Steve Schwartz writes:

>One thing that mathematics allows you to do is to predict the outcome
>of a situation you haven't met before, related to the real world or not.
>This is, of course, accomplished by building on a collection of theorems
>and proofs.  Mathematics may allow you to describe something you already
>know (in that sense, EVERYTHING -- or nearly -- is math).  But without
>that predictive power, there's no real advantage to prefer a mathematical
>description over a loose, verbal one, except that mathematics, as the
>Queen of Sciences, enjoys the prestige of science .

Mathematics cannot help you predict a "real world" outcome unless there
is a conceptual framework in place.  Such a framework (quantum mechanics)
is in place if you are interested in the properties of the hydrogen atom,
which can be accurately calculated to very great precision.  On the other
hand mathematics cannot help you account for the mass of the electron
because their is currently NO conceptual framework for such a calculation.

Sometimes a mathematical description is not relevant.  Aldous Huxley,
in one of his novels, describes the playing of a Bach Suite in terms of
air columns and strings being set into vibration, sound waves generated,
which fall on the tympanum in the ear, etc.  Such a chain of events may
be an interesting subject of study in its own right, but does not tell
you anything about the experience of listening to Bach.

Bernard Chasan