Ancient India can be acredited with many acheivements. Some of them are listed here:
Earliest known precise celestial calculations: Aryabhata, an Indian Mathematician (c. 500AD) accurately calculated celestial constants like earth's rotation per solar orbit, days per solar orbit, days per lunar orbit.
Astronomical time spans: Apart from the peoples of the Mayan civilization, the ancient Hindus appear to be the only people who even thought beyond a few thousand years. Hindu scriptures refer to time scales that vary from ordinary earth day and night to the day and night of the Brahma that are a few billion earth years long.
Theory of creation of the universe: A 9th century Hindu scripture, The Mahapurana by Jinasena claims that the world is uncreated, as time itself is, without beginning and end. And it is based on principles.
Earth goes round the sun: Aryabhata, it so happens, was apparently quite sceptical of the widely held doctrines about eclipses and also about the belief that the Sun goes round the Earth. As early as the sixth century, he talked of the diurnal motion of the earth and the appearance of the Sun going round it.
Binary System of number representation: A Mathematician named Pingala (c. 100BC) developed a system of binary enumeration convertible to decimal numerals. He described the system in his book called Chandahshaastra. The system he described is quite similar to that of Leibnitz, who was born in the 17th century.
Earliest and only known Modern Language: Panini (c 400BC), in his Astadhyayi, gave formal production rules and definitions to describe Sanskrit grammar. Starting with about 1700 fundamental elements, like nouns, verbs, vowels and consonents, he put them into classes. The construction of sentences, compound nouns etc. was explained as ordered rules operating on underlying fundamental structures.
Invention of Zero: Although ancient Babylonians were known to have used what is often called "place holders" to distinguish between numbers like 809 and 89, they were nothing more than blank spaces or at times two wedge shapes like". The first notions of zero as a number and its uses have been found in ancient Mathematical treatise from India.
The word "Algorithm": Al-Khwarizmi's work, De numero indorum (Concerning the Hindu Art of Reckoning), was based presumably on an Arabic translation of Brahmagupta where he gave a full account of the Hindu numerals which was the first to expound the system with its digits 0,1,2,3,...,9 and decimal place value which was a fairly recent arrival from India. The new notation came to be known as that of al-Khwarizmi, or more carelessly, algorismi; ultimately the scheme of numeration making use of the Hindu numerals came to be called simply algorism or algorithm, a word that, originally derived from the name al-Khwarizmi.
Representing Large numbers: Mathematicians in India invented the base ten system in ancient times. But research did not stop there. The practice of representing large numbers also evolved in ancient India. notion of representing large numbers as powers of 10, one that was invented in India, turned out to be extremely handy.
