[FOM] extramathematical notions and the CH
Ignacio Añon
ianon at cim.com.uy
Tue Jan 29 21:31:54 EST 2013
Joe shipman wrote:
"Physics may have much to teach us about math, but in my opinion it
will have nothing to say about non-absolute math like CH. I would be
very interested in criticisms of this opinion."
This is an interesting question. May be in the future we'll have
precise methods to determine whether a given problem is natural or
not, but we don't have that yet.
Could physics shed light on the naturalness or unnaturalness of
certain FOM problems? If it can, it's difficult to imagine that this
would take the shape of anything other than finitary methods.
To mathematicians like Gelfand CH was uninteresting as a problem: he
evidently saw it as unnatural non-absolute math in the sense Joe
shipman means.
Gauss famously never read the letter Abel sent him about the
insolubility of quintic equations: to Gauss algebraic solutions were
trivial and artificial: he thought real mathematics was done by people
like Eisenstein, and, of course, himself.
There seems to be a philosophical divide here, but it's unclear what
that divide is.
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