From: wilson@kusm.kyoto-u.ac.jp (Steve Wilson)
Date: 25 Jan 1999 02:01:02 -0000
Subject: for the list

RE:  What is math?

Last Fall I was asked by my son's previous year's
kindergarten teachers how they should answer the
question:  What is math?  While at Oberwolfach, I bugged
my colleagues, some of whom have already responded to
the question here, about the issue.  I found them quite
reluctant to even discuss the question, although generous
quantities of wine helped.

5 year olds and faculty in other departments (a la
Clarence) deserve reasonable answers and will punish us
if we don't produce.

Some put forth answers which they would go berserk about
if a nonmathematician said them:  e.g. math is a language.
Several structuralists put forth answers of the type "the
study of well defined objects" to which my gut response
is YUCK!  There is more to math than thought process;
taste, beauty and content are relevant.   At any rate,
there was no consensus on what math is and my view
was as easily dismissed by others as theirs was by me.

One thing that is clear:  math is an activity.  This will
come as a shock to most nonmathematicians and so perhaps
should be emphasized.

I was not happy with what most of my colleagues thought
math was, however, there were a few who saw eye to eye
with me.   I do agree that the way of thinking should be
part of the definition, but that we should be thinking
about something.

So I liked a couple:

Investigation of shape and arithmetic.

Math is the SEARCH for PRECISE language to discuss spatial
and quantitative relations.  (an emphasis on both search
and precise)

My summary to my son's teachers:

Now that I have taken another look at the product of my
discussions, I feel that thinking (logically, precisely,
systematically  ??) is certainly part of the definition.
However, one must have something concrete to think
about and in math that is space, geometry, numbers,
relations, patterns, etc.  Math is being able to talk
about such things precisely because some truth has been
exposed, i.e.  understanding; a product of exploring,
discovering and creating.  Certainly communication is
an important part of math.  It does no good to say "wow,
I see the connection" if you cannot show the connection
to someone else. This communication is what we call PROOF!

My summary to the list:

So, personally, math is our attempt to understand numbers
and geometry.

(here both number and geometry are in the broad sense)
(understanding is crucial, we are not just here to gawk
at pretty patterns;  understanding includes that business
about thinking logically and precisely) (our attempt:
math is an active struggle) (this certainly includes chess
under the heading of number and/or geometry).

Steve Wilson


W. Stephen Wilson                   (410) 516-7413
Department of Mathematics      FAX  (410) 516-5549
Johns Hopkins University
Baltimore, MD 21218               wsw@math.jhu.edu

http://www.math.jhu.edu/~wsw/math/wswmathhome.html

email in Japan:  wilson@kusm.kyoto-u.ac.jp
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Address until the start of September, 1999.

W. Stephen Wilson
Department of Mathematics
Faculty of Science
Kyoto University
Kyoto, 606-01, Japan

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