Isaac Newton and Mathematics #

INTRO-                                                      Newton, Sir Isaac (1642-1727), mathematician and physicist, one of the foremost scientific intellects of all time. Born at Woolsthorpe, near Grantham in Lincolnshire, where he attended school, he entered Cambridge University in 1661; he was elected a Fellow of Trinity College in 1667, and Lucasian Professor of Mathematics in 1669. He remained at the university, lecturing in most years, until 1696. Of these Cambridge years, in which Newton was at the height of his creative power, he singled out 1665-1666 (spent largely in Lincolnshire because of plague in Cambridge) as "the prime of my age for invention". During two to three years of intense mental effort he prepared Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as the Principia, although this was not published until 1687.


Life as Mathematician -                        In mathematics too, early brilliance appeared in Newton's student notes. He may have learnt geometry at school, though he always spoke of himself as self-taught; certainly he advanced through studying the writings of his compatriots William Oughtred and John Wallis, and of Descartes and the Dutch school. Newton made contributions to all branches of mathematics then studied, but is especially famous for his solutions to the contemporary problems in analytical geometry of drawing tangents to curves (differentiation) and defining areas bounded by curves (integration). Not only did Newton discover that these problems were inverse to each other, but he discovered general methods of resolving problems of curvature, embraced in his "method of fluxions" and "inverse method of fluxions", respectively equivalent to Leibniz's later differential and integral calculus. Newton used the term "fluxion" (from Latin meaning "flow") because he imagined a quantity "flowing" from one magnitude to another. Fluxions were expressed algebraically, as Leibniz's differentials were, but Newton made extensive use also (especially in thePrincipia) of analogous geometrical arguments. Late in life, Newton expressed regret for the algebraic style of recent mathematical progress, preferring the geometrical method of the Classical Greeks, which he regarded as clearer and more rigorous.