Disclaimer: A paper published with the same name by prof. C.K. Raju has been the inspiration for this blog post which is published here.
It is a well-known fact, at least in academic circles, that Calculus and infinite series originated in India. It developed in India organically, as things usually do. It started with the works of Aryabhata. We know that discovery and inventions are not made for fun but to solve a real problem. As we know that agriculture and overseas trade was the two main sources on which the Indian economy depended.
To get good produce, you need accurate knowledge of rains(monsoon) which requires an accurate calendar for forecast. Accurate time calculations can be done with the help of advanced astronomy. Both of these things are also required for navigation in the oceans.
Europeans due to the dark ages that were enforced upon them by the Church, were quite backward in mathematics, science, and astronomy. They didn’t have a well-developed calendar as well as didn’t have a system for navigation. “European governments offered large prizes for the solution for this navigational problem from the 16th to the 18th c”, notes Mr. Raju.
Jesuit missionaries started mass translation of Sanskrit books into European languages in their Cochin college which worked on the Toledo model of mass translation of Arabic texts. The information that was copied from Indian texts started to appear in European works towards the end of the 16th century. These were 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).
Europeans failed miserably in understanding the Indian arithmetic in their first attempt (translations of Arabic works). Just as they failed with arithmetic so they did with “Indian methods of summing infinite series” using non-Archimedean arithmetic, and a different philosophy, now called Zeroism. The Church dogma came in their way that mathematics is “perfect and error-free”.
An excerpt from Prof. Raju’s work
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.
English