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Ancient Indian Mathematics

Ancient Indian Mathematics

November 22, 2010

When Indians discovered mathematics, did they know what the world was conspiring?

Recently I had a choice to make. In my final year of engineering, I was offered a range of subject specialisations from which I had to select one. On the list I found a subject, which many others appeared to have overlooked. Titled 'Traditional Indian Science and Technology', the name caught my attention and aroused my curiosity. I began to wonder about its relevance and application in today's age. To my surprise, this course opened a whole new world for me. I thought I had dived into a pool, but it turned out to be an ocean of knowledge! For past few months, I have been studying this subject religiously. So here I am, sharing my experience.

Bharatvarsha is the land of knowledge and culture. Visit any village of my country and you will find some very old useful practice being performed there that defies logic. For instance, try out the medical treatment that your grandmother gives for migraine. India, through ages has been the magical land of knowledge. The land that has given birth to teachers like the sage Chanakya, who was successful in stopping the invasion of Alexander the Great. Imagine the power that one brain possessed to stop the great warrior who captured the great kingdoms of Persia and Egypt.

The western education system is based on the concept of ‘Vidya’. Vidya is attained by attaching one’s mind to the senses; namely sight, sound, smell, touch and taste. Let me introduce you to the concept of ‘Jnana’. For ages, Indians acquired knowledge by the attainment of jnana. In India gaining of knowledge was phrased as the ‘realization of truth’. Worthy people realized the truth because they could handle it! They went into deep meditation in search of answers to questions that troubled them. Each of these sages was a ‘Buddha’, seeking answers to his questions. Jnana could only be attained by detaching one’s mind from senses and searching within. The ancient Indian mathematicians, astrologers, architects, surgeons were all sages. They spent years meditating in search of Jnana.

Coming back to mathematics in India, let me make a bold claim. Indians did not just discover zero, they actually discovered mathematics! When the rest of the world was a herd of nomads fighting each other, the subcontinent of Bharatwarsha chanted with vedic mantras. Knowledge flowed like a river in my country.

Indian mathematics dates back to the 28th century BC, when mathematicians of the Indus valley civilization used a decimal system of weights and measures. By 18th century BC, Indian mathematicians were discussing the concept of infinity. The Yajur veda states that “if you remove a part from infinity or add a part to infinity, what remains is infinity.” The Jain text Surya Prajinapti defines five kinds of infinity - an infinite line beginning from an endpoint, an infinite line stretching in both the directions, an infinite plane, an infinite universe, and the infinity of time. Indians discovered zero and infinity, and everything within.

Geometry was never far behind. Astronomy in ancient India was a direct derivation of geometry. The 13th century BC sage Lagadha used geometry to write a book of rules on the movement of the sun and moon. In 8th century BC, sage Baudhayana introduced the concept of quadratic equations, and calculated the square root of two. In the 3rd century BC, Sage Pingalacharya used zero for the first time, and represented it with a dot. He also presented a description of a binary numeral system without which computers would be non-existent today! Sage Aryabhatta introduced trigonometry, among many other things. He also gave a value of p accurate to four decimal places, and obtained whole number solutions to linear equations. This method is followed to this day date by mathematicians across the world. It was us who devised calculus, theory, probability theory, complex numbers, logarithm and algebra. I will stop here. The list though, is endless.

No wonder then, that the greatest mathematicians across the world have rightfully recognized India’s huge contribution. Albert Einstein once said, “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.” That is the beauty, the pride of being an Indian.

So, by the time the world started rediscovering mathematics, India had reached the zenith of knowledge. In fact, most of the rediscovery in the Middle Ages happened the “[ctrl + C] way” as we were open to sharing knowledge. It is unfortunate that India’s contribution to mathematics never received full acknowledgment in modern history, and that much of them were attributed to their Western counterparts. This mass plagiarism went unrecognized due to Euro centrism. What is more unfortunate is that even we, the sons and daughters of the same land, have bought into this rewriting of history.


  • Umakant
    05.08.12 05:34 PM
    Very nice article by Sourav Roy and useful reply by Alfred.
  • Alfred Jones
    Alfred Jones
    08.12.10 04:23 AM

    As an old alumnus of B'lore University's engineering program, I was thrilled to learn about the wider and more progressive range of courses on offer to its engineering students. And kudos to you for choosing to explore India's cultural heritage w.r.t science and mathematics.

    And yes, as Indians, we have plenty to be proud of both when we look back and when we see where we are today. But I'm perplexed by your wholesale assertion that Indians "actually discovered mathematics!". That is a very tall claim to make. And it flies in the face of a lot of archaelogical evidence showing basic mathematical ideas such as counting and other mathematical operations were present *concurrently* in many pockets of the ancient world.

    I have no doubt that the Vedas and other texts lay down *very original* techniques for calculating the answers to various mathematical problems. In fact I have at least one (western) book about the history of mathematics that attributes the invention of a number of highly sophisticated "reckoning techniques" to the vedic periods. But those techniques and underlying ideas are far from the sum total of what modern mathematics is all about.

    I am by no means an expert in ancient Indian mathematics, but isn't it highly unlikely that just one part of the ancient world came up with the foundational ideas underpinning *all* modern mathematics? As a culture, we venerate anyone that demonstrates admirable prowess in science and math. The thousands of top notch engineers and scientists we graduate every year is ample evidence of this. But we also appear to have a pathological need to attribute the invention of *every* original first principle in science and math to some period of Indian history. I run into this all the time in my conversations with fellow Indians both in India and abroad. (In fact, it has become a personal Deepavali tradition of mine to be cornered by a slightly inebriated uncle-in-law and be lectured on how Vedic Indians had nuclear missiles, i.e. "I say, let me tell you something...". I usually nod consent and reach for another helping of Mysore Paak.)

    In contrast, where I thought you hit the nail squarely on the head was when you contrasted the "gnaana" tradition of Indian learning with the "vidya" approach. It is quite possible for one to be *intuitively* aware of a mathematical idea or result, e.g. the Pythagorean theorem. But you can't teach that result to someone else if the only approach you have is the "gnaana" method. (Unless the other chap is also a similarly gifted abstract thinker which, in general, is very improbable.) This is where the "vidya" approach of provability was/is critical to the development of modern mathematics. The core idea being, you have to be able to prove your conclusion, using first principles of logic and axioms, before you can claim legitimacy. While it is true that *some* foundational mathematical ideas originated outside western Europe, what set the West apart is the degree to which they later used the "vidya" method to refine and evolve those basic mathematical ideas. And *that* is no small achievement. In fact, that is a method that has served us extremely well over the years.

    This is not to say that the "gnaana" method is somehow inferior to "vidya". Quite the contrary in fact. There are some aspects of life where "gnaana" is the only viable option. For instance, modern psychological research is discovering that meditation is far more effective in treating all kinds of depression-related symptoms. You can't "quiet the restless mind" using "vidya", you have to use meditative techniques that are derived from the "gnaana" tradition. And India is unsurpassed in the degree to which our ancients explored "gnaana" as the means for spiritual discovery and rejuvenation.

    All in all, this was a very thought provoking piece. I look forward to reading more from you.

  • Merin
    05.12.10 02:05 PM
    This is probably one of my favorite posts. Love how much pride you show for everything our ancestors have discovered. :) And really appreciate that your college offers such courses.
    Would love to read more about this!
  • reality
    27.11.10 12:02 AM

    I will keep an eye on your blog and on the link you mentioned. Thanks.
  • Sourav Roy
    Sourav Roy
    26.11.10 11:41 PM
    @ reality

    Thanks for the support.

    I will recommend you to read more such article on my blog- , where I have written many similar articles.

    I will also recommend you visit the official website of Indian Institute of Scientific Heritage, to know more about the glory of Indian culture.
  • reality
    26.11.10 10:31 PM
    Great article, very interesting. Much respect to you for taking the course and writing about it. I think we need more people like you. I believe that rediscovering the magnificent Indian civilisation that we Indians belong to is the key to making the country as great as it can be.

    We must learn to stop looking outwards all the time and learn to be proud of ourselves and of India.

    Well done.
  • Sourav Roy
    Sourav Roy
    23.11.10 10:30 PM
    @ Krunal Chauhan- Thanks for your support. Well, I too am in love with the film and the beautiful song :) Fills my heart with pride everytime I listen to it!

    @ Shyam- Thanks my friend!
  • shyam
    23.11.10 10:27 PM
    Good you are attending the lecture with full attention!!
    Nice work as always . Keep it up
  • Krunal Chauhan
    Krunal Chauhan
    23.11.10 03:26 PM
    I think you should certainly see the movie Purab aur Paschim .. and that famous song Jab zero diya mere bharat ne ..

    Jai Hind
  • Sourav Roy
    Sourav Roy
    22.11.10 10:01 PM

    Thanks for the honest support.

    Well, we are responsible in a very passive manner. A very small and insignificant example is there in the article itself. Only 10-15 people have registered for the subject, whereas more than half of the students of our college have registered for a subject which they opted only for the sake of marks. Speak about these issues in public and you'll see your own friends cursing you :(

    Well, I have found a starting point- Vedic mathematics. It's high time we learn tricks of Vedic maths. It applies not just in basic mathematical operations but also in leibnitz, euclid's formula etc... Our culture has such deep roots. I have recently started to multiply two 5 digit numbers in less than 1/10 of the time I would have taken on paper. I have started squaring two numbers orally. The secret is Vedic mathematics :)
  • Lisha
    22.11.10 07:40 PM
    Hey Sourav,
    I'm glad u are taking it upon urself to spread the lost glory of Indian History or rather Traditional Sciences :)

    I agree with u for the facts mentioned in the post. But, would like to say that, I really agree with u completely about the last line, that we, ourselves are the reason for the history to get rewritten. But, somehow, just this realization doesn't help. I'm at lost as to what to do for such things? Its too huge to start from any end :(

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