Date: Fri, 15 Jan 1999 14:15:56 -0500 (EST)
From: "Daniel H. Gottlieb" <gottlieb@math.purdue.edu>
Subject: answer to Ronnie Brown's posting.

********************************

Ronnie Brown wrote:

<<On the other hand, I ask colleagues the following questions:

If you study subject X at University, is it reasonable that at the end of
your studies you should have be able to answer:
A) What are the objects of study of X?
B) What are the methods by which these objects are studied?
C) What are the main achievements of X?

One distinguished colleague at another University said he would have
difficulty with question 1! This is interesting, since how can we
persuade Governments to support maths if we cannot answer these questions
in a convincing way to colleagues and to students? Tell me!

Do people think Questions A-C are reasonable?

......

I also find myself asking basic questions on the aims of topology, and
the fundamental structures to be used in pursuing these aims.
...
>>

I think Questions A-C are reasonable. My answer to question A) for
X = Mathematics is that Mathematics is the study of well-defined things.
I thought of this answer over ten years ago, and I analyzed it and compared
it to what we are doing and to what happened in history. Nothing I have
found has convinced me otherwise.

Advancing a point of view such as "Mathematics is the study of well-defined
things" brings in its train a series of questions, such as:
Are chess problems Mathematics? ; or Is the concept of well-defined things
well-defined? . An indication of the strength of my answer to A) is that my
answer to these and similar questions are such that as time goes on I find
myself unable to believe that I entertained serious doubts about their
answers.

My answer to A) for  X = Topology  is that Topology is the study of
continuity.

Dan Gottlieb
gottlieb@math.purdue.edu