The dominating influence of Newton had an unfortunate effect in turning the attention of English and Irish mathematicians away from the important developments taking place on the Continent. In consequence the contribution of Trinity mathematicians during the 18th century was not as distinguished as it otherwise might have been. There were, nevertheless, some able people such as William Hales, Hugh Hamilton, Richard Murray and Matthew Young. When Hales' Analysis Aequationum was published in 1784 the great French mathematician lagrange wrote of it `La clarté et la précision qui régnent dans cet ouvrage et la réunion qu'il présent des méthodes élémentaires et des théories sublimes doivent lui donner un des premiers rangs parmi ceux de son genre.' Hamilton published books on conic sections and on natural philosophy, and Young wrote An enquiry into the principal phenomena of sounds and musical strings. Murray, who was Professor of Mathematics from 1764 until 1795 when he became Provost, was influential as a teacher, particularly towards the candidates for Fellowship. The philosopher George Berkeley, who was a Fellow from 1707 to 1724 was an early critic of the underlying basis of Newton's calculus.

The establishment of the two Chairs of Natural Philosophy and of Mathematics was of particular importance for the development of the mathematical school. Both Chairs were endowed by the Governors of the Erasmus Smith Schools: that of Natural Philosophy in 1724 and of Mathematics in 1762. Another professorship of special relevance to mathematics was that of astronomy which was created by the bequest of provost Andrews who died in 1774, and based in Dunsink Observatory. Many of the incumbents of this chair were distinguished mathematicians: Brinkly, Ball, Whittaker; and the pre-eminent figure in Trinity mathematics, William Rowan Hamilton.

George Berkeley; Fellow 1707 to 1724,Bishop of Cloyne 1734 to 1753. Berkeley was strongly critical of the conceptual basis of Newton's calculus. He would not accept the concept of infinitesimal quantities and wrote scathingly of the "evanescent increments... May we not call them ghosts of departed quantities."