Re: What is a proof?

+ "James A. Donald" <jamesdecheque.com>:

> If a proof is a record of a mental journey in which one
person has
> discovered an important truth, and then made a record
of that
> journey adequate so that a second person can walk the
same path and
> see the same truth, then cryptography could do with
more and better
> proofs.

As a mathematician with a somewhat limited knowledge of
cryptography
(and hence mostly a lurker on this list), I feel strangely
compelled
to respond.

First, I like your metaphor.  If I might build further on
it, it would
be to point out that the first person to explore unknown
terrain often
finds the journey ardous and difficult: He ends up scaling
vertical
cliffs and crossing raging rivers, only later to discover
that there
was an easier path.  Should he not then record the easier
path, rather
than the difficult one that he himself followed initially?

> If, on the other hand, a proof is an argument
impressively decorated
> with mathematical sounding jargon, cryptography could
do with a good
> deal fewer of them.

Agreed.  But sometimes what may seem like jargon made to
impress is
more analogous to a road, or maybe an all-terrain vehicle,
that makes
the wilderness available with less effort (and incidentally
makes it
less wild, but maybe this is where we should leave the
metaphor
behind).  There is nothing wrong with jargon and big
theories if they
fill a real need other than inflating the ego of their
originators or
scaring away outsiders.

- Harald

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