French Mystics, Martin Gardner, and Transcendentality

[mpd@netcom.com (Mike Duvos)]

An anonymous traveler on the Path writes:

 > Actually, the French group is a subsidiary of our Bavarian
 > operation. However, "centuries" is, well, somewhat
 > inaccurate, though the mathematician who first mentioned our
 > existence about that time has since recanted after a visit
 > from the Elders...

"Centuries" was perhaps an exaggeration.  I first became aware of
the existance of the French group when Martin Gardner published
an extremely interesting April Fool's edition of "Mathematical
Games" in Scientific American a number of years back.

The thesis of his piece was that some very simple expressions
involving transcendental numbers such as Pi and E had been proven
to be integers. When you checked them on a calculator, they did
indeed appear to be exact integers, in spite of a well-known
theorem which claimed otherwise.

The clever trick was that they were of course transcendental, but
differed from integers by a small epsilon far beyond the 15 digit
range of most ordinary calculators.

A number of us were trying to figure out how Martin Gardner had
constructed the expressions he had published, and quickly found
that doing so was a non-trivial mathematical problem.  We were
about to give up when a young associate professor walked in,
picked up a piece of chalk, and demonstrated a really clever
trick involving rings which permitted one to crank out such
expressions with the greatest of ease.

When we inquired as to the origin of the work he was citing, we
were told that this really clever mystical order in France had
recently decided to release this particular discovery into the
public domain, where it had served as the source for Martin
Gardner's baffling column.

Perhaps they will give us a factoring algorithm if we ask them
nicely. :)

-- 
     Mike Duvos         $    PGP 2.6 Public Key available     $
     mpd@netcom.com     $    via Finger.                      $