[FOM] A perspective on the thread
ianon at cim.com.uy
Wed May 18 17:42:53 EDT 2011
Some comments on the questions raised by the thread.
During the 1800s Mathematics grew wildly into distinct branches: it is
utterly impossible to grasp the field completely now. What we call FOM
was born at this time.
Today any person trying to master all the mathematical fields fails shamefully.
Let me illustrate my point with a personal anecdote about a field medallist.
I wrote a little paper on semi groups: I used certain invariant
geometry techniques developed by Simon Donaldson and applied them to
I was interested in hearing his opinion, so I sent him the paper.
Soon enough I got a generous response from him: he could not
understand my paper, and told me: "the reason is either my ignorance
about semi groups, or your lack of clarity".
The fact that a genius like Donaldson knew little about semi groups
was surprising to me: I was quite young.
If a mind like that could ignore something as close to his research as
semi groups, imagine the lacunae of ignorance there must be out
So in my view the Foundational work is crucial: any idiot can be a
specialist today, but to do work bringing together different fields is
a real challenge.
FOM does a lot of this encompassing work.
We need people facing up against this difficult challenge of grasping
the mathematical field in its entirety.
Gelfand's lack of foundational knowledge is a pointless argument: how
would Angus Macintyre explain the work mathematicians like Hermann
Weyl and Von Neumann did in FOM?
And a last point: there are a million things we all can't agree on.
But can't we at least agree that Goedel's theorems do not imply the
inconsistency of Peano arithmetic??
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