FOM: More on chess and math

Fri Mar 20 00:22:04 EST 1998

CHess propositions are obviously mathematical, and we know what a mathematical
proof of one would be like.  These proofs only exist in endgame theory and
forced-mate chess problems, but there is what Ilan Vardi calls a "technical gap"
--we accept as axioms propositions we "know" to be true as chessplayers but
cannot prove mathematically.  It is not inconceivable that in the next century
some of the easier "axioms" like (Q)"White wins when receiving Queen odds" will
with the aid of computers be proven mathematically (at least in the same sense
the 4-color theorem has been proven).  Chess is a very good game because the
proposition "the initial position is drawn" is probably not feasibly decidable.
(On the other hand, (F)"The first player does not lose" is conceivably feasibly
provable in chess and quite likely to be feasibly provable in  Go by  "strategy-
stealing" arguments that rely on the symmetry of the initial position).  This is
not where chess essentially differs from math.  What is different about the
process by which chessplayers become convinced of propositions like Q or S?
It's introspective--independent communicable "proof objects" aren't available.JS

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