FOM: an application... A Suggestion...

[Steve Stevenson]

Prof. Simpson:

Hm...I didn't see Prof. Soare's responses in such an incendiary
way. Regardless, I think we're getting off track. I think it might be
useful to discuss where this list is headed and what are the global
issues.

If one looks at the mailing list from the good Major, one is struck by 
the intellectual potential of the readership. This seems like a
historical chance to understand the state of mathematics at the
beginning of the 21st Century --- Hmmm. didn't some guy by the name of 
Hilbert already try this last century? :-). It also provides us with
an opportunity to perhaps set the agenda in the foundations for a
fairly long time.

If we lightheartedly call this the "Children of Hilbert" (or "son of
Bourbaki" in my case) Project, it seems to me that this communications 
medium allows us to ask and cogently discuss three historically
important questions:

	1. What are the problems driving foundational thinking? We've
	   seen a lot of ideas on this list, but do we have a problem
	   list? 

	   How broad is the field? For example, do we consider the
	   conduct of mathematics and computation fair game?
	   Tymoczko's *New Directions...* is certainly well worth
	   discussion as an agenda setter.

	2. If we picture mathematics as a map, with theorems (great
	   and small) as topographical figures and methods of proof
	   labeling the "roads", then how much of the map is known?
	   (See 4.)

	3. Mathematics has traditionally oriented to method rather
	   than problem (science is the other way 'round). Engineers
	   always joke about "To a researcher with a hammer, the whole
	   world looks like a nail." So what are all the hammers? How
	   are those hammers justified?

Prof. Friedman has his list of self-containted messages. This has been 
a great service to the list. But with such a broad readership --- even 
given any individual's credentials --- it is possible to be clueless
in certain areas. I suggest we take up the areas (And certainly, this
is not an exhaustive list) and let folks organize by interest. 

Best regards,

steve
-----
Steve (really "D. E.") Stevenson           Assoc Prof
Department of Computer Science, Clemson,   (864)656-5880.mabell
Support V&V mailing list: ivandv at cs.clemson.edu
------------------------------------------------------------
Stephen G Simpson writes:
 > In his extremely long and angry FOM posting of 2 Aug 1999 12:54:07,
 > Soare demanded that reverse mathematics justify itself in terms of
 > applications to computer science and core math.

 <no need to repeat it all>