We hear much about the necessity of learning about other cultures than our own, so called "western," culture, which is supposed to be in many ways "Eurocentric." I would like to show you with some examples how this has worked rather naturally in the development of the history of mathematics.(1)
In the customary, classical (we may call it), way of looking at the history of mathematics in "western" countries, we may start by stressing the Greek achievement in which our present type of mathematics - theorem with proof derived from axioms - was born. Then we continue, now stressing the European Renaissance mathematics featuring Cardan and Galileo, followed by Descartes, Newton, etc. until our modern times.
In this process we present a courteous bow to the Egyptians with their curious unit fractions, the Babylonians with their sexagesimals, the Indians (of Asia) with their decimal position system. And also to the Arabs," who were so kind as to keep the torch of Greek science ablaze to pass it over to the Europeans," to paraphrase F. Cajori - also providing, we admit, some new algebra.
I do not criticize this method of looking at or teaching the development of mathematics when it is our purpose to show how our college mathematics evolved from the theorem of Pythagoras to the mathematics of Einstein's theory. We do not need much Egyptian or Arabic mathematics for that.
But if it comes to a survey of the history of mathematics as a whole, and especially as a great cultural asset, then this outlook turns out to be a narrow one, turns out to be, let's use the term "Eurocentric," which really is a polite word for the spirit of colonialism. The way the historiography of mathematics has developed in this century has born this out.
Let us first mention the great discoveries connected with names of Neugebauer and Thureu Dangin, showing the wide scope of Babylonian mathematics more than a millennium before the Greek mathematics. I still remember the surprise, even the shock, in the late 1920s when I found out that the theorem of Pythagoras was known and used at least a thousand years before the sage of Croton - in Hammurabi's Babylon. Babylonian clay tablets revealed many more achievements in the numerical solution of equations, compound interest, and applications. The fact that they had many tables, among them tables of Pythagorean number triplets, such as (3,4,5) or (5,12,13), shows this type of mathematics was not just utilitarian, but also "art for art's sake."
We also received a deeper insight into the nature of ancient Egyptian mathematics through the work of Giddings, Van der Waerden, and others: ancient Egytian mathematics had a sophistication of its own. Should we ask ourselves, incidentally, if those stories about the secrets of the pyramids are not all fantasy, but have a rational core? It seems that Martin Bernal, in his provocative Black Athena, which stresses the influence of Egyptian and Near East civilization on the Greeks, thinks so. I like to keep an open eye.
We are still getting new information about the advances in mathematics, especially in the domain of infinitesimals, made by Indian mathematicians as early as the fifteenth and sixteenth century. We find, for instance, certain infinite series only occurring in seventeenth-century Europe, in the works of Nilakartha, around 1500 - in a form, of course, entirely different from ours. An interesting question to ask in the sociology of mathematics is: why didn't they proceed to calcuelus?
Especially the region in the southwest of India, now the state of Kerala, has received attention. Does its tradition live on in the work of our great contemporary Ramanujan, who lived not far from Kerala?
Our appreciation of the mathematics of Islam has also had a facelift, partly through the works of such Russian mathematicians as B. Rosenfeld. We know that they developed an ingenious theory of numerical solutions of equations, a trigonometry and studies on the foundations of geometry (partly already known in Europe at an early day). …