I really wouldn't consider mathematics important to this story at all; they're only present in the way "science" is present in Star Trek - as a convenient and misapplied label for a deus ex machina plot device, in this case, travel through literary stories the author thinks sounds like fun.

If you're a teenager (or an uncritical adult looking for "popcorn reading"), it's not a bad read. But DON'T expect any kind of learned discussion of science or math; Heinlein was known in the 30s and 40s for providing some pretty solid and interesting (for the time) engineering speculation in his fiction, but his pure science is... not so good.

Look to Larry Niven's classic SF stories if you want more thoughtful play with science and math - Niven is famous for actually doing the math to figure out that a large structure (Ringworld) would require a greater tensile strength than ordinary matter can provide. (He's almost equally famous for going back and writing a sequel to fix the problem when a bunch of MIT students did more calculations and determined that the Ringworld's orbit would be unstable.)