Achievements of Ancient Indians in Mathematics & Geometry
It is generally accepted that India was birthplace of several mathematical concepts. It was an important field of knowledge. The key achievements of ancient Indians in mathematics and geometry are as follows:
Indian geometry predates Greek geometry by centuries. It has been argued that Geometry and Mathematics had a ritualistic beginning in India centuries before Greeks or Babylon. In these rituals, Earth was represented by Circular altar and heavens were represented in Square altar. There were eagle shaped altars also.
Sulvasutras deal with complex fire altars of various shapes constructed with bricks of specific shapes and area: the total area of the altar must always be carefully respected. This proves that despite of no existence of algebra, there was an awareness of precise purely geometrical calculations.
Sulva sutras belong to a bigger text Shrauta Sutras. The four major Sulva Sutras, which are mathematically the most significant, are those composed by Baudhayana, Manava, Apastamba and Katyayana. Out of them the oldest belongs to Baudhayana and dates back to 600BC.
Concept of Zero and Decimals
It may not be factually correct that concept of zero was devised by Indians yet, it is evident that knowledge of Indians on zero and decimals further enhanced the knowledge of Arabs and others, who called it Hindsa or Indian art. In second or third century BC, Pingala used the binary numbers in short and long syllabus and used the word Sunya explicitly to refer to zero. Similarly, Lokvibhaga, a jain text belonging to 458 AD was the earliest text to use the decimal place-value system and it uses Sunya word for zero. Further, the origin of modern decimal based place value notation can be traced to Aryabhattiya which states that sthānāt sthānaṁ daśaguṇaṁ syāt “from place to place each is ten times the preceding. Thus, the concept of zero as a digit in the decimal place value notation was developed in India in 4th or 5th century AD.