Isaac Newton (1642-1727) is perhaps the most famous Lucasian Professor of Mathematics. He is probably best known to the average person because of the story of the falling apple and its relationship to the discovery of gravity. Newton discovered the force of gravity, and today the search is for its carrier: gravity waves. The years in between are a fascinating scientific story, detailed in a book edited by the current Lucasian professor, Stephen Hawking, Three Hundred Years of Gravitation.

Newton arrived at Cambridge in 1661, was elected scholar in 1664, graduated BA in 1664/5 in a class of twenty-six from Trinity, and made MA in 1668. During a wonderful surge of scientific production Newton produced three great achievements in the short space of two years. The first great achievement was the invention of fluxions, which resulted in calculus. He used this knowledge to advance his other work. Newton's second great achievement was the discovery of the law of the composition of light, later used in the development of optics. His third great achievement, the discovery of the universal force of gravity, was the basis for the Principia , his ultimate achievement.

Newton served as a member of Parliament representing the university. He took the Lucasian Chair in 1669. He was elected to the Royal Society in 1672, and elected president of the Royal Society in 1703, the year after he retired from the Lucasian professorship. He was knighted in 1705 at Trinity by Queen Anne. Later in life, Newton continued to achieve and was awarded numerous honors. He left Cambridge for London while still Lucasian professor. He was appointed Warden of the Mint in 1696 and Master of the Mint in 1699, when he led the effort for a recoinage.

A milestone event in Newton's life was the controversy with Leibniz. The Leibniz controversy is a low point in the history of science, revolving around the question of who was to receive the credit for the invention of calculus. It seems clear that each discovered it independently, but Newton somewhat earlier. Today we have adopted the notation created by Leibniz because it is easier to use and understand. Newton's notation is blamed for holding back the development of mathematics in England for a century. While it is not uncommon for controversies of this nature to develop, most are not as tangled and acrimonious as this one became.

The facts are not as clear as one would like, but it seems that during the initial stages in the development of calculus, when Newton and Leibniz were on good terms, letters from Newton to Leibniz contained hints of the fluxions. Newton is credited with the earliest discovery, but he asserted that no one should share in the honor of the discovery, implying that Leibniz had completely stolen his ideas. This naturally did not sit well with Leibniz, nor with his supporters. Leibniz developed a method of his own, perhaps with help from Newton's hints, but Leibniz created a more general method, more easily learned than Newton's. Both men were diminished somewhat by this controversy, with negative consequences for British mathematics, whose practitioners followed Newton out of blind loyalty.

He had left Cambridge to avoid the plague in 1665 eturning in 1667, as did many others. Cambridge dismissed everyone in the summer of 1665 and again in the summer of 1666 due to the severity of the plague. Newton's relationship with Isaac Barrow is important but not entirely clear. As a student at Trinity, he seems to have been required to attend Barrow's lectures, with some evidence that he was present at least twice. There is also a story about Barrow's examination of Newton that found Newton wanting in his mastery of Euclid. This story has been relegated to that of a myth by several later Newton scholars. Newton's own notes indicate his study of Euclid took place in his first two years at Cambridge, before this examination allegedly took place. It is an accepted fact that Barrow vacated the Chair in favor of Newton, who at that time had demonstrated his capabilities and impressed Barrow. Barrow acknowledged in his published lectures Newton's help on the manuscript, calling Newton a great genius.

Newton's monumental work Philosophiae Naturalis Principia Mathematica (1687) forever changed science, providing the basis for the modern understanding of the universe. The Principia is composed of three books. The first and second books present the laws and conditions of motions and forces. The third deduces the constitution of the universe from the principles offered in books one and two. The first book deals with the general dynamics in ideal conditions, that is with no friction. The second book deals mainly with fluids and friction.