After some detailed explications of computations, Ritter concludes:
-- there is no "internal necessity" guiding the resolution of problems
along some predetermined unique path;
-- that the practical techniques of computation may well suggest different
directions when mathematicians begin to think more abstractly;
--that one may fruitfully explain some aspects of those techniques by
reference to the "material needs" of the societies that invent and use
them.
This is less exciting than the relativism suggested by the title, but
certainly worth arguing, especially as against the implicit determinism or
teleologism of some histories of mathematics. There are neither
necessitating efficient causes nor inevitable ends in Ritter's account. As
a nonspecialist, I found it fascinating and suggestive.
Ritter, James. "Chacun a sa verite: les mathematiques en Egypte et en
Mesopotamie". In: Elements d'histoire des sciences", ed. M. Serres (Paris:
Bordas, 1989):39-61.
Dennis Des Chene
deschene@jhunix.hcf.jhu.edu