[FOM] comment on the video of the lecture by Voevodsky at IAS
William Messing
messing at math.umn.edu
Mon May 16 17:52:05 EDT 2011
Unlike Neil Tennant, I was not unhappy with Voevodsky's lecture. His
point was not to give an expository lecture on Goedel's work of 80 years
ago. It is clear to me that he could have stated Goedel's second
incompleteness theorem in a completely rigorous manner. This was not
the point of his lecture. Rather it was to address the question of how
mathematics can and will survive if it is found that first order
arithmetic is not consistent. His program for approaching this
question, partially amplified in his December 10, 2010 Institute lecture
on univalent foundations (and available on Voevodsky's home page).
Tennant wrote: If a Fields Medallist working in algebraic geometry and
homotopy theory is able to give an account of GII at only such an
amateurish level, what hope is there for the future of fom in
Departments of Mathematics?
Let us turn the question around and ask whether an expert on the
foundations of mathematics would be less "amateurish" if explaining the
work of any Fields medal winner, except for Paul Cohen.
Voevodsky is not a fool and has been seriously thinking about new
foundations for mathematics, based upon a formalization/axiomatization
of "the world of homotopy types, as opposed to "the world of sets".
Bill Messing
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