The π Series
In the context of its European history, the question of what exactly the branch of mathematics called calculus consists of and what its foundations are is an old and much debated one, raised by mathematicians and philosophers alike already while Newton and Leibniz were alive. The issue was not settled, to the satisfaction of at least the mathematicians, until the 19th century. Little that is worthwhile can be added anew to that discussion. But, given that there are interesting differences in the Indian and European approaches to the “metaphysics of calculus” – a philosophically evocative phrase first used by D’Alembert in the 18th century – even as they are in agreement on the invariable core idea, at least a brief reexamination of some of these issues, in their most basic manifestations, will become unavoidable. The best way to do that seems to be to accompany or interpose the descriptions of the calculus-related material in the Nila work – elementary from our present viewpoint – with the corresponding material as treated in the classrooms of today.
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