Sarbajit,
My take is that contemporary abstract mathematicians have no interest
(as mathematicians) in discerning "truth". "The truth" about existence
is the business of scientists, philosophers and theologians.
Ever since Hilbert's program at the beginning of the twentieth century
to "axiomatize" all of mathematics in the manner of Peano (help me out
here, mathematicians), pure mathematics has been seen as an abstract
exercise in taking arbitrary sets of postulates and reasoning therefrom
- without regard to their "truth". The only value judgment involved is
whether the results (the theorems that ensue) is "mathematically
interesting" - not whether the results matches someone's idea of
"reality". If physicists (or anyone else) want to come along and apply
some of these models to their interests, then so be it. But proximity to
"reality" is not the criteria mathematicians necessarily use for
deciding what to pursue.
The switch from mathematics being seen as "science" to what I have
described above is well epitomized by what happened in plane geometry
during the middle of the nineteenth century. Compare Euclidean,
Lobachevsky and Riemann geometries. The idea began to emerge to play
around with different sets of postulates, reason from there (these are
the theorems) and see if you get a result that one can "marvel at".
Grant
sarbajit roy wrote:
Actually I can follow Glen's line of reasoning (I think).
For example, the way Maths works is that a "theorem" is "proved" by
trying to prove a "conjecture". When that approach fails you end up
proving a "special case" of the conjecture - which in turn gets
elevated to its own status as a "theorem". "Proving" Fermat's Last
Theorem took 3 centuries and generated an equal number of theorems for
mathematicians to solve/prove. The ultimate perpetual machine to keep
mathematicians employed till either the existence of "God" (the grand
unified theorem of everything) is proved or we have 33 billion gods
(theorems) as we do in India.
Sarbajit
On Mon, Apr 26, 2010 at 10:15 PM, Russ Abbott <russ.abb...@gmail.com
<mailto:russ.abb...@gmail.com>> wrote:
I don't follow Glen's 'You can't generalize across all of
math/logic to talk about "why theorems?" any more than you can
generalize over all of natural language and ask "why sentences?" '
The original intent was to ask why there always seems to be hidden
structure -- which is revealed by theorems. It's not the theorems
I'm concerned about; it's the hidden structure.
-- Russ
On Mon, Apr 26, 2010 at 9:29 AM, glen e. p. ropella
<g...@agent-based-modeling.com
<mailto:g...@agent-based-modeling.com>> wrote:
Owen Densmore wrote circa 10-04-26 08:59 AM:
> The OP's "Too many interesting comments to follow up" sorta
sounds like
> "I've lost interest"!
Heh, yeah; but words have consequences! ;-) No (good?) deed goes
unpunished.
--
glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com
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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
