Re: Where do mathematical ideas come from?

hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) writes:

....
>Statistical decision theory, linear programming, and dynamic
>programming started from the problem of developing optimal
>strategies under uncertainty, including inventory management.
>Control theory is another. But aften the problems were
>specified, pure mathematics, and lots of it, often took over.

The (snipped) context may lead some readers to interpret the
last sentence narrowly, as saying (only) that "pure mathematics
....took over" in the sense that the body of definitions, theorems,
etc., that we now call "linear programming" (for one example)
was developed as "pure mathematics". That is of course true,
in spades. But a converse is also true: linear programming
(for instance) is now applied *to and within* other areas of
"pure mathematics". I am especially aware of that example
right at the moment, because I am presently up to my neck in
what is (at least to me) a completely unexpected application
of linear programming to geometric topology; the application
grew out of a problem in "semi-pure" robotics (and not one where
linear programming had previously been seen to be applicable),
but is now (to the extent that I am involved with the research
in question) answering interesting "purely topological" questions,
and giving new points of view on old answers to those questions.

Lee Rudolph
.