  Over the course of the next fifteen years as Lucasian Professor Newton presented his lectures and carried on research in a variety of areas. By 1671 he had completed most of a treatise length account of the  calculus,[2] which he then found no one would publish. This failure appears to have diverted his interest in mathematics away from the calculus for some time, for the mathematical lectures he registered during this period mostly concern algebra. (During the early 1680s he undertook a critical review of classical texts in geometry, a review that reduced his view of the importance of symbolic mathematics.)  His lectures from 1670 to 1672 concerned optics, with a large range of experiments presented in detail. Newton went public with his work in optics in early 1672, submitting material that was read before the Royal Society and then published in the Philosophical Transactions of the Royal Society. This led to four years of exchanges with various figures who challenged his claims, including both Robert Hooke and Christiaan Huygens — exchanges that at times exasperated Newton to the point that he chose to withdraw from further public exchanges in natural philosophy. Before he largely isolated himself in the late 1670s, however, he had also engaged in a series of sometimes long exchanges in the mid 1670s, most notably with John Collins (who had a copy of “De Analysi”) and Leibniz, concerning his work on the calculus. So, though they remained unpublished, Newton's advances in mathematics scarcely remained a secret.