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A TALK BY PROFESSOR C. K. RAJU It is by now well known that the calculus and its infinite series originated in India across a thousand year period, starting from the 5th century Aryabhata. It was needed for agriculture and overseas trade, the two key sources of Indian wealth. Indian monsoon-driven agriculture requires a good calendar, which requires good astronomy (hence precise trigonometric values) needed also for navigation Europeans then were backward in navigation and hence European governments offered large prizes for a solution to the navigational problem from the 16th to the 18th c. In the 16th c., Jesuits had turned their Cochin college into a centre for mass translation of Indian texts (on the 12th c. Toledo model of mass translation of Arabic texts). The content of these Indian texts started appearing in Europe in the later 16th c. and early 17th c. and was used to solve the latitude problem (Gregorian reform) and the problem of loxodromes (Mercator's chart). There is other circumstantial evidence, as in the works of Tycho Brahe (“Tychonic model”, identical to Nilakantha's), Christoph Clavius (trigonometric values, interpolated version of Indian values), “Julian” day numbers (ahargana), Kepler (Parameswaran's observations), Cavalieri, Fermat and Pascal (challenge problem, including probability), and finally Leibniz (“Leibniz” series) and Newton (sine series). However, like Indian arithmetic earlier, Europeans did not understand Indian methods of summing infinite series using “non-Archimedean” arithmetic, and a different philosophy, now called zeroism. They tried to fit it into their religious beliefs about mathematics as “perfect” and error-free. Newton thought, as in his theory of fluxions, that this could be done by making time metaphysical (“mathematical time which flows equably”). The error about time was the reason why his physics failed. This history has contemporary value. Correcting Newton's mistake in understanding calculus leads to a reformulation of physics, and, in particular, the theory of gravitation. This also corrects various problems of infinity that arise from the inadequacy of university calculus, or the Schwartz derivative for quantum field theory, general relativity, and electrodynamics as also the Lebesgue integral for probability, especially in quantum mechanics. The other contemporary value is pedagogical. Calculus with add-on metaphysics makes math very difficult and was globalised during colonialism. Eliminating that redundant metaphysics in math makes math easy to teach. http://ckraju.net/papers/Calculus-story-abstract.html