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A reader named Viswanath replied to my previous post; I started writing a reply, but I realized it was far too long for that window. So here it is, below.

You’ve got something of a point regarding Aryabhatta, but the details as I can perceive them are pretty complicated (as ancient history is, and as far as this armchair historian can read them). Arayabhatta, an Indian living during the Gupta Dynasty, wrote the Aryabhatiya in 499 AD, as a treatise on arithmetic and astronomy, including algebra. (All these and other facts courtesy Wikipedia.) A lost third volume of this work could have been a translation of the Aryabhatiya, and is mentioned by an Indian writer in the 9th century AD, which is interestingly right about at the same time Muhammad ibn Mūsā al-Khwārizmī, (considered the “father of algebra”), publishes The book of Summary Concerning Calculating by Transposition and Reduction in 820 AD. However the origins can also be traced back to the ancient Babylonians, who were working out algebraic methods of computation in the 1st millennium BC.

Two significant contributions were made by Greeks Hero of Alexandria, and Diophantus (2nd century AD), who may have gleaned something from mathematical information trickling back to the Greek world from Takshashila. Takshashila was an important center of Hindu and Buddhist learning from the 5th century BC to the 6th century AD, within the important Gandharan Kingdom.

Now here’s where it gets interesting. The westernmost reaches of the Gandharan Kingdom lie on the border of present-day Afghanistan – previously the ancient Persian Empire – subsequently the easternmost penetration of Alexander the Great’s empire. The Persians captured Babylon in the 6th century BC, and Alexander the Great conquered the Persian Empire in the 3rd century BC. A few centuries after Alexander, the Gandharan Empire entered its Graeco-Bactrian phase, and you can see the effects really plainly in the art of the period: sculptures clearly evincing Hindu, Persian and Greek influences simultaneously.

We recall that the origins of algebra come, in part, from the ancient Babylonians. Can you see where I’m going with this?

As with most scientific and engineering advancements in the course of human history, little bits are picked up here and there, added together, and flashed into Eureka! by pure chance, sometimes. (Two great general histories on this topic are The Day the Universe Changed and The Pinball Effect, both by James Burke.) Now, I don’t know a great deal about the history of mathematics, and this is just my theory, but it seems to me that by looking at the patterns of cultural communication, and the totality of the timeline, that the mathematical advances of algebra may well have grown outward from the Babylonian Empire, through the Persians, and flowed with Alexander’s armies into India, where it rested for a time. And then was communicated back through the Roman Empire in its greatest seat of learning, the Library of Alexandria. When Rome fell, Alexandria degraded. During the Middle Ages, the most profound nexus of knowledge and cultural transmission in Europe was Al-Andalus, where the act of translation between Jews, Christians, Greeks and Muslims kept water flowing in the Alhambra’s Generalife.

In other words, there was a basic fact of religious tolerance and civilizational organization throughout Islamic society at that time. To this, the West owes a great deal. Including algebra, where in its fullest and most systematic designs were delineated by Muhammad ibn Mūsā al-Khwārizmī, at a time and place where knowledge – almost lost – could be sheltered. Acknowledging that was critical, in my view, toward establishing a dialogue toward creating more open Islamic societies. IMHO, Viswanath, it does not appear that Obama was “talking for glory,” and while your interest in reminding us of Indian contributions to the world’s scientific heritage is notable, as you can see through this analysis it can’t really fit very well into a speech that was already Obama’s longest.

Anyone who’s got a background in this area, I’d love to hear details, corrections or clarifications on this stuff.

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