"Cascade Point" by Timothy Zahn (1983, won the 1984 Hugo award) contains
fictionalized mathematical analysis of higher-order dimensions of
The novel concerns future space travel whereby spacecraft enter a higher
dimension using a field generator, then rotate the spacecraft within the
field which results in translational displacement of the craft (i.e. it
travels forward in space). The spacecraft then stops rotating, turns off the
field generator, and the craft is then back in normal space, several light
years away from where it started the maneuver.
The mathematical analysis comes in to play when they passengers and crew of
one starship find that they have inadvertantly entered one of the branching
dimensions and must find their way back to their original dimension. There
are numerous references to mathematical models of "cascade theory", Riemann
surfaces, curve fitting of statistical and empirical data, geometric
intuition, and the many problem inherent in trying to visualize or develop
visual representations of mulitple dimensions.