A beautiful and brilliant woman organizes a team of scientists (and a mathematician) who together make fusion energy efficient and invent a flying submarine...and perhaps a timemachine as well. When one of the team members disappears and another seems to have found a manuscript written by him a hundred years in the future inside a "flying saucer" with a fractal surface, the truth becomes elusive.
As you can see from that description, math is not really central to
this work. It is intriguing that the ship is described as having a surface
based on the Von Koch snowflake curve since the book, written in 1956,
predates the current interest in "fractals" (a word which had not yet even
been coined when the book was written.) Although in more recent works, fractals are always presented as coming from chaos theory, it is presented in this book as a
pathological example in topology that the character had previously sought
to understand. The fact that the resulting
surface area would be infinite (even though the volume finite) is used to
explain unusual properties of the ship. Other mathematical aspects of the
book include the claim that in "the future", language is mathematically
analyzed ("an operational calculus of semantic probability") and reorganized so that all expressions
are explicit and precise. Math is also frequently used as an analogy in
the book:
 There is an interesting analogy
made using the snowflake curve describing science as a finite geometric object with
infinite boundary...room for everyone.

"Men and women can never be really happy together until we have worked out
the algebra of love so that we can say exactly what we mean, and prove the
equation of consummation."
 "He had as much success...as he would have had trying to teach a
fifthcentury Athenian differential calculus to stop him worrying about the
paradox of the tortoise and the hare."
 "Roughly, I think he went on to define Mentality as the rate of change
of behaviour and this puts Mentality in the class of rational abstractions
such as Velocity and Gravityl then if you like to use thw word Mind,
remember it is just a handy abbreviation...just as Speed is for Velocity."
 "All expression can be defined within this space of three dimensions.
A mathematical expression is high in discipline but close to zero of
ambiguity and may be anywhere on the scale of communication. Poetry and
painting and music  the arts in general  may be at any point on a scale
of discipline but are never at zero of ambiguity, though they may have
limited value as communication..."
The author of the book was a famous physiologist working on
electroencephalography. His predictions of the future are interesting both
in how wrong they are as well as occasionally how prescient they
were. For instance, he predicts the birth control pill and the fact that
it helps prevent cancer (both science fiction when the book was written,
even if not particularly far fetched) and he was also a bit ahead of the
curve on "free love"...a topic which he seems to have felt very strongly
about. However, I am surprised that a man with his training would not seem
to understand the chromosomal aspects of sex determination in the male
gametes, or that he would claim that "the degrees of living freedom [are]
so few" that when we find life elsewhere in the universe it is almost
certain to be exactly like us with "only trivial differences".
Contributed by
Joel Schneider, Children's Television Workshop
"The artifact of the title is the Von Koch curve, which is well known now in
the fractal business as the snowflake curve. A time machine figures in
the story and is in the shape of a threedimensional snowflake curve. I
asked my eighthgrade teacher what that would look like. She suggested that
I figure it out myself. Working on the problem off and on over several
years, I solved it and that's what started me on the road to mathematics. I
found a copy of the book a copy a few months ago thanks to a used book site
on the web. Rereading it after all these years was fun. There's a moral in
my story for teachers."

This book has also been published as Further Outlook. Contributed by
Prem
Maybe my ratings are little out as I read the book more than thirty years back. Anyway I enjoyed it and the curve is still in my memory and I realy drew it step by step till the pencil and paper could not do the job. Maybe I try on the computer now.

