Reflections on mathematics, teaching and Ramanujan at a film theatre
Last Saturday morning, I found myself emerging from a Mumbai cinema teary-eyed, at the end of the movie The Man Who Saw Infinity - the story of Srinivasa Ramanujan, a "self-taught" mathematician from Madras (now Chennai) and a clerk in the Madras Port Trust, who got himself invited to do research in advanced mathematics at Trinity College, Cambridge in 1914, and who had to return to India five years later because of ill-health, to die of tuberculosis.
I stood there trying to decode the sudden rush of tears in my eyes. Was it because Ramanujan was a mere 32 when he died, or was it because of the triviality of the reason for his poor health - which, as the film presents it, was because of the vegetarian Ramanujan's malnutrition in a country where, at least at that time, even potato chips were cooked in animal fat?
The answer as to why the Ramanujan story had saddened me so much came to me in a set of cascading thoughts. The first source of my sadness was that even today, a century after Ramanujan, recognition for academic or scientific worth in India is dependent on Western certification; in Ramanujan's time from British universities and in our time from American universities. The second source of my sadness was at the silly levels to which the awe about mathematics has risen to not just in this film but in many other fields of life - mathematical competence is presented as the ultimate competence. My final source of sadness, I realised was about the way the Ramanujan story is always presented - him being self-taught, that is to say, out of divine contemplation, not from teachers and text books.
Let's start with the bit about Ramanujan being self-taught. The truth was that Ramanujan was what we would today call a college-drop out. After a through grounding in mathematics at the school level, he joined Government Arts College, Kumbakonam (founded 1854) and dropped out from there, joined Pachaiyappa's College in Madras (founded 1842) and dropped out from there as well.
In other words, Ramanujan was in an environment where mathematics teaching was flourishing. At the time Ramanujan joined them, both the Government Arts College in Kumbakonam and Pachaiyappa's College had already been in existence for more than half a century. And there is little doubt that mathematics acumen was revered in those parts of India: when my mother's younger sister won the Madras University gold medal in mathematics in the 1950s, the celebration at my grandparents' home in Salem lasted days; we children were all allowed to eat unlimited home-made ice cream all of that week.
What's more, by the time Ramanujan was born, the use of formalised methods of teaching mathematics had existed for at least a thousand years in India.
Algebra, the core of mathematical thinking, was brought to the western world thanks to the compilation of Indian techniques in the 8th century AD book Al-kitab al-mukhtasar fi hisab al-gabr wa'l-muqabala roughly translated as The Book of Calculation by Completion and Balancing, by the Baghdadi teacher and author Muhammad ibn Musa al-Khwarizmi. The modern term "algorithm" is the Anglicisation of "al-Khwarizmi", and "algebra" the Anglicisation of "al-jabr". His book, On the Calculation with Hindu Numerals, written about 825 was translated into Latin as Algoritmi de numero Indorum, is what took mathematics to the West.
The final source of my sadness was with the way modern life (and the film) fetishises mathematics. The Great Recession which the world has been struggling in vain to overcome since 2008 and which has brought many countries to their knees and destroyed many millions of jobs world-wide can be directly traced to those mathematical artefacts called "mortgage-backed securities" and "collateralised debt obligations". The mystical qualities attached to the value of these artefacts made even otherwise rational policy makers overlook their fragility. Their mathematical complexity created the awe which suspended rationality and allowed bond and securities salesmen to sell billions of dollars' worth of that stuff world-wide.
Modern-day economists also wrap their sometimes simplistic assumptions in complex mathematics to make them sound more credible. Alan Jay Levinovitz, an assistant professor of philosophy at James Madison University in Virginia, calls this "the new astrology" - and says that, by fetishising mathematical models, economists have turned economics into a highly paid pseudoscience. He quotes the economist Paul Romer of New York University about macroeconomics being plagued by "mathiness" and thus failing to progress as a true science should, and that current debates among economists are often as pointless as those between 16th-century advocates of heliocentrism and geocentrism - whether the sun or the earth was at the centre of things. "Mathematics", says Mr Romer, "can help economists to clarify their thinking and reasoning... but the ubiquity of mathematical theory in economics also has serious downsides: it creates a high barrier to entry for those who want to participate in the professional dialogue, and makes checking someone's work excessively laborious. Worst of all, it imbues economic theory with unearned empirical authority".
If Ramanujan lived in our times, though, his existence would have been far different than being a penurious teacher of mathematics - the highest starting salaries in the world today are for "data scientists" and the highest valuations are for start-ups whose business models are based on detecting and exploiting mathematical patterns. We would have found Ramanujan presiding over a billion-dollar start-up or running a mega hedge-fund.
First published in Business Standard. Courtesy and Copyright Business Standard
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