Re: [HM] Is Greek mathematics the *real* thing?

Kim Plofker (Kim_Plofker@Brown.edu)
Wed, 4 Nov 1998 18:45:47 -0500 (EST)

I think Moshe' Machover's question, and much of the recent discussion
on Littlewood and the Greeks, etc., although extremely interesting,
approaches the issue backwards. I would prefer to put it as follows:
Of course we students of modern mathematics have some sort of preference for
the work of the Greek mathematicians, not because we and they are the only
ones doing _good_ mathematics, but because we and they are the only ones
doing _Greek_ mathematics. As Augustus De Morgan pointed out, the peculiar
inspiration of Euclid and his colleagues was to shift the focus of
mathematical endeavour away from getting the answer to a problem, and
towards thoroughly exploring the consequences of _restricting_ the
allowable problems and methods of solution. In essence, that's what modern
mathematicians still do, and it is in some ways qualitatively different
from
(although not necessarily better than) the mathematics of non-Western
cultures. Littlewood's remark betrays a bias not of race, but of era:
in fact, we feel a special kinship to the Greeks not because they are
"Fellows of another college" at _our_ university, but because we are Fellows
of a college at theirs.

Kim Plofker
Department of History of Mathematics
Brown University

>I would like to ask a heretical question.
>
>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?
>
>
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