[FOM] "Mere" correctness of a proof
Timothy Y. Chow
tchow at math.princeton.edu
Sat Sep 1 16:38:08 EDT 2018
David Fernandez Breton wrote:
> Although correctness in mathematics is not negotiable, and it
> constitutes a "sine qua non" of mathematical practice, I believe (and
> I'm sure others will agree) that correctness, by itself, is worth very
> little, if it's not accompanied by some aesthetic appeal and sense of
> understanding. A proof of the RH of which we do not understand anything,
> other than the fact that it is correct (as witnessed by some
> computerized proof checker) will probably not be very valuable (cf. the
> proof of the four colour theorem).
It would be worth at least $1 million.
More seriously, "mere" correctness serves the valuable function that it
will convince the mathematical community to study the proof, and extract
whatever value can be extracted from it. The issue with a purported
solution of a famous problem that is difficult to read is that the
potential reader has to deal with the nagging suspicion that the proof is
wrong and therefore studying it will be largely a waste of time.
Tim
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