Indian mathematics - Ashok Sridhar Column

If Indian mathematicians like Aryabhata and Madhava were responsible for some of the greatest advancements in mathematics, then how come almost no one is aware of it? This could well be the first question to brew in the minds of those who read any revealing article on Indian mathematics. And they are not to be blamed for their ignorance; the problem lies with the education system in India and the perceived Eurocentrism, among others. These allegations will be justified subsequently.

According to mathematical historians, the main reasons for the misplaced credits for many Indian achievements are, not necessarily in that order, the following (the opinions of yours truly are italicised):

• Lack of proofs - Most of the works by Indian mathematicians of yore contain no proofs. They concepts and results were formulated in poetic form. Probably the best example is Aryabhatiya, Aryabhata’s masterpiece, a concise astronomical treatise of 118 verses written in a poetic form, of which 33 verses are concerned with mathematical rules. Many historians cite the lack of proofs for various theorems as the main reason for the step-motherly treatment of Indian mathematics.

  Though it is quite true that many theorems/formulae propounded by Indian mathematicians are sans proof, their value should never be downgraded. After all, these concepts did not come out of nowhere. As they say, there is no smoke without fire!




• Perceived lack of rigour in Indian mathematics - many historians feel that Indian mathematics lacks rigour and concepts were developed not for the sake of mathematics itself, but for religious reasons. For instance, the ‘Pythagorean theorem’ was actually developed in India, before Pythagoras’ time. It first appeared in Sulbasutras, a mathematical text from the Vedic period* that described the rules for the construction of sacrificial altars. If the ritual sacrifice was to be successful then the altar had to conform to very precise measurements.

  By all means such opinions are just lame excuses to overlook Indian accomplishments. Does anyone consider the Egyptian pyramids to be banal just because they are tombs? Does anyone deem European advancements in technology to be worthless just because wars and colonisation were the prime movers behind their technological development?




• Oral transmission - Many a concept, masterly composed as poetic verses by Indian mathematicians of yesteryear were transmitted orally for centuries before they were eventually written down. By the time they were written down, many such concepts were ‘reinvented’ elsewhere, thus depriving us of the due credit.



• Eurocentrism - It cannot be denied that the history of India as we know it was (re)written by the Europeans. To them, it is unthinkable that people who were considered less academically and culturally advanced than them could achieve such heights. Some mathematical historians went to such extents that they ‘dated’ Indian concepts in such a way that they always postdate similar European accomplishments and declared that the Indians got hold of the European ideas and tailored them.

  This is plain arrogance and/or ignorance on the part of such people. Even now, many people do not realise that Indian culture was well ahead of other contemporary cultures for the best part of four millenniums! Even after knowing the truth, the human tendency is to try and invent reasons to reject it if the truth is bitter. That is what is currently happening - many mathematical historians still try to find reasons not to accept Indian dominance in mathematics, even though proofs unearthed reinforce the claims on the ingenuity of our mathematicians.




• Contemporary Indians - It is extremely sad that many Indians themselves are sceptical about the reality. They are not able to believe that a country that is lagging behind the West in almost all the spheres was once the land of thinkers and supremely gifted people. Moreover, not many Indians take pride and interest and propagate these facts. Pathetic state of affairs indeed!

  Is it due to the fact that we were enslaved for a millennium? Or, is it due to the beliefs of many Indians that the westerners are superior and that whatever they say must be correct? This is an inexplicable form of racial superiority pervading India.

  Germany is popularly known as ‘Das Land der Dichter und Denker’. This German phrase means ‘the land of poets and thinkers’. It is true! Similarly, yours truly would call India, ‘the land of age-old culture and pioneering thoughts’. Let us take pride in ourselves and march ahead!




• Education system - None of the history books prescribed by various boards of education in India bother to discuss our achievements in mathematics and astronomy even though most of them predate other similar achievements elsewhere by centuries. This is a fundamental problem that has lead to the lack of awareness among Indians about their own countries’ past glory. It is thus evident that there is more than one factor that has lead to misplaced credits that are unambiguously ours. Of these, we can address and rectify the problems with our education system and purge any trace of Eurocentrism from our own minds. It is undeniable that the Europeans have achieved great many things in science and technology and this modern world has its base firmly rooted to their concepts. But, at the same time, it is high time to open our eyes and mind and realise that India has been, for a long time, a true champion in its own right and intellectually influenced a number of civilisations without ever being bellicose.

• An overview of Indian mathematics - by J.J. O'Connor and E.F. Robertson
• Indian mathematics – redressing the balance – by Ian G. Pearce

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