Let Newton be! by Jhn Fauvel et al

By Jhn Fauvel et al

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To define differentiation (finding tangents to curves) and integration (finding areas under curves) as inverse processes is an example of this unific­ ation, although later mathematicians were to revert to regarding an integration as a type of summation. As we shall see, Newton’s algebraic symbolism was developed from Descartes, and was particularly powerful. However, his calculus notation was perhaps none too successful— although it was no hin­ drance to Newton himself, who worked largely in isolation.

N E W T O N S M A T H E M A T I C A L WO R K 79 The priority dispute on the origins of the calculus had continued to fester since the turn of the century. In 1 7 1 1 Leibniz went so far as to complain to the Royal Society about the accusations, and in 17 1 2 the Royal Society set up a committee whose report was published the following year as the Commercium epistolicum. This apparently impar­ tial account and adjudication of the dispute found in Newton’s favour, and against Leibniz. Not until many years later did it become clear that Newton himself— ^the President of the Society— had written part of the Commercium epistolicum, and also the subsequent anonymous account of it published in 1 7 1 5 in the Royal Society’s Philosophical Transactions.

Newton went far beyond any existing work, by taking the known values of y when n is an integer, and ‘interpolating’ between these values to find the corresponding values when u is a fraction, such as i. This leads to infinite series, such as the above series for (i + Ethodum gtntralem, qusm Je Curvarum quanti­ tate per lufinitam terminorum Seriem menfuranJa, elm excogitaveram, in fequentibm breviter expltcatam pmim quam aamatt dimmfiratam babes. M A S! It is fairly typical of the efficiency with which Newton let his work be published that De analyst, written in 1669, first appeared in print in 1 7 1 1 .

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