Newsgroups: sci.math
From: hoey@ai.etl.army.mil (Dan Hoey)
Date: 24 Jul 89 16:25:19 GMT
Subject: Re: Clicking on Irregular Shapes (and the four color problem)

jk...@andrew.cmu.edu (Joe Keane) writes:

>hoey@ai.etl.army.mil (Dan Hoey) rites:

>>There is still no real consensus among mathematicians on whether
>>this amounts to a proof of the four-color theorem, though it is
>>certainly very strong evidence for the theorem being true.

>I think any proof is just `strong evidence for the theorem being true'.

I must disagree.  Not that proofs can contain errors--no one denies
that they can.  But a proof is more than ``evidence'', it is evidence
that is understandable, and which has been understood, and which can
be checked for correctness by being understood by other mathematicians.
At least, this is the understanding of ``proof'' that has been held
among mathematicians before it became possible to manipulate the
objects of mathematics without understanding them.

This is my understanding of a viewpoint that was hotly debated when
Appel and Haken's results first came out.  I have not followed the
course of the debate over the years, but I have heard that the furor
is dying down not so much by conversion, but by attrition of the more
conservative viewpoints.

I did not, and will not, participate in that debate.  It is a topic
for philosophers of mathematics, which I am not.  I am presenting this
only to sketch a distinct opinion.

Dan