NEWTON, ISAAC (b. Woolsthorpe, England, 25 December 1642; d. London, England, 20 March 1727), mathematics, dynamics, celestial mechanics, astronomy, optics, natural philosophy.

    with Montague and with the Royal Society, and met Huygens and others, including Locke, with whom he thereafter corresponded on theological and biblical questions. Richard Bentley sought Newton's advice and assistance in preparing the inaugural Boyle Lectures (or sermons), entitled “The Confutation of Atheism” and based in part on the Newtonian system of the world.

Newton also came to know two other scientists, each of whom wanted to prepare a second edition of the Principia. One was David Gregory, a professor at Edinburgh, whom Newton helped to obtain a chair at Oxford, and who recorded his conversations with Newton while Newton was revising the Principia in the 1690's. The other was a refugee from Switzerland, Nicolas Fatio de Duillier, advocate of a mechanical explanation of gravitation which was at one time viewed kindly by Newton. Fatio soon became perhaps the most intimate of any of Newton's friends. In the early autumn of 1693, Newton apparently suffered a severe attack of depression and made fantastic accusations against Locke and Pepys and was said to have lost his reason.15

In the post-Principia years of the 1690's, Newton apparently became bored with Cambridge and his scientific professorship. He hoped to get a post that would take him elsewhere. An attempt to make him master of the Charterhouse “did not appeal to him”16 but eventually Montague (whose star had risen with the Whigs' return to power in Parliament) was successful in obtaining for Newton (in March 1696) the post of warden of the mint. Newton appointed William Whiston as his deputy in the professorship. He did not resign officially until 10 December 1701, shortly after his second election as M.P. for the university.17

Mathematics. Any summary of Newton's contributions to mathematics must take account not only of his fundamental work in the calculus and other aspects of analysis--including infinite series (and most notably the general binomial expansion)--but also his activity in algebra and number theory, classical and analytic geometry, finite differences, the classification of curves, methods of computation and approximation, and even probability.

For three centuries, many of Newton's writings on mathematics have lain buried, chiefly in the Portsmouth Collection of his manuscripts. The major parts are now being published and scholars will shortly be able to trace the evolution of Newton's mathematics in detail.18 It will be possible here only to indicate highlights, while maintaining a distinction among four levels of dissemination of his work: (1) writings printed in his lifetime, (2) writings circulated in manuscript, (3) writings hinted at or summarized in correspondence, and (4) writings that were published only much later. In his own day and afterward, Newton influenced mathematics “following his own wish,” by “his creation of the fluxional calculus and the theory of infinite series,” the “two strands of mathematical technique which he bound inseparably together in his ‘analytick’ method.”19 The following account therefore emphasizes these two topics.

Newton appears to have had no contact with higher mathematics until 1664 when--at the age of twenty-one--his dormant mathematical genius was awakened by Schooten's “Miscellanies” and his edition of Descartes's Géométrie, and by Wallis' Arithmetica infinitorum (and possibly others of his works). Schooten's edition introduced him to the mathematical contributions of Heuraet, de Witt, Hudde, De Beaune, and others; Newton also read in Viète, Oughtred, and Huygens. He had further compensated for his early neglect of Euclid by careful study of both the Elements and Data in Barrow's edition.

In recent years20 scholars have come to recognize Descartes and Wallis as the two “great formative influences” on Newton in the two major areas of his mathematical achievement: the calculus, and analytic geometry and algebra. Newton's own copy of the Géométrie has lately turned up in the Trinity College Library; and his marginal comments are now seen to be something quite different from the general devaluation of Descartes's book previously supposed. Rather than the all-inclusive “Error. Error. Non est geom.” reported by Conduitt and Brewster, Newton merely indicated an “Error” here and there, while the occasional marginal entry “non geom.” was used to note such things as that the Cartesian classification of curves is not really geometry so much as it is algebra. Other of Newton's youthful annotations document what he learned from Wallis, chiefly the method of “indivisibles.”21

In addition to studying the works cited, Newton encountered the concepts and methods of Fermat and James Gregory. Although Newton was apparently present when Barrow “read his Lectures about motion,” and noted22 that they “might put me upon taking these things into consideration,” Barrow's influence on Newton's mathematical thought was probably not of such importance as is often supposed.

A major first step in Newton's creative mathematical life was his discovery of the general binomial theorem, or expansion of (a + b)n, concerning which he wrote, “In the beginning of the year 1665 I found the Method of approximating series & the Rule for