Why we need to celebrate India’s knowledge legacy
If our policy and curriculum makers take a little more interest, much of the learning of mathematics can happen in a trans-disciplinary manner around the discoveries from ancient India.
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Almost all of us have studied elementary geometry in school and are acquainted with the theorem of Pythagoras. It is elegant and elementary while also being important since it has many applications. What many of us may not be aware of is that this theorem had been discovered in India a few hundred years before Pythagoras.
What is even less well-known is that Pythagoras had visited India. There are documents from Greece dating back to before the start of the Christian era as well as just after the Christian era that describe his visit to the country. Whilst in India, it seems Pythagoras was deeply influenced by Jain philosophy and he became a vegetarian. Unfortunately, these facts are not mentioned at all in most schools when the subject is taught. And even in the schools where teachers mention it, they do so only in passing. It is a no brainer that it would make the teaching of geometry far more interesting if we could include some of these facts from history when teaching mathematics. Actually, it would make the teaching of mathematics far more interesting if we could incorporate into the content some of the applications and historical context that led to profound mathematical discoveries in India from since several hundred years before the time of Christ.
The roots of Math
I shall attempt to create a description by way of a modest sample of what could be taken from India’s history in a practical manner that could manifestly increase the appreciation of the subject by students. So, in the context of the theorem of Pythagoras, it is important to note that the theorem is recorded in ancient Indian texts that go under the collective name the Sulbasutras. The word sulba means a piece of cord or string and sutra stands for a formula or an aphorism.
The ancient Indian theorem under the name Sulbasutras (R) predates the theorem by Pythagoras (L) by a few hundred years. (Photo: Wikimedia Commons and Facebook/ International Bulletin of Mathematical Research)
It so happens that during the Vedic age in ancient India, all Vedic rituals were centred around performing sacrifices at fire altars. Each of these sacrifices demanded specific shapes for the fire altars.
Blazing a trail
These altars were geometrically intricate in shape and had to be constructed to precise requirements of the area. Thus sophisticated geometry grew in India around the construction of these fire altars. This happened much before the time it developed in Greece. Most historians agree that the sulbasutras were created and recorded orally several hundred years before the time of Christ.
My concern is, if our policy and curriculum makers take a little more interest, much of the learning of mathematics in a trans-disciplinary manner can happen around the sulbasutras and other such discoveries from ancient India. I use the word trans-disciplinary since these topics can be taught in a hands-on and practical manner and the students can gain insights into history and architecture through the geometry of the sulbasutras. Interestingly, each of the these has been authored by a solitary mathematician, and each of them was palpably good architects. The important lesson we, in India, must imbibe from these powerful knowledge traditions of the past is, it was always trans-disciplinary and hands-on in nature.
Our young students could gain much insight into how geometry can be put to practical use and how it was discovered by our ancients if we were to bring a little bit of the prescriptions and mathematics of the sulbasutras into play. Incidentally, the oldest of the sulbasutras was authored by the mathematician Baudhayana in 800 BCE. We must remember that Pythagoras was around 500 BCE. Baudhayana’s sulbasutra clearly mentions in great detail this theorem. There are indications of an algorithmic method to construct the proof. This algorithmic method for providing proofs is one of India’s greatest contributions. Of course, there have been other instances of extraordinary mathematics created in India before and after the time of Christ and which is outside the realm of the sulbasutras.
All of this profound mathematics happened well before the rest of the world discovered it. It can do a world of good to our pedagogical practices if we could apply our minds to bring it in creative fashion into our curriculum. In around 200 BCE, an Indian prosodist by the name of Pingala was working on creating new metres in Sanskrit poetry. Pingala was attempting to create these new metres by combining long and short sounds of existing metres. He was dabbling in permutations and combinations. The Greeks and Europe had not even heard of permutations and combinations then. While doing so, Pingala discovered a very important mathematical tool that was rediscovered in Europe about 1,800 years later as Pascal’s triangle.
The disappointing part of this story is that we teach permutations and combinations to our school students but fail to mention Pingala’s discovery and the practical applications he made with it in poetry. Doing this, especially with the advent of computers is easy and interesting. Additionally, it creates greater curiosity and inventiveness in young minds. I can vouch for this since I have experimented with these for several years. What we also imbibe from such stories is that knowledge and skills are two sides of the same coin and when put into play through a trans-disciplinary approach, it brings all-round benefits. Our ancients knew this well but we have forgotten it. Judge for yourself by looking at our school curriculum.
(Courtesy of Mail Today)