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His will is referenced in the Oxford Dictionary of National Biography and is held by The National Archives. It was stated in the old Dictionary of National Biography that Keill left no will. On 31 August 1721, Keill died in London from a sudden illness, possibly food poisoning. The marriage created great scandal at the time as Clements was from a lower class.
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In 1717, Keill married Mary Clements, a woman 25 years his junior and the daughter of an Oxford bookbinder. However, Newton himself eventually grew tired of Keill as he stirred up too much trouble. In his later years, Keill became involved in the controversy regarding Gottfried Leibniz's alleged plagiarisation of Newton's invention of calculus, serving as Newton's chief defender. On 9 July 1713, he was awarded the DM degree. In 1712, Keill returned to Oxford as Savilian Professor of Astronomy. His responsibilities included explaining old manuscripts to the sovereign. In 1711, Keill accepted the position of decypherer to Anne, Queen of Great Britain. He accompanied at least one group of German refugees to the British Province of New York. In 1709, Keill was appointed treasurer of a charitable fund to resettle war refugees from the German states. However, after failing to get an academic appointment at Oxford in 1709, Keill left the university to seek a government position. In 1700, he was elected a Fellow of the Royal Society. This publication, along with his teaching, gained Keill notice in the English academic community. His volume contained scientific attacks on Burnet, René Descartes, Baruch Spinoza, Thomas Hobbes and Nicolas Malebranche. He instructed his students on the laws of motion, the principles of hydrostatics and optics, and Newtonian propositions on light and colours. After being appointed a lecturer in experimental philosophy at Hart Hall, Keill started giving lectures and performing experiments based on Newton's findings. Keill then attended Balliol College, Oxford, obtaining an MA on 2 February 1694.
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In 1692, he obtained his bachelor's degree with a distinction in physics and mathematics. Keill studied at Edinburgh University under David Gregory. His brother, James Keill, became a noted physician. His father was Robert Keill, an Edinburgh lawyer. Keill was born in Edinburgh, Scotland on 1 December 1671.