Posted: June 15, 2002.
A very interesting article by Professor Doron Zeilberger -though
author seems to be unnecessarily angry at Atiyah. He perhaps expects a
certificate for new areas from people like Atiyah, who are successful
today. But usually it does not happen, people who are successful today
get so involved in enjoying their success that they often get blinded to
emerging new realities and ideas. They wish world to continue as it was
when they succeeded and they think about new ideas with contempt and
people doing it as not of as highest order as they are -so they will
never give such certificates. People who want such certificates -only
thing they get is agony.
Zeilberger's agony is visible in his article. I have seen lot of people
in tifr and other Institutions suffer in similar manner - but on the
other hand those people who enjoy
not only research but changing times and watching this behavior, rarely
get puzzled.
I feel apart from his anger - zeilberger's prediction is very right. I
admire him for writing in hard-core language. I have been saying now for
several years that in very near future new generation of people will be
as much surprised about our spending
so much time and effort in last century on analytical thinking as today
we
are surprised about time spent by scientist and philosophers in earlier
century in religious rituals and thinking. Groups or 4 colour problems
are not the only thing which will change - After all most of scientific
analysis today is devoted to
predicting what might happen in any event or mental logical exercise. If
that
prediction can be obtained with sufficient accuracy by things like
simulation that will replace analytical thinking as main research
activity. People will admire new style much more. But it does not mean
analytical thinking will go away - it may become a little bit like
religion - but still beauty and enjoyment of exact thinking towards
complete truth will remain and many will be attracted to it regards
Navin Singhi
TIFR
Mumbai, India
email-singhi@tifr.res.in
singhi@niksandnids.com
Posted: July 20, 2003.
Hi Doron,
Your opinion towards Atiyah I agree with, but on some conditions.
1. The computer one uses should also be able to represent non-computable notions, like infinite sets, quantifiers, etcetera. For this it is necessary to have some formalizations of proofs (but the mathematician should not be bothered with this more than necessary).
2. The computer should do things in a reliable way. In the light of 1, this means that there should be a small proof-checker (that can on its turn be checked by hand).
3. The user still should be a good mathematician, knowing what a proof is etcetera. Together wit the machine he or she or it may produce new math.
So your other opinion about child abuse I do not agree with. Only after you know what is rigour, one can appreciate math and invent new math. But one should not overdo, as I did 40 years ago.
Now as to Atiyah again, his main point is that he wants romantic proofs.
I feel compassion, as once I was like that too. There is still work to do for the romantic biologists, that prefer to watch birds and catch butterflies over to sit in from of a computer and do gene research. And actually cool mathematics has its romanticism too. No wonder you got an email in favour of your opinion from someone at TIFR, Bombay. In this country they speak about cool lovers, while in the Netherlands they like it hot.
But the last month the whether showed that the meteorological climate definitely changed: hot for a long long times. So soon our lovers will be cool as well.
Best regards, Henk