FOM: social construction of mathematics?

Julio Gonzalez Cabillon jgc at
Thu Mar 19 20:50:41 EST 1998

Dear Reuben,

      On Thu, 19 Mar 1998 09:32:16 -0700 (MST) you wrote:
| ...
| The answer that math is uniquely specified as that study of human
| ideas which has science-like reproducibility and consensus was my
| own answer to that question.
| ...
| The only one in my view who actually dealt with it was Shipman,
| who showed it failed to distinguish math from chess.  I responded
| by saying that my criterion singled out math and math-like
| activities such as chess. I left it to Shipman, as a certified
| chess whiz, to figure out the difference between math and chess.
| I haven't heard from him about that.
| ...

Some chess propositions *are* THEOREMS (in the math sense) within
the theory of the game, some are plausible CONJECTURES, some are,
up to now, unclearly valued propositions (uncertain positions).

Professional chessplayers (say Shirov, Anand, ..., Deep Blue!)
possess an extraordinary "intuition" (whatever this means) in so
far they "know" when the "plausible conjectures" are theorems
(= winning positions) even though there were no (formal) proofs
yet available for them. These professionals are capable of showing
how these conjectures can be turned into chess theorems just
actually playing the proper moves against any defense chosen.

I agree with Joe Shipman when he remarks:

   ..."prove that if you remove Black's Queen in the initial
   position of a chess game White has a forced win"  -- here
   we are extremely far from anything like a mathematical
   proof but any chess expert is more certain this is true
   than any number theorist is certain there isn't still a
   hidden mistake somewhere in Wiles's proof. The analogy is
   imperfect because with an "n is prime" statement we can
   do better since we have a probabilistic bound."
   [Cf. FOM list, December 16, 1997 / 01:47:58 -0500]

Best regards,

Julio GC

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