[FOM] Great Achievements of F.O.M. 1

William Messing messing at math.umn.edu
Mon May 23 09:48:02 EDT 2011

With regard to Harvey's opening paragraphs concerning how FOM is viewed 
in Mathematics Departments in the United States, I think that there is 
some truth, but what is stated appears to me to be a caricature of the 
more complicated reality. 

Mathematics, like other academic and intellectual activities, as it is 
done by people, has fashions, styles, ....  The same applies to FOM, 
Philosophy, ....  But it is not correct to believe that all subjects 
outside FOM are treated equally in all mathematics departments.  
Particularly these days when many Universities are having financial 
trouble, the problems that have "always" been present, become worse. 

Consider, for example, the question of pure versus applied mathematics.  
It is obvious that each of these is more interested in recruiting 
colleagues who work within their domain.  Within pure mathematics, there 
are many who think that arithmetic geometry, in particular over fields 
of finite characteristic, is not serious mathematics.

The following anecdote, where I do not reveal the names (as FOM tends to 
censor what it regards as too "frank") is, I think, revealing.

Twenty years ago, I approached a colleague who works in non-linear PDE 
with a strong emphasis on its applied aspects, and told  him that a very 
distinguished French mathematical analyst, X, would be visiting our 
department for a month.   My colleague immediately responded: "X works 
on ODE, which is completely trivial."  I told him that X is, in fact, 
most famous for his work in PDE.  To which my colleague responded 
"Linear PDE, that's also trivial."

I am sure that many of us can recount such anecdotes. 

My sense is that Voevodsky's interest in foundational questions is a 
positive sign for FOM.  Those who have posted on FOM critically with 
regard to "his understanding or lack of understanding" of Goedel's 
second incompleteness theorem seem to  have not understood that 
Voevodsky's interest in foundations is very positive for the FOM 
community.  The fact that there will be a special year at the Institute 
for Advanced Study devoted to his "univalent foundations" project is, in 
my view, a very exciting prospect for FOM.

Bill Messing

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