Mathematician who tracked down India's maths heritage
India, Aug. 31 -- Physicist and the country's pre-eminent math historian, PP Divakaran, who died recently in Kochi, was a cherished friend of mine for over six decades. We first met at the Tata Institute of Fundamental Research (TIFR) and immediately fell into a discussion about the ground breaking work on parity violation by TD Lee and CN Yang, a topic that had captivated physicists worldwide, and for which they won the Nobel Prize in 1957. What immediately struck me was the remarkable clarity with which Divakaran, or PPD, as his friends called him, explained the intricate details of their research. His ability to distil complex ideas into understandable points was extraordinary, and would be the hallmark of his eventual work. The second thing about PPD that would soon become evident was the breadth of his interests and his polymathic ability to synthesise them. Sometime in the 1960s, when I was teaching at IIT Kanpur, he came to visit us and expressed a desire to see a temple nearby which was famous for its Gupta-period architecture. As we explored the temple with him, his profound knowledge of its architectural nuances left us all in awe.
Over the years, he and I would meet across the country at various institutes of learning - the Institute of Mathematical Sciences (IMSC), Chennai, and then for a substantial period at the Harish-Chandra Research Institute, Prayagraj, formerly Allahabad, where he gave a series of lectures on neutrino physics. A set of three lectures he delivered there set the tone for my research interest for the next ten years. I bring up these meetings because through them I realised PPD's unstinting generosity towards other scholars, whether it was editing their papers or guiding them with their research projects.
His interest shifted to studying mathematicians from Kerala, and as was his wont, he dived into it deeply. His text, The Mathematic of India: Concepts, Methods, Connection is a testament to his tremendous intellect, and put ancient Indian mathematicians and their contributions on the international map. He shone a light on the radicalism and the rationality of ancient Indian mathematicians. Aryabhata, he noted, may have been a "godless secularist" because his writings do not invoke any identifiable Hindu god.
PPD noted in his writings that Aryabhata's unwavering rationality was in direct contrast to what some of his supporters referred to as "pauranika" (traditional) or "sruti" (scriptural) knowledge. This is further supported by the criticism Aryabhata received from his most notable opponent, Brahmagupta. PPD pointed out that Brahmagupta's attacks were directed less at Aryabhata's astronomy and mathematics and more at his divergence from accepted wisdom and traditions.
PPD, who retired from TIFR in 1996, studied Aryabhata's work, Aryabhatiya, and pointed to verses 3 and 4 of the text's Gitika section as the first indication of his ground breaking theories. These verses list the number of "revolutions" (or periods of motion) for all the grahas (celestial bodies) within a yuga (a specific period of time in Hindu cosmology). The author considers this list of revolutions to be the initial hint of Aryabhata's theory of a spinning Earth. This idea would have been a radical departure from the prevailing geocentric models of the time.
The two other key points that PPD raised in his study of the ancient mathematicians were the advanced state of Indian trigonometry and the decline of Indian mathematics after the 16th century. He argued that the expansion of trigonometric functions like sine and cosine and their inverses were studied by the Nila school of mathematics in Kerala before they were developed by Western mathematicians. He supported this claim with rigorous evidence. PPD's work was appreciated by David Mumford, the Fields Medallist renowned for his work on algebraic geometry. PPD also noted that this period of mathematical innovation and creativity was not followed by steady progress. Instead, the Nila school marked the end of an "essentially autonomous progression of mathematical thought in India," he wrote. While he acknowledged various reasons for this, the "immediate trigger was the arrival of Portuguese colonialists on the shores of Kerala"....
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