thanks to Eric Heisler for suggesting this addition to the list.
