About aryabhatta in sanskrit language about gopala school

Aryabhatiya is a Sanskrit poem composed of concise verses. Each verse states a mathematical or astronomical fact or algorithm, however, due to its succinct nature no proofs are shown. Additionally, puns are used to aid memorisation. That is the consequence of the privileged position of orality in Sanskrit literature. This tradition originated from Vedas , the oldest sacred text we know in India.

Even treatises on secular and technical subjects were ideally considered as knowledge to be learned by heart, not merely kept in a book for reference. Anuj Misra gives another view, why should mathematicians in India abandon their tradition? Therefore, ideas about reasoning and reality in Sanskrit philosophy and logic are explicitly linked to the understanding of linguistic statements.

What philosophers need to probe is their grammatical interpretation rather than their analogies with mathematical entities.

Jambudweep map

Invention of a place value system which is the base of Hindu-Arabic numeral system we use now. Invention of an algorithm for solving first-order Diophantine equations. And he gave out the first table of sines though the Greek mathematician Hipparchus and his successor created tables of chord before him , which was widely used by Arabic and Persian mathematicians even years later.

He specifically states that the value is approximated, but we could not learn more as the relevant statement is too short.

Jambudvipa

Developed a heliocentric model. What makes it even greater is that, as far as we know, he was the first one to state the orbits of planets are elliptical, that is years before Kepler. However, Aryabhata made several mistakes in his book: the definition of a square, calculation of the volume of a pyramid and sphere. His successor Bhaskara I, also a later commentator on the Aryabhatiya, fixed it by adding equal diagonal to definition.