FOM: I have no problem with "basic" questions requiring arcane and JSHIPMAN at
Wed Oct 22 16:47:23 EDT 1997

technical concepts to be answered properly -- it is more
interesting if they do!  But it's not unfair to require the
statement of Faltings's result to be intuitively clear before
admitting it has as much general interest as Matiyasevich's; the
truly fundamental question here is "how many solutions do
polynomials have" and Faltings's result is a partial answer
because it does not apply to large classes of polynomials.
Matiyasevich's result is a complete answer (of a slightly dif-
ferent question) and is therefore as fundamental as the question
is (though more technical).  This is not to slight Faltings; his
theorem is more impressive as a piece of mathematics!--J Shipman

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