[FOM] Is anyone working on CH?
Timothy Y. Chow
tchow at alum.mit.edu
Mon Oct 22 17:10:13 EDT 2007
Arnon Avron wrote:
>BTW: I have already said on FOM that for me FLT will be considered proved
>only when it reaches the point when the proof is presented in a textbook
>style so that any mathematician who wish to devote a reasonable time for
>it can follow and check the proof for himself. I take it as unbearable
>and against the whole spirit of mathematics that someone like John
>McCarthy would say that he knows he will never be able to understand the
>proof (as he said here on FOM not long ago). A proof that is accepted
>only because of the authority of some experts and is not really
>accessible to the majority of mathematicians is not a proof yet (and most
>probably, may I add, contains some very-difficult-to-spot subtle
>mistakes).
I agree that any indigestible proof admits room for improvement. But why
do you say that such a proof is *not even a proof*? Are you worried only
about possible error and reliance on expert authority? Then consider, for
example, the four-color theorem. That is still not at the point where any
single human being can check every detail in a reasonable amount of time
without any electronic assistance. While, as I said, this situation
leaves room for improvement, would you say that the proof of the
four-color theorem is *not a proof*? There is now a fully
machine-checkable proof of the four-color theorem, and so the possibility
of a mistake is infinitesimal. On what basis would you declare (if indeed
you do declare) that this proof is *not a proof* (as opposed to an
*unsatisfying* proof)?
Tim
More information about the FOM
mailing list