FOM: Suggestions to improve Hersh's definition

[JOE SHIPMAN, BLOOMBERG/ NEW YORK]

   I don't think including arithmetic is right, that would exclude some things
like synthetic geometry if they were carried on in isolation (as they are in
10th grade math classes where only the geometrical and not the arithmetical
part of Euclid is used).  As you point out, you don't want to require a unified
mathematics, individual branches carried out on their own are OK.  I think you
need two more pieces: 1) a distinction between investigations and proved results
2) a requirement on communicability of proofs (i.e. they must be publishable,
in some archivable form such as print or videotape)--you don't need to talk
about deductive systems, you just need a proof object which on its own is
capable of inducing the reproducibility and consensus.
   The chessplayers individually develop their intuition so they know a
proposition is true, but it's not strictly communicable even in interactive
form--I can't convince you White doesn't lose the initial position by playing
you with White and always at least drawing, if you are a good enough player to

regularly beat me even when you have the Black pieces.      Regards--Joe


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Any two bounded subsets of 3-space with nonempty interior are equidecomposable.