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Isaac Newton was born in Lincolnshire, near Grantham, on December 25, 1642, and died at Kensington, London, on March 20, 1727. He was educated at Trinity College, Cambridge, and lived there from 1661 till 1696, during which time he produced the bulk of his work in mathematics; in 1696 he was appointed to a valuable Government office, and moved to London, where he resided till his death.


His father, who had died shortly before Newton was born, was a yeoman farmer, and it was intended that Newton should carry on the paternal farm. He was sent to school at Grantham, where his learning and mechanical proficiency attracted some attention.  In 1656 he returned home to learn the business of a farmer, but spent most of his time solving problems, making experiments, or devising mechanical models; his mother noticing this, sensibly resolved to find some more congenial occupation for him, and his uncle, having been himself educated at Trinity College, Cambridge, recommended that he should be sent there.



Sir Isaac Newton


Sir Isaac Newton



In 1661 Newton accordingly entered as a student at Cambridge, where for the first time he found himself among surroundings which were likely to develop his powers. He seems, however, to have had but little interest for general society or for any pursuits save science and mathematics. Luckily he kept a diary, and we can thus form a fair idea of the course of education of the most advanced students at an English university at that time. He had not read any mathematics before coming into residence, but was acquainted with Sanderson's Logic, which was then frequently read as preliminary to mathematics. At the beginning of his first October term he happened to stroll down to Stourbridge Fair, and there picked up a book on astrology, but could not understand it on account of the geometry and trigonometry. He therefore bought a Euclid, and was surprised to find how obvious the propositions seemed. He thereupon read Oughtred's Clavis and Descartes's Géométrie, the latter of which he managed to master by himself, though with some difficulty. 


The interest he felt in the subject led him to take up mathematics rather than chemistry as a serious study. His subsequent mathematical reading as an undergraduate was founded on Kepler's Optics, the works of Vieta, van Schooten's Miscellanies, Descartes's Géométrie, and Wallis's Arithmetica Infinitorum: he also attended Barrow's lectures. At a later time, on reading Euclid more carefully, he formed a high opinion of it as an instrument of education, and he used to express his regret that he had not applied himself to geometry before proceeding to algebraic analysis.  Newton was forced to leave Cambridge when it was closed because of the plague, and it was during this period that he made some of his most significant discoveries. With the reticence he was to show later in life, Newton decided not to publish his results.


Newton suffered a mental breakdown in 1675 and was still recovering through 1679. In response to a letter from Hooke, he suggested that a particle, if released, would spiral in to the center of the Earth.  Hooke wrote back, claiming that the path would not be a spiral, but an ellipse. 


Newton, who hated being bested, then proceeded to work out the mathematics of orbits. Again, he did not publish his calculations. Newton then began devoting his efforts to theological speculation and put the calculations on elliptical motion aside, telling Halley he had lost them (Westfall 1993, p. 403). Halley, who had become interested in orbits, finally convinced Newton to expand and publish his calculations. Newton devoted the period from August 1684 to spring 1686 to this task, and the result became one of the most important and influential works on physics of all times, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) (1687), often shortened to Principia Mathematica or simply "the Principia."


In Book I of Principia, Newton opened with definitions and the three laws of motion now known as Newton's laws  (laws of inertia, action and reaction, and acceleration proportional to force). Book II presented Newton's new scientific philosophy which came to replace Cartesianism. Finally, Book III consisted of applications of his dynamics, including an explanation for tides and a theory of lunar motion. To test his hypothesis of universal gravitation, Newton wrote Flamsteed to ask if Saturn  had been observed to slow down upon passing Jupiter.  The surprised Flamsteed replied that an effect had indeed been observed, and it was closely predicted by the calculations Newton had provided. Newton's equations were further confirmed by observing the shape of the Earth to be oblate spheroidal,  as Newton claimed it should be, rather than prolate spheroidal,  as claimed by the Cartesians. Newton's equations also described the motion of Moon  by successive approximations, and correctly predicted the return of Halley's Comet. Newton also correctly formulated and solved the first ever problem in the calculus of variations  which involved finding the surface of revolution which would give minimum resistance to flow (assuming a specific drag law).


Newton invented a scientific method which was truly universal in its scope. Newton presented his methodology as a set of four rules for scientific reasoning. These rules were stated in the Principia and proposed that: 


(1) we are to admit no more causes of natural things such as are both true and sufficient to explain their appearances, 

(2) the same natural effects must be assigned to the same causes, 

(3) qualities of bodies are to be esteemed as universal, and 

(4) propositions deduced from observation of phenomena should be viewed as accurate until other phenomena contradict them.


These four concise and universal rules for investigation were truly revolutionary. By their application, Newton formulated the universal laws of nature with which he was able to unravel virtually all the unsolved problems of his day. Newton went much further than outlining his rules for reasoning, however, actually describing how they might be applied to the solution of a given problem. The analytic method he invented far exceeded the more philosophical and less scientifically rigorous approaches of Aristotle and Aquinas. 


Newton refined Galileo's experimental method, creating the compositional method of experimentation still practiced today. In fact, the following description of the experimental method from Newton's Optics could easily be mistaken for a modern statement of current methods of investigation, if not for Newton's use of the words "natural philosophy" in place of the modern term "the physical sciences." Newton wrote, "As in mathematics, so in natural philosophy the investigation of difficult things by the method of analysis ought ever to precede the method of composition. This analysis consists of making experiments and observations, and in drawing general conclusions from them by this way of analysis we may proceed from compounds to ingredients, and from motions to the forces producing them; and in general from effects to their causes, and from particular causes to more general ones till the argument end in the most general. This is the method of analysis: and the synthesis consists in assuming the causes discovered and established as principles, and by them explaining the phenomena preceding from them, and proving the explanations."  


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, and 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, and 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.  


Newton formulated the classical theories of mechanics and optics and invented calculus  years before Leibniz. However, he did not publish his work on calculus  until after Leibniz had published his. This led to a bitter priority dispute between English and continental mathematicians which persisted for decades, to the detriment of all concerned. Newton discovered that the binomial theorem  was valid for fractional powers, but left it for Wallis to publish (which he did, with appropriate credit to Newton). Newton formulated a theory of sound, but derived a speed which did not agree with his experiments. The reason for the discrepancy was that the concept of adiabatic propagation did not yet exist, so Newton's answer was too low by a factor of , where  is the ratio of heat capacities of air. Newton therefore fudged his theory until agreement was achieved.


In Optics (1704), whose publication Newton delayed until Hooke's death, Newton observed that white light could be separated by a prism  into a spectrum of different colors, each characterized by a unique refractivity, and proposed the corpuscular theory of light. Newton's views on optics were born out of the original prism  experiments he performed at Cambridge. In his "experimentum crucis" (crucial experiment), he found that the image produced by a prism  was oval-shaped and not circular, as current theories of light would require. He observed a half-red, half-blue string through a prism,  and found the ends to be disjointed. He also observed Newton's rings,  which are actually a manifestation of the wave nature of light which Newton did not believe in. Newton believed that light must move faster in a medium when it is refracted  towards the normal, in opposition to the result predicted by Huygens's wave theory.


Newton also formulated a system of chemistry in Query 31 at the end of Optics. In this corpuscular theory, "elements" consisted of different arrangements of atoms, and atoms consisted of small, hard, billiard ball-like particles. He explained chemical reactions in terms of the chemical affinities of the participating substances. Newton devoted a majority of his free time later in life (after 1678) to fruitless alchemical experiments.


Newton was extremely sensitive to criticism, and even ceased publishing until the death of his arch-rival Hooke. It was only through the prodding of Halley that Newton was persuaded at all to publish the Principia Mathematica. In the latter portion of his life, he devoted much of his time to alchemical researches and trying to date events in the Bible. After Newton's death, his burial place was moved. During the exhumation, it was discovered that Newton had massive amounts of mercury in his body, probably resulting from his alchemical pursuits. This would certainly explain Newton's eccentricity in late life. Newton was appointed Warden of the British Mint in 1695. Newton was knighted by Queen Anne. However, the act was "an honor bestowed not for his contributions to science, nor for his service at the Mint, but for the greater glory of party politics in the election of 1705" (Westfall 1993, p. 625).


As Newtonian science became increasingly accepted on the Continent, and 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, and defending himself against critics, as well as carrying out his official duties. Newton was modest, diffident, and a man of simple tastes. He was angered by criticism or opposition, and harboured resentment; he was harsh towards enemies but generous to friends. In government, and at the Royal Society, he proved an able administrator. He never married and lived modestly, but was buried with great pomp in Westminster Abbey.


Newton single handedly contributed more to the development of science than any other individual in history. He surpassed all the gains brought about by the great scientific minds of antiquity, producing a scheme of the universe which was more consistent, elegant, and intuitive than any proposed before. Newton stated explicit principles of scientific methods which applied universally to all branches of science. This was in sharp contradistinction to the earlier methodologies of Aristotle and Aquinas, which had outlined separate methods for different disciplines.


Although his methodology was strictly logical, Newton still believed deeply in the necessity of a God. His theological views are characterized by his belief that the beauty and regularity of the natural world could only "proceed from the counsel and dominion of an intelligent and powerful Being." He felt that "the Supreme God exists necessarily, and by the same necessity he exists always and everywhere." Newton believed that God periodically intervened to keep the universe going on track. He therefore denied the importance of Leibniz's vis viva as nothing more than an interesting quantity which remained constant in elastic collisions and therefore had no physical importance or meaning.


Newton, was the first to place dynamics on a satisfactory basis, and from dynamics he deduced the theory of statics: this was in the introduction to the Principia published in 1687. The theory of attractions, the application of the principles of mechanics to the solar system, the creation of physical astronomy, and the establishment of the law of universal gravitation are due to him, and were first published in the same work, but of the nature of gravity he confessed his ignorance, though he found inconceivable the idea of action at a distance. The particular questions connected with the motion of the earth and moon were worked out as fully as was then possible. The theory of hydrodynamics was created in the second book of the Principia, and he added considerably to the theory of hydrostatics which may be said to have been first discussed in modern times by Pascal. The theory of the propagation of waves, and in particular the application to determine the velocity of sound, is due to Newton and was published in 1687. In geometrical optics, he explained amongst other things the decomposition of light and the theory of the rainbow; he invented the reflecting telescope known by his name, and the sextant. In physical optics, he suggested and elaborated the emission theory of light.


Although earlier philosophers such as Galileo and John Philoponus had used experimental procedures, Newton was the first to explicitly define and systematize their use. His methodology produced a neat balance between theoretical and experimental inquiry and between the mathematical and mechanical approaches. Newton mathematized all of the physical sciences, reducing their study to a rigorous, universal, and rational procedure which marked the ushering in of the Age of Reason. Thus, the basic principles of investigation set down by Newton have persisted virtually without alteration until modern times. In the years since Newton's death, they have borne fruit far exceeding anything even Newton could have imagined. They form the foundation on which the technological civilization of today rests. The principles expounded by Newton were even applied to the social sciences, influencing the economic theories of Adam Smith and the decision to make the United States legislature bicameral. These latter applications, however, pale in contrast to Newton's scientific contributions.


It is therefore no exaggeration to identify Newton as the single most important contributor to the development of modern science. The Latin inscription on Newton's tomb, despite its bombastic language, is thus fully justified in proclaiming, "Mortals! rejoice at so great an ornament to the human race!" Alexander Pope's couplet is also apropos: "Nature and Nature's laws lay hid in night; God said, Let Newton be! and all was light."


Newton published an edition of Geographia generalis by the German geographer Varenius in 1672. His own letters on optics appeared in print from 1672 to 1676. Then he published nothing until the Principia (published in Latin in 1687; revised in 1713 and 1726; and translated into English in 1729). This was followed by Opticks in 1704; a revised edition in Latin appeared in 1706. Posthumously published writings include The Chronology of Ancient Kingdoms Amended (1728), The System of the World (1728), the first draft of Book III of the Principia, and Observations upon the Prophecies of Daniel and the Apocalypse of St John (1733). 





Engineering and Science, Caltech, No. 2, pp. 15-16, Winter 1991.

Andrade, E. N. da C. Sir Isaac Newton. Greenwood Pub., 1979.

Bell, E. T. "On the Seashore: Newton." Ch. 6 in Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré. New York: Simon and Schuster, pp. 90-116, 1986.

Christianson, G. E. In the Presence of Creation: Isaac Newton and His Times. New York: Free Press, 1984.

De Gandt, F. Force and Geometry in Newton's Principia. Princeton, NJ: Princeton University Press, 1995.

Fauvel, J.; Flood, R.; Shortland, M., and Wilson, R. (Eds.). Let Newton Be! New York: Oxford University Press, 1988.

Gjertsen, D. The Newton Handbook. London: Routledge, 1986.

Guicciardini, N. Reading the Principia: The Debate on Newton's Mathematical Methods for Natural Philosophy form 1687 to 1736. Cambridge, England: Cambridge University Press, 1999.

Hall, A. R. Isaac Newton: Adventurer in Thought. Cambridge, England: Cambridge University Press, 1996.

Lines, M. E. On the Shoulders of Giants. Philadelphia: Inst. of Phys., 1994.

Manuel, F. E. A Portrait of Isaac Newton. Da Capo Press, 1990.

Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. Gravitation. San Francisco, CA: W. H. Freeman, 1973.

Newton, I. The Principia: Mathematical Principles of Natural Philosophy (Trans. I. B. Cohen and A. Whitman). Berkeley, CA: University of California Press, 1999.

Turnbull, H. W. The Mathematical Discoveries of Newton. London, England: Blackie and Sons, 1945.

Westfall, R. S. The Life of Isaac Newton. Cambridge: Cambridge University Press, 1994.

Westfall, R. S. Never at Rest: A Biography of Isaac Newton. New York: Cambridge University Press, 1988.

White, M. Isaac Newton: The Last Sorcerer. Reading, MA: Addison-Wesley, 1997.










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