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Baudhayana was an Indian mathematician and philosopher who is sometimes considered to have been a direct pupil of Vyasa. If this is so, then this pushes his dating back from c.800BCE to about c.3000BCE.
Baudhayana was the author of one of the earliest Sulba-sutras (texts dealing with geometry and mathematical principles). His writings contain several important mathematical concepts that were later attributed to the Greeks. One such example is the Pythagorean Theorem.
Baudhayana writes:
dirghasyaksanaya rajjuh parsvamani tiryadam manica yatpi thagbhute kurutastadubhyam karoti
“A rope stretched along the length of a diagonal produces an area that the vertical and horizontal sides make together.”
This appears to be referring to a rectangle, although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides. If restricted to right-angled isosceles triangles, however, it would constitute a less general claim, but the text seems to be quite open to unequal sides.
This is clearly the earliest statement of what is known today as the Pythagorean Theorem.
Baudhayana also wrote an extensive commentary on Vyasa’s Vedanta-sutras but the text is no longer available today. Ramanuja followed Baudhayana in his interpretation of Vedanta. In his own Vedanta commentary, Sankara also respectfully refers to this commentary, although he differs from it and pointedly attempts to refute it.
SOURCES:
Mathematics in the Making in Ancient India – G. Thibaut (Munshiram Manoharlal Publishers 1984)
http://en.wikipedia.org/wiki/Baudhayana
