Mathematics in the pre-classical era
Supplementary Vedas like the Shula Sutras are considered to date from 800 to 200 BCE. There are four, named after their authors: Baudhayana (800 BCE), Manava (750 BCE), Apastamba (600 BCE), and Katyayana (200 BCE). The sutras contain the famous Pythagoras theorem. Some scholars (such as Seidenberg) feel that this theorem is already present in the Shatapatha Brahmana. Much later, Bhaskaracharya gave an algebraic proof of this theorem, as opposed to the geometric proof that existed.
The Shulba Sutras introduce the concept of irrational numbers, numbers that are not the ratio of two whole numbers like the square root of 2. The sutras give a way of approximating the square root of a number using rational numbers through a recursive procedure which in modern language would be a ‘series expansion’. This predates, by far, the European use of Taylor series.
Mathematics of this period seems to have been developed for solving practical geometric problems like the construction of altars. However, the study of the series expansions for certain functions already hints at the development of an algebraic perspective. In later times, it shifted towards algebra, with simplification of algebraic formula and summation of series.
- See V Kumar Murty, ‘Contributions of the Indian Subcontinent to Civilization’, Prabuddha Bharata, 100/1 (1995), 134–5.