[FOM] Re Timothy Chow's Re on harvey friedman's number theorists (8 Apr) Part Two

Gabriel Stolzenberg gstolzen at math.bu.edu
Sun Apr 9 20:09:47 EDT 2006

   After submitting a reply to Harvey Friedman's message about number
theorists'interests in "effective" bounds and algorithms,  I realized
that I hadn't been sufficiently careful about this in my reply to Tim
Chow.  I want to try to correct this here.

   Tim wrote:

> > and you'll quickly find that even the papers that don't have the
> > words "effective" or "explicit" in the title are deeply concerned
> > with effective methods in Diophantine approximation.  For him, a
> > nonconstructive theorem such as Roth's theorem is little more than
> > a starting point that guides his search for effective (and better,
> > computationally efficient) methods.

   And I replied, in part:

>  Tim, you're talking about "effective" and "computationally efficient"
> methods.  That's great stuff.  I'm with you.

   But in saying this, I ignored the fact that, in the statement above,
"effective" is somehow less good than "computationally efficient."  In
which case, I need to know what is meant here by "effective."

   Gabriel Stolzenberg

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