FOM: Questions for Hersh
rhersh at math.unm.edu
Fri Jan 23 08:01:57 EST 1998
Yes, you're right. My characterization of math does not exclude chess.
Thank you for pointing out this oversight.
I'm sorry to give up the present characterization. It is succinct and
catchy. But you have shown it is incomplete.
No doubt there are several remedies.
One natural approach would be to put in something about a deductive
system, which I think is traditional. However, this slights the
essential role of intuition and conjecture. Also, I don't want
to exclude Egyptian and Babylonian (and other) non-deductive
mathematical practises from inclusion as mathematics.
Another natural approach would be to put in something about
physical interpretations. I am aware of the tremendous importance
of physical interpretations in the development and social acceptance
of mathematics. Still, I don't want to make it part of the definition.
I can imagine an isolated school of mathematicians who know nothing
and do nothing but analytic number theory (which I presume can
be a reasonably good example of pure math without physical interpretation;
if you disagree, think of something else.) Such work on a pure
subject free of applications would still be acknowledged to be
I propose adding the inclusion of arithmetic as the distinctive feature of
mathematics vs. chess and any other chess-type counterexamples you
have up your sleeve.
This presupposes knowing what arithmetic is, which I think is not
a problem. But we now have a two-stage characterization, first
arithmetic, then the rest of math, which is not very appealing
Thanks for your help.
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