Sir Issac Newton.

Sir Isaac Newton PRS (25 December 1642 – 20 March 1726/27[a]) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

Isaac Newton was born (according to the Julian calendar, in use in England at the time) on Christmas Day, 25 December 1642 (NS 4 January 1643[a]) "an hour or two after midnight",[8] at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. His father, also named Isaac Newton, had died three months before. Born prematurely, Newton was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug.[9]When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough (née Blythe). Newton disliked his stepfather and maintained some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and the house over them."[10]Newton's mother had three children (Mary, Benjamin and Hannah) from her second marriage.[11]

From the age of about twelve until he was seventeen, Newton was educated at The King's School, Grantham, which taught Latin and Greek and probably imparted a significant foundation of mathematics.[12] He was removed from school and returned to Woolsthorpe-by-Colsterworth by October 1659. His mother, widowed for the second time, attempted to make him a farmer, an occupation he hated.[13] Henry Stokes, master at The King's School, persuaded his mother to send him back to school. Motivated partly by a desire for revenge against a schoolyard bully, he became the top-ranked student,[14]distinguishing himself mainly by building sundials and models of windmills.[15]

In June 1661, he was admitted to Trinity College, Cambridge, on the recommendation of his uncle Rev William Ayscough, who had studied there. He started as a subsizar—paying his way by performing valet's duties—until he was awarded a scholarship in 1664, guaranteeing him four more years until he could get his MA.[16] At that time, the college's teachings were based on those of Aristotle, whom Newton supplemented with modern philosophers such as Descartes, and astronomers such as Galileo and Thomas Street, through whom he learned of Kepler's work. He set down in his notebook a series of "Quaestiones" about mechanical philosophyas he found it. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his BA degree in August 1665, the university temporarily closed as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student,[17] Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus,[18] optics, and the law of gravitation.

In April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity.[19][20] Fellows were required to become ordained priests, although this was not enforced in the restoration years and an assertion of conformity to the Church of England was sufficient. However, by 1675 the issue could not be avoided and by then his unconventional views stood in the way.[21]Nevertheless, Newton managed to avoid it by means of special permission from Charles II.

His studies had impressed the Lucasian professor Isaac Barrow, who was more anxious to develop his own religious and administrative potential (he became master of Trinity two years later); in 1669 Newton succeeded him, only one year after receiving his MA. He was elected a Fellow of the Royal Society (FRS) in 1672.[4]

Newton's work has been said "to distinctly advance every branch of mathematics then studied."[23] His work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newton's mathematical papers.[24] The author of the manuscript De analysi per aequationes numero terminorum infinitas, sent by Isaac Barrow to John Collins in June 1669, was identified by Barrow in a letter sent to Collins in August of that year as "[...] of an extraordinary genius and proficiency in these things."[25]

Newton later became involved in a dispute with Leibniz over priority in the development of calculus (the Leibniz–Newton calculus controversy). Most modern historians believe that Newton and Leibniz developed calculus independently, although with very different mathematical notations. Occasionally it has been suggested that Newton published almost nothing about it until 1693, and did not give a full account until 1704, while Leibniz began publishing a full account of his methods in 1684. Leibniz's notation and "differential Method", nowadays recognised as much more convenient notations, were adopted by continental European mathematicians, and after 1820 or so, also by British mathematicians.[citation needed]

Such a suggestion fails to account for the calculus in Book 1 of Newton's Principia itself and in its forerunner manuscripts, such as De motu corporum in gyrum of 1684; this content has been pointed out by critics[Like whom?] of both Newton's time and modern times.[citation needed]

His work extensively uses calculus in geometric form based on limiting values of the ratios of vanishingly small quantities: in the Principia itself, Newton gave demonstration of this under the name of "the method of first and last ratios"[26] and explained why he put his expositions in this form,[27] remarking also that "hereby the same thing is performed as by the method of indivisibles."[28]

Because of this, the Principia has been called "a book dense with the theory and application of the infinitesimal calculus" in modern times[29] and in Newton's time "nearly all of it is of this calculus."[30] His use of methods involving "one or more orders of the infinitesimaĵlly small" is present in his De motu corporum in gyrum of 1684[31] and in his papers on motion "during the two decades preceding 1684".