A history of Indian mathematics

As many readers of this blog know, I’m fascinated by the history of discovery. While you certainly can be a good scientist without a knowledge of the history of discovery, there is much to learn from not just what is known, but also how it was discovered. Usually the stories behind discoveries are almost as fascinating as the discoveries themselves. Additionally, reading about the stories behind the discoveries also sometimes are humbling experiences; and makes you realize how much work might have gone into some findings, or how much some other discoveries was based on a collective work many individuals preceding the discoverer.

Additionally, reading about the history of discovery also makes you realize that knowledge or discovery was never restricted to one group or place alone, but different civilizations at different times had bursts of creativity, resulting in important discoveries. From there you can begin to understand how some societies progressed more rapidly than others. For example, Jared Diamond in his Guns, germs and steel uses this knowledge to understand how western societies managed to reach their current level of domination.

Anyway, coming to this post, I have always been a little disappointed in the way Indian history was taught to us in our schools. This is particularly true about the history of discovery (in science and mathematics) in India. There was the old colonial school of thought (which some people still have) that the foundation of all knowledge came from the west (starting with Egypt, Greece and Rome). Yet any historian knows that in the ancient world, there were thriving civilizations in Persia, India and China, and more importantly, there was not just trade, but well established and vibrant exchange of ideas and practices across these regions. This automatically suggests that there must have been some good ideas and discoveries in all these regions, in order for them all to be advanced (for the time) societies. There’s also the opposite (and rather amusing) view that comes from an excessively Indian nationalistic prism, which more or less states that all knowledge that exists in the world was discovered in India first (come on, tell me you’ve heard this one). Again, given the evidence (about vibrant civilizations in contact with each other across Europe and Asia), this isn’t likely to be true either. That said, there was nothing worthwhile that was ever taught to us about Indian science and mathematics.

As I read more about Indian mathematics in particular, I was fascinated by how rich the field was, and how much it has contributed to the field of mathematics in general. Some contributions are quite well known; and many of us are aware of the modern numeral system and the use of zero, first developed in India. This number system was later adopted (and improved) by the Arabs and Persians, from whom it reached Europe, and is now called the Hindu-Arabic numeral system. Some other contributions, like the development of the decimal system are also well known.

Anyway, here is a fantastic article by J.J. O’Connor and E.F. Robertson, on the excellent Mac tutor, on the history of Indian mathematics. This briefly mentions contributions like the numeral system, but also describes (or links to more articles about) major contributions and discoveries in algebra, trigonometry (including an independent discovery of the Pythagoras theorem at about the same time as Pythagoras), quadratic equations, the invention of the “Taylor” series, the value of pi, and much more, all of which makes absolutely fascinating reading.

I found it well worth my time to read more about it here (Indian mathematics, The sulbasutras, Indian numerals). Fascinating.