[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 

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)?


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