What is a proof?

Harald Hanche-Olsen hanche at math.ntnu.no
Mon Sep 10 12:14:53 EDT 2007

+ "James A. Donald" <jamesd at echeque.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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