Date: Sat, 23 Jan 1999 09:17:01 +0900
From: Andrzej Kozlowski <andrzej@tuins.ac.jp>
Subject: Re: Klein's  comments

Actually I honestly do not think I have ever met a mathematician so
simple minded and lacking in introspection that he would never consider
the question of the nature of his subject and of what he is doing. John
Klein might be the first one but I simply do not believe him. In fact
almost everybody starts thinking about these questions as an undergraduat
e or before and keeps coming back to them from time to time for the rest
of his life. The problem is, however, that one soon discovers that
frustrating fact that there is apparently no connection at all between
being good at mathematics and being able to give good answers to such
questions. In fact, almost all answers given sound  as if they were
cribbed from our  predecessors and  seem either trivial  or vague and
based on "not well defined" concepts, which we associate with woolly
minded humanists. So at this point we tend to react like (I think) Gauss
did in the case of the Fermat conjecture: when you can't solve a problem
declare that you never had any interest in such an unimportant matter.
However, I think this matter is becoming vitally important, more than at
any time in history. I once heard Atiyah say that if human beings
naturally  possessed great computing abilities they would never have
developed mathematics (he was not retired then).  Well now we are on the
verge of acquiring such abilities. Here in Japan the process is clearly
visible: in a number of smaller universities mathematics departments are
being abolished and replaced by "information science". Nobody seems to
care about this much because they are still doing what they were doing
before, but the next generation will be different. From what I hear about
the reforms in math education in US schools I also get the impression
that mathematics is also being replaced by some other subject, though I
find it difficult to determine what it is. It seems to be a much more
tolerant one, in which there are "no right or wrong answers".  Anyway, I
am convinced that computer  or information science is now becoming a
deadly threat to mathematics. Unless we can justify what we do in
relation to what it does and show in what respect we are not replaceable
by them, we will be replaced. If fact I believe that to survive
mathematics will have to reclaim back those aspects of computer science
that properly belong to it and make the ever growing influence of
information technology work for it and not  against it.
There is an interesting sub-question: does it all have anything to do
with topology? Personally I think it does, but I guess I had better stop
here. I have to go back to my main  preoccupation these days: the nearly
impossible problem of computing the likely value of my retirement pension
in 2024.


Andrzej Kozlowski

___________________________________________________
Date: Sat, 23 Jan 1999 11:27:37 -0500 (EST)
From: "John R. Klein" <klein@math.wayne.edu>
Subject: Re: 4 responses to Klein

If I've managed to offend anyone (it seems that I have), please
accept my apologies.

John Klein