FOM: suspect

[Lou van den Dries]

    My name is Lou van den Dries, I am a professor of mathematics 
at the University of Illinois, and my interests include FOM. 
    I would have reacted earlier to some recent messages of Harvey, 
but I broke my right arm a week ago in a stupid accident, and had to 
take it easy for a few days. Let me get back into the ring. 
I won't descend to the level of Harvey's message to Thayer, but will 
otherwise not mince words, following the example of the "new rules" message.
    Below GII refers to "general intellectual interest".

   Previously I called Harvey's notion of GII suspect.
In an earlier round when Harvey and Steve appealed to GII, 
their ultimate recourse was: "you just don't get it", and "you are
congenitally 
incapable of grasping certain basic facts". (Addressing Anand and me, I
believe.) 
They, Harvey and Steve, claimed to be experts on the matter of GII, 
and we, as "pure mathematicians", had lost or had not developed these
instincts. 

   My *experience* in the course of 30 years has indeed made me suspicious of
certain wide spread instincts that Harvey and Steve may have in mind here, 
and which I share: these instincts, covered by a thin veneer of questionable 
philosophy, are often used to justify ignorance of major developments in 
mathematical thought of the last 200 years that are outside of the
*relatively minor* 
and *exceedingly familiar* FOM-line:  Cantor, Frege, Goedel, ...  
Agreed, the basic ideas of this last line are of fairly general
*mathematical* interest, 
and easy to grasp (since one starts from scratch), but I consider it
preposterous to 
claim that the more recent development in the FOM-line (reverse math, for
example) 
has this "general interest" character with respect to mathematics and
computer science, 
let alone science in general. This is not to deny certain virtues of FOM as
pursued 
by Harvey and Steve: I do value the connections to certain parts of
combinatorics, 
but why exaggerate the (future) impact of this on the rest of mathematics?
   By the way, I do consider P=NP as of general mathematical interest, and
recognize 
that the origin of this problem is partly in FOM (and partly in number
theory and 
computer science), but present research around P=NP can hardly be claimed
under the 
FOM flag (and probably Harvey doesn't.)
   In one of his last messages Harvey puts forward an astonishingly
ambitious goal
for his intellectual activities: to make it possible that those of us with
intellectual 
gifts can become once again as Aristotle and Leibniz were in their time,
rising far 
above the level of being only an expert in a *relatively* small area.
Fantastic! 
This would surely be of revolutionary significance. But from what i know of
Harvey's 
work in FOM, there is *nothing* there to make this ambition remotely
plausible even 
with respect to, say, the major accomplishments of mathematics as of 1900. 
On the contrary, FOM-preoccupations tend to make it harder to catch the
spirit in 
which math is and was done, and is best understood: I have been thoroughly
exposed 
to FOM throughout my career, and to other parts of mathematics as well, and
I have 
experience in relating the two, as to their various claims and ways of
doing things.) 
  And mathematics is only a small part of the big picture Harvey conjures up! 
  Actually, I think it would be an interesting project to equip the average
research 
mathematician of today with the mathematical knowledge, and more
importantly, the 
mathematical flair and instincts of, say, Hilbert and Poincare, to mention
the most 
prominent mathematicians of 1900. This would perhaps be a doable project,
but of a 
much more modest scope than Harvey's. FOM would play a role, but in my
opinion not 
a dominant one, in this limited enterprise. 
   Harvey's reactions to Franzen and Thayer (followed by the promulgation
of the 
"new rules") have confirmed my other suspicions on Harvey's GII, which
Thayer made 
explicit: clearly, Harvey's appeals to GII are often mere bluff and bluster, 
a stick to hit the opposition with. 
   Nothing wrong with blustering on your own FOM list where you are the boss 
(as someone reminded us a while ago), though I wonder if this is how you sway
serious intellectual opinion to your side. But why claim that the other guy 
(me in this case) must be the only one on the fom-list to doubt that certain 
FOM matters are GII-stuff, when you surely know better? The messages of
Thayer and 
Franzen immediately refuted that particular claim. Does that explain the
savage reaction?
 
Lou van den Dries