In 1664, while still a student, Newton read recent work on optics & light by the English physicists Robert Boyle & Robert Hooke; he also studied both the mathematics & the physics of the French philosopher & scientist René Descartes. He investigated the refraction of light by a glass prism; developing over a few years a series of increasingly elaborate, refined, & exact experiments, Newton discovered measurable, mathematical patterns in the phenomenon of colour. He found white light to be a mixture of infinitely varied coloured rays (manifest in the rainbow & the spectrum), each ray definable by the angle through which it is refracted on entering or leaving a given transparent medium. He correlated this notion with his study of the interference colours of thin films (for example, of oil on water, or soap bubbles), using a simple technique of extreme acuity to measure the thickness of such films. He held that light consisted of streams of minute particles. From his experiments he could infer the magnitudes of the transparent "corpuscles" forming the surfaces of bodies, which, according to their dimensions, so interacted with white light as to reflect, selectively, the different observed colours of those surfaces.The roots of these unconventional ideas were with Newton by about 1668; when first expressed (tersely & partially) in public in 1672 & 1675, they provoked hostile criticism, mainly because colours were thought to be modified forms of homogeneous white light. Doubts, & Newton's rejoinders, were printed in the learned journals. Notably, the scepticism of Christiaan Huygens & the failure of the French physicist Edmé Mariotte to duplicate Newton's refraction experiments in 1681 set scientists on the Continent against him for a generation. The publication of Opticks, largely written by 1692, was delayed by Newton until the critics were dead. The book was still imperfect: the colours of diffraction defeated Newton. Nevertheless, Opticks established itself, from about 1715, as a model of the interweaving of theory with quantitative experimentation.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 & John Wallis, & of Descartes & 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) & 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" & "inverse method of fluxions", respectively equivalent to Leibniz's later differential & 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 the Principia) 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 & more rigorous.Newton's work on pure mathematics was virtually hidden from all but his correspondents until 1704, when he published, with Opticks, a tract on the quadrature of curves (integration) & another on the classification of the cubic curves. His Cambridge lectures, delivered from about 1673 to 1683, were published in 1707.
Newton had the essence of the methods of fluxions by 1666. The first to become known, privately, to other mathematicians, in 1668, was his method of integration by infinite series. In Paris in 1675 Gottfried Wilhelm Leibniz independently evolved the first ideas of his differential calculus, outlined to Newton in 1677. Newton had already described some of his mathematical discoveries to Leibniz, not including his method of fluxions. In 1684 Leibniz published his first paper on calculus; a small group of mathematicians took up his ideas.In the 1690s Newton's friends proclaimed the priority of Newton's methods of fluxions. Supporters of Leibniz asserted that he had communicated the differential method to Newton, although Leibniz had claimed no such thing. Newtonians then asserted, rightly, that Leibniz had seen papers of Newton's during a London visit in 1676; in reality, Leibniz had taken no notice of material on fluxions. A violent dispute sprang up, part public, part private, extended by Leibniz to attacks on Newton's theory of gravitation & his ideas about God & creation; it was not ended even by Leibniz's death in 1716. The dispute delayed the reception of Newtonian science on the Continent, & dissuaded British mathematicians from sharing the researches of Continental colleagues for a century.
According to the well-known story, it was on seeing an apple fall in his orchard at some time during 1665 or 1666 that Newton conceived that the same force governed the motion of the Moon & the apple. He calculated the force needed to hold the Moon in its orbit, as compared with the force pulling an object to the ground. He also calculated the centripetal force needed to hold a stone in a sling, & the relation between the length of a pendulum & the time of its swing. These early explorations were not soon exploited by Newton, though he studied astronomy & the problems of planetary motion.
Correspondence with Hooke (1679-1680) redirected Newton to the problem of the path of a body subjected to a centrally directed force that varies as the inverse square of the distance; he determined it to be an ellipse, so informing Edmond Halley in August 1684. Halley's interest led Newton to demonstrate the relationship afresh, to compose a brief tract on mechanics, & finally to write the Principia.Book I of the Principia states the foundations of the science of mechanics, developing upon them the mathematics of orbital motion round centres of force. Newton identified gravitation as the fundamental force controlling the motions of the celestial bodies. He never found its cause. To contemporaries who found the idea of attractions across empty space unintelligible, he conceded that they might prove to be caused by the impacts of unseen particles.Book II inaugurates the theory of fluids: Newton solves problems of fluids in movement & of motion through fluids. From the density of air he calculated the speed of sound waves.Book III shows the law of gravitation at work in the universe: Newton demonstrates it from the revolutions of the six known planets, including the Earth, & their satellites. However, he could never quite perfect the difficult theory of the Moon's motion. Comets were shown to obey the same law; in later editions, Newton added conjectures on the possibility of their return. He calculated the relative masses of heavenly bodies from their gravitational forces, & the oblateness of Earth & Jupiter, already observed. He explained tidal ebb & flow & the precession of the equinoxes from the forces exerted by the Sun & Moon. All this was done by exact computation.
Newton's work in mechanics was accepted at once in Britain, & universally after half a century. Since then it has been ranked among humanity's greatest achievements in abstract thought. It was extended & perfected by others, notably Pierre Simon de Laplace, without changing its basis & it survived into the late 19th century before it began to show signs of failing. See Quantum Theory; Relativity.Newton, Sir Isaac (1642-1727), mathematician & 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, & 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.As a firm opponent of the attempt by King James II to make the universities into Catholic institutions, Newton was elected Member of Parliament for the University of Cambridge to the Convention Parliament of 1689, & sat again in 1701-1702. Meanwhile, in 1696 he had moved to London as Warden of the Royal Mint. He became Master of the Mint in 1699, an office he retained to his death. He was elected a Fellow of the Royal Society of London in 1671, & in 1703 he became President, being annually re-elected for the rest of his life. His major work, Opticks, appeared the next year; he was knighted in Cambridge in 1705.As Newtonian science became increasingly accepted on the Continent, & especially after a general peace was restored in 1714, following the War of the Spanish Succession, Newton became the most highly esteemed natural philosopher in Europe. His last decades were passed in revising his major works, polishing his studies of ancient history, & defending himself against critics, as well as carrying out his official duties. Newton was modest, diffident, & a man of simple tastes. He was angered by criticism or opposition, & harboured resentment; he was harsh towards enemies but generous to friends. In government, & at the Royal Society, he proved an able administrator. He never married & lived modestly, but was buried with great pomp in Westminster Abbey.Newton has been regarded for almost 300 years as the founding examplar of modern physical science, his achievements in experimental investigation being as innovative as those in mathematical research. With equal, if not greater, energy & originality he also plunged into chemistry, the early history of Western civilization, & theology; among his special studies was an investigation of the form & dimensions, as described in the Bible, of Solomon's Temple in Jerusalem.
