FOM: natural examples

[Steve Stevenson]

S B Cooper writes
 > Applications are found after the theory is developed, not before. A math
 > problem gets solved, then by accident some engineer gets hold of it and
 > says, 'Hey, isn't this similar to...? Let's try it.' For instance, the
 > laws of aerodynamics are basic math. They were not discovered by an
 > engineer studying the flight of birds, but by dreamers -- real
 > mathematicians -- who just thought about the basic laws of nature. If you
 > tried to do it by studying birds' flight, you'd never get it. You don't
 > examine data first.  You first have an idea, then you get the data to
 > prove your idea.

Not universally true. Finite element methods were used very
successfully by engineers long before Strang and Fix wrote the
book. The history of mathematics when written by an unbiased observer
surely intertwines with all human endeavros. A few quotes come to mind:

    "Mathematics: may it never be of any use to anyone!"  

				Henry John Stephen Smith, 1826 - 1883.

    "The deep significance of certain problems for the advance of
mathematical science in general and the important role which they play
in the work of the individual investigator are not to be denied.  As
long as a branch of science offers an abundance of problems, so long
it is alive; a lack of problems foreshadows extinction or the
cessation of independent development.  Just as every human undertaking
pursues certain objects, so also mathematical research requires its
problems.  It is by the solution of problems that the investigator
tests the temper of his steel; he finds new methods and new outlooks,
and gains a wider and freer horizon."  

		David Hilbert, {\em Bull AMS}. {\bf 8}. 102, 437--479.

    "As mathematics travels far from its empirical source, or still
more, if it is a second and third generation only indirectly inspired
by ideas coming from ``reality,'' it is beset with very grave
dangers. It becomes more and more purely aestheticizing, more and more
purely {\em l'art pour l'art}. .... In other words, at a great
distance from its empirical source, or after much ``abstract''
inbreeding, a mathematical subject is in danger of
degeneration. At the inception the style is usually classical; when it
shows signs of becoming baroque, then the danger signal is up.''.

   J. von Neuman (1943. ``The Mathematician.'' In *In the Works of the
			   Mind.* Chicago, IL: University of Chicago.)

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