Re: Explanations

[William Messing <messing@math.umn.edu>]

I agree with what Andre wrote concerning proofs.

Ronnie, you will certainly recall Grothendieck's letter to you in which
he recalled that at the first Seminaire Cartan he was initially quite
perplexed as to how the singular chain complex of a topological space,
gigantic in size, could possibly lead to concrete computations and
applications.  As he said, he soon realized that it is not the size that
matters, but understanding things properly, that is, in the correct
order or manner.  In the same letter he recalled that initially he was
mystified as to how one would ever be able to make concrete calculations
in etale cohomology, until, after, as he1 put it, several days of
intense thought, he saw that understanding the cohomology of curves,
with perhaps arbitrary constuctible torsion sheaves (torsion prime to
the characteristic of the field over which one is working) was the key.

Concerning proofs constructed by people as opposed to computer assisted
proofs, many years ago Deligne remarked that while he did not believe in
computer assisted proofs, he was not going to look for a counterexample
to the proof of the four color theorem.

Best regards,

Bill Messing

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