> I would like to ask a heretical question.
I like heretical questions!
>
> Is there no *objective* progress, no development, no advance in
> mathematics? Would we not be justified in thinking that our present
> mathematics (as practiced and tought in universities around the world) is
> *objectively* much more advanced than--and in *this* sense superior to--the
> mathematics of the ancient world? And along this *objective* scale of
> progress, is not the mathematics of ancient Greece (as exemplified, say, in
> the writings of Archimedes) considerably more advanced than the mathematics
> of ancient Egypt and Mesopotamia, as far as we can tell from the documents
> that have come down to us? Or are such non-relativist thoughts simply the
> result of class bias, Eurocentrism and the damage inflicted by imperialism
> on our thinking?
>
I have thought about this question in my paper. As you say, our
present mathematics contains immeasurably more content than any
non-Western culture. In fact, it contains the entire content of these
ancient results (as we know them) as a tiny subset, and often more
precise arguments to support them.
But:
-- Comparison of the *amount* of mathematics produced confuses the
*actual* power/superiority with *potential* power. Western
mathematics has had immeasurably more resources devoted to it, and
there is no way to answer whether, say, the medieval Chinese approach
would have produced more/better results, given the equivalent
centuries and personnel applied to it.
-- Continuing my fantasy, I imagine that a modern, well-developed
"Chinese mathematics" would develop in ways quite distinct from our
own. Our desire to reduce to axioms is not present in Chinese
mathematics, whereas some of their (fantasized modern) computational
math might be well beyond ours. We value the study of analysis and
transcendental numbers, Lebesgue integration, and so forth at least
partly because of the relations that arise when we axiomatize (and
study pathological cases); the Chinese might prefer to emphasize
other subdisciplines.
Who is to say which emphasis is better? We can make a firm conclusion
only by agreeing at the outset on what we value about mathematics,
and that is culturally bound. (That being said, a culturally bound
answer is not then automatically valueless; just restricted).
Comments, as always, are welcomed.
Cheers, Glen
=================================
Glen Van Brummelen (Sec/Treas, CSHPM)
The King's University College
9125 - 50 St.
Edmonton, AB, CANADA T6B 2H3
Ph. (403)-465-8369
Fax (403)-465-3534
gvanbrum@kingsu.ab.ca
Alternate e-mail address: vanbrumm@compuserve.com