The Teaching of Differentials

Extract

Most mathematicians are aware of the unhappy controversy between Newton and Leibniz about the priority of the discovery of the Infinitesimal Calculus. This controversy lasted from 1707 to 1716, and, as Rouse Ball writes, “ it occupies a place in the scientific history of the early years of the eighteenth century quite disproportionate to its true importance”. It is, however, remarkable that this controversy is to a large extent responsible for the fact that even to-day much of the teaching of Elementary Calculus in this country is given in an unsatisfactory manner. The notation of differentials was invented by Leibniz in 1675, at about the same time as Newton invented his “ fluxions”. The bitterness of the aftermath of that unhappy controversy, however, resulted in the almost complete disappearance of the differential from English mathematics.