FOM: geometrical reasoning

[Robert Tragesser]

To make a point as simply as possible, a related probem:

        In a combination of the published and (Now incresingly availble)
full audio recordings of Feymann Lectures,  he takes great pains to always
give a mathematical and a physical demonstration of a thesis,  anmmd
considers it sa deep failing on his part when he can give only the
mathematical demonstrations but not the physical. (The physical is of
course loosely mathematical,  but is regarded by him as more proper, 
"elementary".)   I think that he is mainly concerned with the direction
from the (relatively) pure mathematics to the elementary physical
demonstration,  that it is for him a moral failing when he has to rely on
the formal mathematics too much.
        Currently,  we see the problem going the other way.  A problem in
physics/biology/chemistry is solved by the intermediate step of using
computer power to achive a solution (of course one has to come up with "the
equations",  but the computer is used to show that they do the right thing.
 Then the problem is to come up with a purely mathematical demonstration
that there is a solution to the equations giving the right numbers.  (I
assume anyone on this list can think of a dozzen examples -- I'd suypply
some if needed.)  The general dispute is just how necessary is this last
step to anything but the mathematical conscience? (This seems to me to the
the most important point of the extended AMS agon about the value of
rigorous proof.)
        This latter situation seems analogous to the Dirichlet Problem.
        By the way,  unless I've misread him,  Mark Steiner (in his new
book),  whatever else its great virtues,  seems to fail to give this ever
so fundamental problem a systematic appreciation.

robert tragesser