Collins was elected a fellow of the Royal Society 24 October 1667, and on 11 November of that year communicated an exposition of a theorem by the Jesuit Jacques de Billy. He contributed further "An Account concerning the Resolution of Equations in Numbers", a survey of recent algebra improvements made in England, and "A Solution of a Chorographical Problem"; while a letter written to John Wallis, 3 October 1682, was imparted to the society 20 May 1684. This was designed as preliminary to a formal treatise on algebra, never written.