[FOM] Is anyone working on CH?

Martin Davis martin at eipye.com
Sun Oct 21 16:12:02 EDT 2007

Arnon Avron wrote:
 > One remark: one way in which it has already affect
 >"normal" mathematics is by throwing from it propositions
 > that have been proved to be undecidable. Are there now
 > (what you call) "normal" mathematicians that are trying
 > to solve the problem of CH? Will anybody put it now
 > anywhere on the list of the most important open problems
 > of mathematics? Yet CH certainly was a problem of
 > "normal" mathematics at the time Hilbert formulated his
 > famous list of problems!

My answer to the two questions you raise is: Yes, yes!

Hugh Woodin has been carrying out a fascinating 
attack on CH. You can read about it in two recent 
numbers of the Notices of the AMS, hardly an obscure publication.

Gödel certainly regarded CH as one "of the most important open problems
of mathematics" and, diffidently mentioning 
myself in the same sentence, I do too.

Arnon, you mention elsewhere Fermat's last 
theorem. As I'm sure you know, the proof of FLT 
that was found is not even formalizable in ZFC, 
going far beyond the bounds you suggest as 
already causing trouble. (ZFC + an inaccessible 
will do.)  I haven't heard any mathematicians 
question whether FLT has indeed been proved because of this.

People who have thought about the matter suggest 
that using various work-arounds  the proof could 
be brought down to something like 3rd order 
number theory. Is it really so improbable that FLT is unprovable in PA?

BTW I share your dislike of the term "normal mathematician".


                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at eipye.com
                          (Add 1 and get 0)

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