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From: blostein@qucis.queensu.ca (Dorothea Blostein)
Newsgroups: comp.theory,sci.logic,sci.math
Subject: Re: Question About the Four Color Proof
Message-ID: <786@qusunu.queensu.CA>
Date: 6 Jul 90 17:33:18 GMT
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Organization: Queen's University, Kingston
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Apparently there has been some discussion about the correctness of the
programs used to prove the four color theorem.  As far as I know, there
has not been "a long standing bug in the program which only recently had been
discovered and corrected".  (As Wolfgang Haken's daughter I certainly
would have heard about this from my father.)  There have been long-standing
rumors of unknown origin about errors in the program.  Truly interested
parties can refer to Contemporary Mathematics Volume 98, American Mathematical
Society, 1989.  This 740 page volume is entitled "Every Planar Map is Four
Colorable", by Kenneth Appel and Wolfgang Haken.  This volume reviews the
proof and gives a detailed account of the nature of the errors that have
been found, when they were found, how long they took to repair etc.
Independent implementations of the necessary algorithms have been used
to verify the correctness of the program results.

I'll end with a  quote from page 22 of the above-mentioned volume:

"How does one go about checking a 400-page unavoidability proof for a set of
1476 configurations?  J. L. Doob, the most eminent probabilist we know, has
stated Doob's Rule: 'If you open a mathematical paper at random, on the
pair of pages before you, you will find a mistake.'  (A weaker version of
Doob's rule replaces the words 'you will find a mistake' by 'there is
a mistake'.)   ...
When the proof was announced in 1976,  Doob offered Haken a bet that within
five months an error would be found.  Haken offered an amended bet that
every error that came to his attention would be repaired within two weeks...
Haken won that bet, ..."