希腊与印度数学的对比Contrast between Greek and Hindu mathematics

100° Contrast between Greek and Hindu mathematics.

There are many differences between Greek and Hindu mathematics. In the first place, the Hindus who worked in mathematics regarded themselves primarily as astronomers, and thus Hindu mathematics remained largely a handmaiden to astronomy; with the Greeks, mathematics attained an independent existence and was studied for its own sake. Also, due to the caste system, mathematics in India was cultivated almost entirely by the priests; in Greece, mathematics was open to any who cared to study the subject. Again, the Hindus were accomplished computers but mediocre geometers; the Greeks excelled in geometry but, in general, cared little for computational work. Even Hindu trigonometry, which was meritorious, was arithmetical in nature; Greek trigonometry was geometrical in character. The Hindus wrote in verse and often clothed their works in obscure and mystic language; the Greeks strove for clarity and logicality in presentation. Hindu mathematics is largely empirical with proofs or derivations seldom offered; an outstanding characteristic of Greek mathematics is its insistence on rigorous demonstration. Hindu mathematics is of very uneven quality, good and poor mathematics often appearing side by side; the Greeks seemed to have an instinct that led them to distinguish good from poor quality and to preserve the former while abandoning the latter.

A good deal of the contrast between Greek and Hindu mathematics is perpetuated today in the differences between many of our elementary geometry and algebra textbooks. We owe our geometry to the Greeks, our algebra to the Hindus. Only recently, with the emphasis on the "new mathematics," have our algebra textbooks begun to attain a rigor, a logicality, and a qualitative selectiveness of material comparable to that found in the elementary geometry texts.