[FOM] on Harvey Friedman's Re "Harvey's re effective number theorists"

Gabriel Stolzenberg gstolzen at math.bu.edu
Sat Apr 15 14:56:42 EDT 2006

   To get this out more quickly, I'm going to do it in installments.
This is the first.

   I begin with a quote in Harvey's message of April 13 from mine
of April 12.  This is followed by Harvey's comment on it and then
my reply.

> >  Harvey seems to be right about Roth's theorem and Falting's.

> I have been constantly arguing with people on the FOM from its
> beginning in 1997 till this day. I don't recall a SINGLE case where
> someone has openly and unequivocably stated that I was right about
> a matter that was not completely formal. You have come as close as
> anyone (but note your word "seems").

   Harvey, initially, I didn't have "seems" but when I thought more
about it, I decided that it would be dishonest to omit it.

   I wished to acknowledge that your evidence---quotes, titles from
the literature and a helpful comment by a number theorist---has a
plausible reading that is consistent with your position.  I saw much
interest in bounds and nothing that indicated that the interest in
possibly unrealistic ones was anything more than "intrinsic."

   However, for several reasons, this is not enough for me.  For one
thing, I don't see how my experience with these matters (in the '70's),
which made a strong impression on me, fits with your view.  This is my
problem, not yours.  But the disconnect is too glaring for me to ignore.
I would need an account of how number theorists got from there to here.

   My most important reason for reserving judgment is my memory of
the considerable discipline that it took to develop a constructivist
mindset and, after I had, finding that almost everything that I had
recently believed about it was false.  If I want to make sure that I
get the number theorist mindset right, I have to be prepared to do
something similar.

   To be continued.

   With best regards,


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