in this final chapter we will consider the important contributions to the reform of the calculus which took place in Cambridge and Dublin. There is a link between the two universities, since John Brinkley, one of the most influential Dublin reformers, was educated at Cambridge and brought the heritage of Maskelyne and Waring to Ireland. Furthermore, both the Dublin and the Cambridge reformers were deeply concerned with the teaching of mathematics. Their attempt to reform the teaching of mathematics (and the calculus in particular) was much bolder than that of Playfair in Edinburgh, while – as we have seen – in the military schools such a project could not be implemented. The Dublin group insisted more on the teaching of applied mathematics (mechanics, physical astronomy, optics, etc.), whereas the Cambridge group was definitely purist–algebraist. A distinction must also be made at the level of research: in Ireland the stimulus came from Laplace, while in Cambridge the reformers were followers of Lagrange. Scholars of William Rowan Hamilton's optics, quaternions and mechanics, as well as scholars of the algebras of Peacock, Boole and De Morgan, will find this distinction quite significant.

Fluxions in Cambridge

During the late eighteenth century, Cambridge did not appear a promising centre of mathematical reform. Notwithstanding the fact that mathematics had become the most important subject in the education and in the ranking of students, their curriculum did not include any of the advances made after the 1720s.