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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