The Calculus Story by David Acheson

Author:David Acheson
Language: eng
Format: epub
Publisher: Oxford University Press
Published: 2017-09-08T04:00:00+00:00

The history of this result is a little curious. It was first published by Leibniz, without any derivation or proof, in the Acta Eruditorum for 1682, but he had discovered it much earlier, in about 1674, while working in Paris.

It is likely, however, that the Scottish mathematician James Gregory knew the result a few years earlier still.

What seems more certain is that the result was known to mathematicians in Kerala, India much earlier, and possibly three centuries before Leibniz or Gregory, for it is now often attributed to Madhava, who founded the Kerala school. Their methods, however, were rather different, and more highly geometrical.

In any event, if we are to use calculus to see, at last, how π and the odd numbers are connected, we are going to need virtually all of the most important ideas we have seen so far.

It will therefore be helpful, I think, to split the argument into several stages.

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