FOM: Re: Einstein, Godel, Turing, Hardy

[Mark Steiner]

	On the aesthetic component of mathematics: I attributed to Hardy the
view, not that aesthetic criteria are useful in evaluating mathematics,
but that aesthetic criteria are actually used in deciding whether or not
concepts count as mathematical concepts or not.  These criteria might
govern the concepts themselves, or the reasoning (theorems, proofs)
these concepts support.   Hardy seems to take an extreme view, according
to which aesthetics is the ONLY criterion, and according to which
applied mathematics is ugly and not mathematics.  Otherwise, however,
the idea that the reason why chess is not mathematics (for example)
involves aesthetics essentially is a very widely held view among great
mathematicians and scientists like Von Neumann, Dirac, Wigner, and many
others.  In fact, I interviewed many mathematicians on this subject
while I working the applicability of mathematics as a philosophical
problem,  and I never heard anything different.  What Harvey says
doesn't really contradict this formally, since I'm talking about how
mathematics is defined in fact, rather than how it should be defined.
This definition will affect what gets published and who gets tenure and
prizes.  I believe this view is consistent also with what Charlie Silver
says.
	As for the EVALUATION of mathematics as beautiful, and thus having
g.i.i., and I strongly agree with Charlie that this is a different
issue, I should add that there is already a philosopher of aesthetics
(in our department) who ranks mathematical achievements alongside great
works of art such as paintings, symphonies.  He even uses the beauty of
mathematics to bolster his view that beauty is an objective property
(aesthetic realism).  Whether I agree with the philosophy is not the
point here: he appears on TV and radio and in the media, and expresses
these views with great vigor.  I believe he thus increases the g.i.i.
even among the general public who are incapable of appreciating directly
what mathematicians are doing.