At His Birth on Christmas Day, 1642, in Woolsthorpe, Lincolnshire, England, Newton Was

Isaac Newton (1642-1727)

At his birth on Christmas day, 1642, in Woolsthorpe, Lincolnshire, England, Newton was so tiny and frail that he was not expected to live. Yet despite his boyhood frailty, he lived to the age of 85. As a delicate child, he was a loner, interested more in reading, solving mathematical problems, and mechanical tinkering than in taking part in the usual boyish activities.

Until the time Newton entered Cambridge University in 1661, there was little inkling as to his mental prowess. His shyness kept him from making friends easily, and he did not mix with his more boisterous fellow students. At the university he took courses in Latin, Greek, Hebrew, logic, geometry, and trigonometry, and he attended lectures in astronomy, natural philosophy, and optics. His leisure time was spent reading works by Kepler and by Descartes, the inventor of analytic geometry, and filling his notebooks with remarks on the refraction of light, the grinding of lenses, and the extraction of roots of algebraic equations.

Newton received his baccalaureate degree--without any great distinction--and then returned to his home in Woolsthorpe because of the plague that was sweeping Europe. Over a period of 18 or so months at home, which were probably the most productive years of his life, Newton discovered the expansion of the general binomial (a+b)n, invented the "fluxions" (differential calculus), demonstrated that white light was composed of different colors of light, discovered the “Law of gravitation”, and laid the foundations of celestial mechanics.

In 1668 Newton constructed the world's first reflecting telescope. It had an aperture of 1 inch and a tube length of 6 inches, which led Newton to say of it: "This small instrument, though in itself contemptible may yet be looked upon as the epitome of what may be done this way." Not satisfied with his first effort, he completed an improved and somewhat larger reflector with an aperture of nearly 2 inches.

The publication of his book The Mathematical Principles of Natural Philosophy in 1687, which embodied his mathematical principles and ideas on gravitation and the system of the world, marked the peak of Newton's creative career. The Principia represents the thought and study of more than 20 years, and it ranks in importance with Ptolemy's Almagest and Copernicus's De Revolutionibus. His treatise Opticks appeared in 1704, but most of it was written many years earlier.

Many tributes followed Newton's death in 1727. One that stands out was made by the great French mathematical astronomer Lagrange, who said: "Newton was the greatest genius who ever lived, and the most fortunate; for we cannot find more than once a system of the world to establish." However, Newton said of himself: "If I have seen further than other men, it is because I have stood upon the shoulders of giants." In poet Alexander Pope's Epitaph for Newton are these lines:

Nature and Nature's laws lay hid in night;

God said, "Let Newton be!" and all was light.

The mathematicians considered in the last chapter commenced the creation of those processes, which distinguish modern mathematics. The extraordinary abilities of Newton enabled him within a few years to perfect the more elementary of those processes, and to distinctly advance every branch of mathematical science then studied, as well as to create some new subjects. Newton was the contemporary and friend of Wallis, Huygens, and others of those mentioned in the last chapter, but though most of his mathematical work was done between the years 1665 and 1686, the bulk of it was not printed - at any rate in book-form - till some years later.

I propose to discuss the works of Newton more fully than those of other mathematicians, partly because of the intrinsic importance of his discoveries, and partly because this book is mainly intended for English readers, and the development of mathematics in Great Britain was for a century entirely in the hands of the Newtonian school.

Isaac Newton 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 excited 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.

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.

There is a manuscript of his, dated May 28, 1665, written in the same year as that in which he took is B.A. degree, which is the earliest documentary proof of his invention of fluxions. It was about the same time that he discovered the binomial theorem.

On account of the plague the College was sent down during parts of the year 1665 and 1666, and for several months at this time Newton lived at home. This period was crowded with brilliant discoveries. He thought out the fundamental principles of his theory of gravitation, namely, that every particle of matter attracts every other particle, and he suspected that the attraction varied as the product of their masses and inversely as the square of the distance between them. He also worked out the fluxional calculus tolerably completely: this in a manuscript dated November 13, 1665, he used fluxions to find the tangent and the radius of curvature at any point on a curve, and in October 1666 he applied them to several problems in the theory of equations. Newton communicated these results to his friends and pupils from and after 1669, but they were not published in print till many years later. It was also whilst staying at home at this time that he devised some instruments for grinding lenses to particular forms other than spherical, and perhaps he decomposed solar light into different colours.

Leaving out details and taking round numbers only, his reasoning at this time on the theory of gravitation seems to have been as follows. He suspected that the force, which retained the moon in its orbit about the earth, was the same as terrestrial gravity, and to verify this hypothesis he proceeded thus. He knew that, if a stone were allowed to fall near the surface of the earth, the attraction of the earth (that is, the weight of the stone) caused it to move through 16 feet in one second. The moon's orbit relative to the earth is nearly a circle; and as a rough approximation, taking it to be so, he knew the distance of the moon, and therefore the length of its path; he also knew that time the moon took to go once round it, namely, a month.