India may have proved Pythagoras Theorem before Greece

Subhash Kak
Subhash KakSep 26, 2015 | 12:55

India may have proved Pythagoras Theorem before Greece

Some commentators in India are upset that Rajnath Singh asserted in a recent lecture that the Pythagoras Theorem was known in India centuries before it was discovered in Greece.

They see this assertion as a part of a pattern of the invention of an imagined glorious past by spokesmen of Modi's government that has no basis in fact.

So how do we know what really happened in the past? The writing of history is a social process where evidence is gathered and then considered judgements made. There is no dispute amongst historians of science that Baudhayana in around 800 BC in his Shulba Sutra, nearly three centuries before Pythagoras, stated the theorem and also provided a geometrical proof. In another early Shulba Sutra, credited to Apastamba, a numerical proof is also provided.


The Greek proof of the theorem is generally credited to Euclid who lived around 300 BC and Pythagoras's discovery of the theorem is just an oral tradition. It is believed that Pythagoras who was born on the island of Samos travelled to many countries including Egypt, and possibly India, and some see him as one who brought Indian ideas to Greece.

What are the Shulba Sutras? They are manuals related to geometric and algebraic constructions of the altars on which the vedic ritual was performed. These altars were to be designed to different shapes and sizes and they required the solution to various geometric problems including those of equating a circular area of a certain radius to that of a square area. In other words, the rishis who did the Shulba not only knew the Pythagoras theorem but they also had knowledge of pi and iterative techniques.

It is possible that the knowledge of the Pythagoras Theorem in India is much older than Baudhayana and he is merely the first one who happened to describe it in his sutras. This is because vedic altars had been constructed for centuries before him and it is quite possible that much in the sutras is older knowledge.


We can say with Rajnath Singh that mathematical knowledge in ancient India (BC) was more advanced than in any other nation. Let me give two more pieces of evidence in support.

First, consider binary numbers that are at the basis of the mathematics used in computers. The German philosopher Gottfried Leibniz is credited with their modern discovery in 1695. But Pingala in India, who wrote the Chhandah Shastra, the famous book on verse meters, described binary representation in it. The motivation was to consider indexing of meters that are sequences of short and long syllables. Pingala is variously dated to fourth century BC to second century AD. According to legend he was the younger brother of the great grammarian Panini, which would place him in fourth century BC.

Second, let us turn to the amazing creation of the grammar of Sanskrit in 4,000 algebraic rules by Panini. Scholars consider it one of humanity's greatest intellectual achievements of all time. The modern fields of linguistics and structuralism owe to it. Scholars claim that the idea of formal rules in language - associated in our times with the theories of Noam Chomsky - which shaped the development of computer programming has origins in the the formal rules of the Paninian grammar.


I am astonished that many commentators in India are ignorant of the basic history of Indian science and rake up false controversies. I don't think anyone is suggesting that one should claim glory based on untruth but it seems fine to talk up the tradition of science in India to inspire the youth to study science subjects.

Last updated: September 26, 2015 | 12:58
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