What are the differences between the Aryabhattas theory and orthodox theory in the ancient India
Answers
Explanation:
He ranks with Archimedes, Euclid, Isaac Newton and Leonard Euler as one of the greatest mathematicians of the world.
He began a new epoch in Indian astronomy and mathematics, that continued for more than a millennium. His book Aryabhateeyam is a masterpiece of brevity and eloquence.
But what did Aryabhata actually do? Aryabhata did not invent zero; or gravity; or the heliocentric system.
As I wrote in my first essay, even Indian mathematics and Sanskrit scholars are stunningly ignorant of Aryabhata’s actual accomplishments.
Since we are equally ignorant of almost all of ancient India’s glories, this is not specifically galling; just generally abysmal.
Only Bhaskara was, perhaps, as popular and admired, but unlike Newton’s apple or Watt’s tea kettle, or the anecdotes of Birbal or Tenali Raman, we don’t even have popular legends about him.
But we are so creative, we blame the British for this situation, decades after they left.
Ever computed a square root? Aryabhata.
Cube root? Aryabhata.
Summed up a series of numbers? Aryabhata.
Series of squares? Aryabhata.
Divided by a fraction by multiplying by its inverse? Aryabhata.
Computed the areas of triangles, circles, trapeziums? Aryabhata.
Calculated sines? Aryabhata.
And that’s just the simple mathematics we learn in school.
Wait! Did he invent all of these? Ah, that’s the question. Aryabhata himself claims not a single invention.
He explicitly states that “by the grace of Brahma, the precious jewel of knowledge (jnana-uttama-ratnam) has been extracted from the sea of true and false knowledge (sat-asat-jnaana-samudraat), by the boat of my intellect (sva-mati-navaa).”
As Euclid compiled five centuries of geometrical discoveries of the Greeks, Aryabhata compiled several centuries of mathematical and astronomical discoveries of Indians.
Sulba Sutra and Jain mathematicians knew how to compute square roots, but Aryabhata was the first to describe the algorithm.
We don’t know if cube roots were calculated earlier, his algorithm is the oldest extant. His sine calculations are considered much superior to those listed by Varahamihira. His kuttakara algorithm to find solutions is considered ingenious even today.
It is not feasible to explain his mathematical and astronomical discoveries in a magazine article for the general reader. There are excellent translations, technical papers, books that do that.
This essay’s purpose is to provoke you to read them, and marvel at Aryabhata’s sva-mati-navaa. And to place Aryabhata and his work in historical context.
Manuja Grantham
The 18 siddhantas were attributed to rishis. But every jyotisha siddhanta after Aryabhata and Varahamihira, is attributed only to men, not rishis.
These arose from commenting, understanding, questioning, correcting, improving existing siddhantas and inventing or discovering new concepts.