[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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