On the myriad mathematical traditions of ancient Greece (Q697114)

The main point of this causerie is a rejection of the widespread identification of ancient Greek mathematics with the formal structure and methodological sophistication found in a handful of canonical works or, more accurately, in selected portions of them. It points to the plurality of mutually interacting traditions (the great theoretical tradition, that of practical mathematics and mechanical engineering, and the Pythagorean-Platonic tradition) and to the far from homogeneous nature of the first of these, the one most spoken of in mathematical texts and most books on the history of mathematics. This discussion is related to the impact of the reading of Greek mathematics (in its diversity) on later authors from Thābit ibn Qurrah to Newton and to the contemporary reception of Greek mathematics through the mirror presented by Hilbert's Grundlagen der Geometrie. Rowe concludes that mathematical knowledge, as a general rule, is related to various other types of knowledge, that its sources are varied, and that the form and content of its results are affected by the cultures within which it is produced. Those who have produced mathematics have done so in quite different societies, within which these producers have had quite varied functions .