At Oxford Keill lectured on Newton's work and was soon appointed as a lecturer in experimental philosophy at Hart Hall :-
He therefore offered the first course on Newtonian natural philosophy, and the first reputedly based on 'experimental demonstrations', at either of the English universities. Judging from the published version of his lectures (Introductio ad veram physicam, Oxford, 1701), many of his demonstrations were mathematical rather than experimental, being based on 'thought experiments' (imagined experiments) rather than real manipulations.Keill was appointed deputy to the Sedleian professor of natural philosophy in 1699, a post he held until 1704. Keill was elected a Fellow of the Royal Society in 1701 and remained at Balliol College until his scholarship ran out in 1703 when he transferred to Christ Church. Despite acting as Sedleian professor of natural philosophy for five years, he failed to be appointed to fill the position when it became vacant in 1704. Similarly he was unlucky to fail in his application for the Savilian Professor of Astronomy which became vacant on David Gregory's death in 1708. Feeling that he would not progress further in Oxford, after his two failures, he decided to look for a government position. He was appointed treasurer of the fund set up to help protestant refugees from the Rhenish Palatinate. During the War of the Grand Alliance (1689-97), the troops of Louis XIV of France invaded the Rhenish Palatinate and many of the inhabitants fled for their lives. The fund helped those who wished to settle in England. Many wished to settle in North America and Keill accompanied a party who sailed to New England. He returned in 1711 and considered taking up a post as a mathematician in the Republic of Venice. However he was appointed to undertake decoding work for Queen Anne and decided to remain in England. In the following year the Savilian Professorship of Astronomy in Oxford became vacant again and this time Keill was appointed taking up the post in 1712.
Keill acted as a propagator of Newton's philosophy and argued against Whiston and others. He claimed that Leibniz had plagiarised Newton's invention of the calculus and he served as Newton's avowed champion. The part played by Keill in the controversy over who invented the calculus is fully brought out in . In fact Leibniz, in a 1705 article, had commented on Newton's elegant use of fluxions comparing it to Fabri who had:-
... substituted the advance of movements for the method of Cavalieri.This did not provoke any reaction from Newton until 1711 when Keill suggested that this could be interpreted as suggesting that Newton's fluxions were a moving version of Leibniz's differentials. Keill responded by accusing Leibniz of plagiarizing Newton in the Philosophical Transactions of the Royal Society and Leibniz wrote to the Royal Society asking that he withdraw his accusation. Keill maintained his position and Leibniz wrote to Newton asking him to tell Keill to withdraw his accusations.
The position went from bad to worse when Johann Bernoulli discovered an error in Newton's work. He wrote two articles explaining Newton's error and suggested that they demonstrated that Newton could not have invented the calculus independently of Leibniz since he was incapable of it. Keill wrote to Newton on 26 April 1714:-
I have read both pieces ... inserted in the Journal Litéraire and I think I never saw anything written with so much impudence, falsehood and slander as they are both. I am of the opinion that they must be immediately answered and I am now drawing up an answer which I will finish as soon as I hear from you ...Again Keill wrote to Newton on 19 May 1714:-
I am almost confident that he wrote that paper on purpose to show that you did not understand second fluxions ...Keill did write a reply in the Journal Litéraire which he intended as a defence of national honour. Although Keill and Newton seemed very friendly at this time it appeared that Newton grew tired of Keill's stirring up trouble. Newton made it up with Johann Bernoulli although Keill never did.
In 1717 Keill married Mary Clements. However :-
... his choice of wife was regarded as something of a scandal - Mary Clements was held to be of very inferior rank, being the daughter of James Clements, an Oxford bookbinder. Perhaps the attraction for Keill was the fact that she was twenty-five years younger. They had a son who became a linen draper in London ...Keill's work Euclides elementorum libri priores sex published in 1715 studies trigonometry and logarithms. He also wrote on forces between particles and on theories of the origin of the universe. He wrote up more of his lectures in Introductio ad veram (published in Leiden in 1725). In these he wrote:-
The only true philosophers are those who would account for all effects and phenomena by the known established laws of motion and mechanics.Two years before he died, Keill was left a fortune on the death of his brother James. Rather strangely, despite being very wealthy, he did not make a will. He died at his home of a severe fever and was buried at St Mary's Church, Oxford.
Article by: J J O'Connor and E F Robertson