Short story (Analog Science Fiction/Science Fact, October 1978 Vol. 98 No 10) concerning the very nature of mathematical discovery. It was later rewritten in the form of a play, which the author has graciously allowed me to freely distribute here.
I enjoyed reading the play very much. The joke about the mathematical
universe being filled up with infinite series is funny, even if the
mathematician in me can't help but say "Wait, that doesn't make any sense."
The portrayal of the mathematician, in many ways, is very realistic even if
not flattering. However, my main objection is that this story (actually,
all I read is the play) creates the impression that mathematicians do not
think of coming up with axioms as creating a universe from scratch. Of
course, that's what it is and that is one of the joys of mathematics (just
as one of the wonders of mathematics is that we seem to be able to
find so much application for these fantasy universes in our real one).
Dr. Kasman:
I was delighted to come across your website for reasons that I suppose
are obvious, as the author of one of the stories you list, above. Obviously
I have a great interest in mathematical fiction, so I'm happy to have a
site
that has compiled such fiction, but of course it's nice to have my story at
least see a bit of the light of day.
As per your request [I merely posted a request for information about the
story in this location. ak], I can't exactly evaluate the story objectively, but
I can indicate what it's about and how mathematics plays a role in the
story, as described below.
"Art thou mathematics" is concerned with the nature of mathematical
objects as well as the process of mathematical discovery (or invention,
which is part of the point of the story). The plot hinges around the
rather
whimsical question of "where" mathematical space is, and whether
mathematical space can actually contain the mathematical objects assigned
to
it. The central plot element is that at some point (in the near future,
presumably) it becomes clear that new mathematical discoveries are no
longer
being made, and that in fact new calculations can't even be carried out;
the
story itself takes the form of a mathematician recounting to an
investigative committee how he determined what the problem was, and how he
addressed the problem. The key mathematical concept developed in the plot
is
the concept of transfinite mathematics, which Georg Cantor developed to
demonstrate, among other concepts, that there are different sizes of
infinity.
I might add that a few years ago I rewrote, and in my opinion greatly
improved, the story as a play that was performed offoffBroadway here in
New York City. While still concerned with the basic questions of discovery
in mathematics, the play also works as a satire of academic life (I'm an
academic too, though I'm a professional biologist: my interest in
mathematics is more of a hobby). At least the satirical part of the play
went over very well to audiences, and at least a few people seemed
genuinely
excited by the concepts.
Thanks again for your wonderful site.
Sincerely,
Charles V. Mobbs, Ph.D.
Associate Professor
Mt. Sinai School of Medicine
New York, NY 10029

Note: In the play, the mathematician introduces the idea of
uncountable infinities in order to explain how there can be a proper
infinite subset of an infinite set. In fact, there is no need to introduce
Cantor's ideas of infinity here. The fact that infinite subsets do not
have to be the entire set are clear from examples involving only positive
integers. For example, notice that the powers of 2 (2, 4, 8, 16, ...) is
an infinite subset of the set of positive integers, but that doesn't mean
that all positive integers are powers of two!
