Shulba Sutras

"Anyway, the damage had been done and the Sulvasutras have never taken the position in the history of mathematics that they deserve."

"However, Seidenberg was told by the Indologists that these Sutras, or any Vedic text for that matter, were definitely written later than 1700 BC. But mathematical data cannot be manipulated just like that, and Seidenberg remained convinced of his case: “Whatever the difficulty there may be [concerning chronology], it is small in comparison with the difficulty of deriving the Vedic ritual application of the theorem from Babylonia. (The reverse derivation is easy)… the application involves geometric algebra, and there is no evidence of geometric algebra from Babylonia. And the geometry of Babylonia is already secondary whereas in India it is primary.” [To satisfy the indologists, he said that the Shulba Sutra had conserved an older tradition, and that it is from this one that the Babylonians had learned their mathematics:] “Hence we do not hesitate to place the Vedic (…) rituals, or more exactly, rituals exactly like them, far back of 1700 BC. (…) elements of geometry found in Egypt and Babylonia stem from a ritual system of the kind described in the Sulvasutras.”"

"In the Shulba Sutra appended to Baudhayana’s Shrauta Sutra, mathematical instructions are given for the construction of Vedic altars. One of its remarkable contributions is the theorem usually ascribed to Pythagoras, first for the special case of a square (the form in which it was discovered), then for the general case of the rectangle: “The diagonal of the rectangle produces the combined surface which the length and the breadth produce separately.”"

"The Sulvasutras are a class of works, preserved in various schools, such as those of Baudhayana, Apastamba, and Katyayana, which are often referred to as manuals of altar construction. (Others include those of Satyasadha, Manava, Maitrayani, and Varaha.) In these texts, the construction of a wide variety of altars is described—square, circular, or falcon-shaped—the form depending on the type of ritual to be performed. In certain of these sutras, the formula that came to be known in the West as the theory of Pythagoras is expressed. Thibaut (1875), who was the first to translate the sutras into English, felt that "the general impression we receive from a comparison of the methods employed by Greeks and Indians respectively seems to point to an entirely independent growth of this branch of Indian science" (228). Such a statement was quite significant in Thibaut's time, since the scientific achievements known to the Indo-Aryans were generally held to have been borrowed from the Greeks."

"Neugebauer has shown that these values [of irrational numbers in the Sulvasutras] are identical with those found in certain Babylonian cuneiform texts. . . .He tried to imply that the Indian value after all represented the Babylonian one. . . .As we have shown, there is certainly no proof of such an assertion and the Indian value is certainly derivable from the methods contained in the sulbasutras themselves" (Sen and Bag 1983, 11)."

"Yet long before 1937 people had suggested a non-Greek origin to Greek mathematics; and long before 1943 people had pointed out that sacred books of the East contain the ‘Pythagorean numbers’ [and indeed the ‘theorem’]. Such numbers are mentioned in the Sulvasutras; ancient Indian works on altar constructions. […] Neugebauer does not mention the Sulvasutras in his book Vorlesungen über Geschichte der Antiken Mathematischen Wissenschaften, nor does B. L. van der Waerden them in his book Science Awakening. Why this omission?"