Sir Isaac Newton (January 4, 1643 – March 31, 1727) was an English physicist, mathematician, astronomer, alchemist, inventor, and natural philosopher, who is generally regarded as one of the most accomplished and influential scientists in history.
In his work Philosophiae Naturalis Principia Mathematica, Newton enunciated his law of universal gravitation and three laws of motion. He thus laid the groundwork for classical mechanics, also known as Newtonian mechanics, which held sway in the physical sciences until the advent of quantum mechanics around the beginning of the twentieth century. By deriving Kepler’s laws of planetary motion from this system, he was the first to show that the motions of bodies on Earth and celestial bodies are governed by the same set of natural laws. The unifying and predictive power of his laws was integral to the scientific revolution and advancement of the heliocentric model of the solar system.
Among other scientific work, Newton realized that white light is composed of a spectrum of colors and further argued that light consists of corpuscles (particles). He enunciated the principles of conservation of momentum and angular momentum, and he developed a law describing the rate of cooling of objects when exposed to air. Furthermore, he studied the speed of sound in air and voiced a theory of the origin of stars.
Newton and Gottfried Wilhelm Leibniz share the credit for playing major roles in the development of calculus in the Western world. This area of mathematics has since proved of enormous value for the advancement of science and technology. Newton also made contributions to other areas of mathematics, having derived the binomial theorem in its entirety.
In addition to his monumental work in mathematics and science, Newton was a devout Christian, although a somewhat unorthodox and non-Trinitarian one. He claimed to study the Bible every day, and he wrote more on religion than he did on science. He thought that his scientific investigations were a way to bring to light the Creator’s work and the principles used by the Creator in ordering the physical universe.
Newton was born in Woolsthorpe-by-Colsterworth (at Woolsthorpe Manor), a hamlet in the county of Lincolnshire. As he was born prematurely, no one expected him to live. His mother, Hannah Ayscough Newton, is reported to have said that his body at that time could have fit inside a quart mug (Bell 1937). His father, Isaac, had died three months before Newton’s birth. When Newton was two, his mother went to live with her new husband, leaving her son in the care of his grandmother.
After beginning his education at village schools, Newton attended the King’s School in Grantham (Grantham Grammar School) from the age of 12. His signature remains preserved on a windowsill at Grantham. By October 1659, he had been removed from school and brought back to Woolsthorpe, where his mother attempted to make a farmer of him. Later reports of his contemporaries indicate that he was thoroughly unhappy with the work. It appears that Henry Stokes, master at the King’s School, persuaded Newton’s mother to send him back to school to complete his education. This he did at age 18, achieving an admirable final report. His teacher’s praise was effusive:
His genius now begins to mount upwards apace and shine out with more strength. He excels particularly in making verses. In everything he undertakes, he discovers an application equal to the pregnancy of his parts and exceeds even the most sanguine expectations I have conceived of him.
In June 1661, he matriculated to Trinity College, Cambridge. At that time, the college’s teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers such as Descartes and astronomers such as Galileo, Copernicus, and Kepler. In 1665, he discovered the binomial theorem and began to develop a mathematical theory that would later become calculus. A manuscript of his, dated May 28, 1665, is the earliest evidence of his invention of fluxions (derivatives in differential calculus). Soon after Newton obtained his degree in 1665, the University closed down as a precaution against the Great Plague. For the next 18 months, Newton worked at home on calculus, optics, and a theory of gravitation.
The only account of a romantic relationship in Newton’s life is connected to his time at Grantham. According to Eric Temple Bell (1937) and H. Eves:
At Grantham, he lodged with the local apothecary, William Clarke, and eventually became engaged to the apothecary’s stepdaughter, Anne Storer, before going off to Cambridge University at age 19. As Newton became engrossed in his studies, the romance cooled and Miss Storer married someone else. It is said he kept a warm memory of this love, but Newton had no other recorded “sweethearts” and never married.
Newton became a fellow of Trinity College in 1669. In the same year, he circulated his findings in De Analysi per Aequationes Numeri Terminorum Infinitas (On Analysis by Infinite Series), and later in De methodis serierum et fluxionum (On the Methods of Series and Fluxions), whose title gave rise to the “method of fluxions.”
Newton is generally credited with the binomial theorem, an essential step toward the development of modern analysis. It is now also recognized that Newton and Leibniz (the German polymath) developed calculus independently of each other, but for years a bitter dispute raged over who was to be given priority and whether Leibniz had stolen from Newton (see below).
Newton made substantial contributions toward our understanding of polynomials (such as the discovery of “Newton’s identities”) and the theory of finite differences. He discovered “Newton’s methods” (a root-finding algorithm) and new formulae for the value of pi. He was the first to use fractional indices, to employ coordinate geometry to derive solutions to diophantine equations, and to use power series with confidence and to revert power series. He also approximated partial sums of harmonic series by logarithms (a precursor to Euler’s summation formula).
He was elected Lucasian professor of mathematics in 1669. At that time, any fellow of Cambridge or Oxford had to be an ordained Anglican priest. The terms of the Lucasian professorship, however, required that the holder not be active in the church (presumably to have more time for science). Newton argued that this should exempt him from the ordination requirement, and Charles II, whose permission was needed, accepted this argument. Thus a conflict between Newton’s religious views and Anglican orthodoxy was averted.
Mathematician and mathematical physicist Joseph Louis Lagrange (1736–1813) described Newton as “the greatest genius that ever existed and the most fortunate, for we cannot find more than once a system of the world to establish.”
In July 1992, the Isaac Newton Institute for Mathematical Sciences was opened at Cambridge University. The Institute is regarded as the United Kingdom’s national institute for mathematical research.
The dispute over who first developed calculus
As with many areas of mathematics, calculus was developed through years of work by a number of different people. In particular, it was conceived and significantly developed by Indian mathematicians such as Bhaskara (1114–1185), Madhava of Sangamagrama (1340–1425), and members of the Kerala School founded by Madhava.
In the Western world, the two who contributed the most to the development of calculus were Newton and Leibniz. They worked independently and used different notations. Although Newton worked out his method some years before Leibniz, he published almost nothing about it until 1687 and did not give a full account until 1704. Newton did, however, correspond extensively with Leibniz. Meanwhile, Leibniz discovered his version of calculus in Paris between 1673 and 1676. He published his first account of differential calculus in 1684 and integral calculus in 1686.
It appears that Newton went further in exploring the applications of calculus; moreover, his focus was on limits and concrete reality, while that of Leibniz was on the infinite and abstract. Leibniz’s notation and “differential method” were universally adopted on the Continent, and after 1820 or so, in the British Empire. Newton claimed he had been reluctant to publish his work on the subject because he feared being mocked for it. Today, credit is given to both men, but there was a period when a nasty controversy pitted English mathematicians against those on the European continent, over who should be regarded as the originator of calculus.
Starting in 1699, some members of the Royal Society accused Leibniz of plagiarism, especially because letters of correspondence between Newton and Leibniz often discussed mathematics. The dispute broke out in full force in 1711. Thus began the bitter calculus priority dispute, which marred the lives of both Newton and Leibniz until the latter’s death in 1716, and continued for about a hundred years more. In 1715, just a year before Leibniz’s death, the British Royal Society handed down its verdict, crediting Newton with the discovery of calculus and concluding that Leibniz was guilty of plagiarism. Newton and his associates even tried to get ambassadors in the diplomatic corps in London to review old letters and papers in the hope of gaining support for the Royal Society’s findings. It later became known that these accusations were false, but Leibniz had already died.
This dispute, although it centered on questions of plagiarism and priority of discovery of calculus, also involved issues of national pride and allegiance. In fact, England did not agree to recognize the work of mathematicians from other countries until 1820. It is thought that this state of affairs may have retarded the progress of British mathematics by at least a century.
From 1670 to 1672, Newton lectured on optics. During this period, he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colors, and that a lens and second prism could recompose the multicolored spectrum into white light. He concluded that the spectrum of colors is inherent in the white light and not added by the prism (as Roger Bacon had claimed in the thirteenth century).
By separating out a colored beam and shining it on various objects, Newton showed that the colored light does not change its properties. He noted that regardless of whether a beam of colored light was reflected, scattered, or transmitted, it stayed the same color. Thus the colors we observe are the result of how objects interact with the incident, already-colored light, not the result of objects generating the color. Many of his findings in this field were criticized by later theorists, the most well-known being Johann Wolfgang von Goethe, who postulated his own color theories.
From this work, Newton concluded that any refracting telescope would suffer from the dispersion of light into colors, and he therefore invented a reflecting telescope (today known as a Newtonian telescope) to bypass that problem. By grinding his own mirrors and using “Newton’s rings” to judge the optical quality of his telescope, he was able to produce an instrument superior to the refracting telescope, due primarily to the wider diameter of the mirror. (Only later, as glasses with a variety of refractive properties became available, did achromatic lenses for refractors become feasible.) In 1671, the Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. When Robert Hooke criticized some of Newton’s ideas, Newton was so offended that he withdrew from public debate. The two men remained enemies until Hooke’s death.
Newton argued that light is composed of particles, which he called corpuscles, but he also associated them with waves to explain the diffraction of light (Opticks Bk. II, Props. XII-XX). Later physicists favored a purely wavelike explanation of light to account for diffraction. Today’s quantum mechanics introduces the concept of “wave-particle duality,” according to which light is made up of photons that have characteristics of both waves and particles.
Newton is believed to have been the first to explain precisely the formation of the rainbow from water droplets dispersed in the atmosphere in a rain shower. Figure 15 of Part II of Book One of Opticks shows a perfect illustration of how this occurs.
In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. Newton was in contact with Henry More, the Cambridge Platonist, on alchemy, and now his interest in the subject revived. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. In the opinion of John Maynard Keynes, who acquired many of Newton’s writings on alchemy, “Newton was not the first of the age of reason: he was the last of the magicians.”
As Newton lived at a time when there was no clear distinction between alchemy and science, his interest in alchemy cannot be isolated from his contributions to science 4. Some have suggested that had he not relied on the occult idea of action at a distance, across a vacuum, he might not have developed his theory of gravity.
In 1704, Newton wrote Opticks, in which he expounded his corpuscular theory of light. The book is also known for the first exposure of the idea of the interchangeability of mass and energy: “Gross bodies and light are convertible into one another….” Newton also constructed a primitive form of a frictional electrostatic generator, using a glass globe (Opticks, 8th Query).
Gravity and motion
In 1679, Newton returned to his work on gravitation and its effect on the orbits of planets, with reference to Kepler’s laws of planetary motion, and consulting with Hooke and John Flamsteed on the subject. He published his results in De Motu Corporum (1684). This contained the beginnings of the laws of motion.
The Philosophiae Naturalis Principia Mathematica (now known as the Principia) was published on July 5, 1687, with encouragement and financial help from Edmond Halley. In this work, Newton stated the three universal laws of motion that were not to be improved upon for more than 200 years. He used the Latin word gravitas (weight) for the force that would become known as gravity and defined the law of universal gravitation. Although his concept of gravity was revised by Einstein’s Theory of Relativity, it represents an enormous step in the development of human understanding of the universe. In Principia, Newton also presented the first analytical determination, based on Boyle’s law, of the speed of sound in air.
Newton’s three laws of motion can be stated as follows:
- First Law (the Law of Inertia): An object at rest tends to stay at rest and an object in motion tends to stay in motion unless acted upon by a net external force.
- Second Law: In mathematical terms, F = ma, or force equals mass times acceleration. In other words, the acceleration produced by a net force on an object is directly proportional to the magnitude of the net force and inversely proportional to the mass. In the MKS system of measurement, mass is given in kilograms; acceleration, in meters per second squared; and force, in Newtons (named in his honor).
- Third Law: For every action, there is an equal and opposite reaction.
With the Principia, Newton became internationally recognized. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed a strong friendship that lasted until 1693. The end of this friendship led Newton to a nervous breakdown.
In the 1690s, Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry More’s belief in the infinity of the universe and rejection of Cartesian dualism may have influenced Newton’s religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works—The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733)—were published after his death. He also devoted a great deal of time to alchemy (see above)
Newton was a member of the Parliament of England from 1689 to 1690 and again in 1701, but his only recorded comments were to complain about a cold draft in the chamber and request that the window be closed.
In 1696, Newton moved to London to take up the post of warden of the Royal Mint, a position he obtained through the patronage of Charles Montagu, First Earl of Halifax, then Chancellor of the Exchequer. He took charge of England’s Great Recoinage, somewhat treading on the toes of Master Lucas (and finagling Edmond Halley into the job of deputy comptroller of the temporary Chester branch). Newton became Master of the Mint upon Lucas’ death in 1699. These appointments were intended as sinecures, but Newton took them seriously, exercising his power to reform the currency and punish clippers and counterfeiters. He retired from his Cambridge duties in 1701. Ironically, it was his work at the Mint, rather than his contributions to science, that earned him a knighthood from Queen Anne in 1705.
Newton was made President of the Royal Society in 1703 and an associate of the French Académie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by prematurely publishing Flamsteed’s star catalog.
Newton died in London in 1727 and was buried in Westminster Abbey. His niece, Catherine Barton Conduitt, served as his hostess in social affairs at his house on Jermyn Street in London. He was her “very loving uncle,” according to his letter to her when she was recovering from smallpox.
The law of gravity became Newton’s best-known discovery. He, however, warned against using it to view the universe as a mere machine, like a great clock. He said that gravity explains the motions of the planets, but it cannot explain who set the planets in motion, and that God governs all things and knows all that is or can be done.
His scientific accomplishments notwithstanding, the Bible was Newton’s greatest passion. He devoted more time to the study of Scripture and alchemy than to science. Newton claimed to have a fundamental belief in the Bible as the Word of God, written by those who were inspired and that he studied the Bible daily. Newton himself wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture. Newton also placed the crucifixion of Jesus Christ at April 3, 33 C.E., which is now the accepted traditional date. He also attempted, unsuccessfully, to find hidden messages within the Bible. Despite his focus on theology and alchemy, he investigated biblical passages using the scientific method—observing, hypothesizing, and testing his theories. To Newton, his scientific and religious experiments were one and the same, observing and understanding how the world functioned.
Newton rejected the church’s doctrine of the Trinity and probably endorsed the Arian viewpoint that Jesus was the divine Son of God, created by God (and thus not equal to God). T.C. Pfizenmaier argues, however, that Newton more likely held the Eastern Orthodox view of the Trinity, rather than the Western one held by Roman Catholics, Anglicans, and most Protestants In his own day, he was also accused of being a Rosicrucian (as were many in the Royal Society and in the court of Charles II).
Newton wrote more on religion than he did on natural science. He believed in a rationally immanent world, but he rejected the hylozoism (doctrine that all matter has life) implicit in the thought of Leibniz and Baruch Spinoza. Thus, the ordered and dynamically informed universe could be and needed to be understood by an active reason, but this universe, to be perfect and ordained, had to be regular.
Newton’s effects on religious thought
Robert Boyle’s mechanical concept of the universe provided a foundation for attacks that were made against pre-Enlightenment “magical thinking” and the mystical elements of Christianity. Newton gave completion to Boyle’s ideas through mathematical proofs and was highly successful in popularizing them. Newton refashioned the world governed by an interventionist God into a world crafted by a God who designs along rational and universal principles. These principles were available for all people to discover, allowing us to pursue our aims fruitfully in this life, not the next, and to perfect ourselves with our rational powers. The perceived ability of Newtonians to explain the world, both physical and social, through logical calculations alone is the crucial concept that led to disenchantment with traditional Christianity.
The mechanical philosophy of Newton and Robert Boyle was promoted by rationalist pamphleteers as a viable alternative to the belief systems of pantheists (who considered God as immanent in or equivalent to the universe) and enthusiasts (who claimed to feel God’s intense presence). It was also accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians (who took the position that God values the moral condition of a person’s soul more than the individual’s doctrinal beliefs). The clarity of scientific principles was seen as a way to combat the emotional and metaphysical superlatives of the enthusiasts and the threat of atheism At the same time, the second wave of English deists used Newton’s discoveries to demonstrate the possibility of a “natural religion,” in which an understanding of God is derived from a rational analysis of nature rather than from revelation or tradition.
Newton saw God as the master creator whose existence could not be denied in the face of the grandeur of all creation. The unforeseen theological consequence of his concept of God, as Leibniz pointed out, was that God was entirely removed from the world’s affairs, since the need for intervention would only evidence some imperfection in God’s creation, something impossible for a perfect and omnipotent creator. Leibniz’s theodicy cleared God from the responsibility for “l’origine du mal” (the origin of evil) by removing God from participation in his creation. The understanding of the world was brought down to the level of simple human reason, and humans, as Odo Marquard argued, became responsible for the correction and elimination of evil.
On the other hand, latitudinarian and Newtonian ideas were taken to an extreme by the millenarians, a religious faction dedicated to the concept of a mechanical universe, but finding in it the same enthusiasm and mysticism that the Enlightenment had fought so hard to extinguish.
Effects on Enlightenment thought
Enlightenment philosophers chose a short list of scientific predecessors—mainly Galileo, Boyle, and Newton—as their guides for applying the singular concept of Nature and Natural Law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.
Newton’s concept of the universe based on natural and rationally understandable laws became seeds for Enlightenment ideology. Locke and Voltaire applied concepts of natural law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied natural concepts of psychology and self-interest to economic systems; and sociologists critiqued how the current social order fit history into natural models of progress.
Newton and the counterfeiters
As warden of the Royal Mint, Newton estimated that 20 percent of the coins taken in during the Great Recoinage were counterfeit. Counterfeiting was treason, punishable by death. Despite this, convictions of the most flagrant criminals could be maddeningly impossible to achieve. Newton, however, proved equal to the task.
He assembled facts and proved his theories with the same brilliance in law that he had shown in science. He gathered much of that evidence himself, disguised, while he spent time at bars and taverns. For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton was made a justice of the peace, and, between June 1698 and Christmas 1699, conducted some 200 cross-examinations of witnesses, informers, and suspects. Newton won his convictions and in February 1699, he had ten prisoners waiting to be executed.
Newton’s greatest triumph as the king’s attorney was against William Chaloner, a rogue with a deviously intelligent mind. Chaloner set up phony conspiracies of Catholics, and then turned in the hapless conspirators whom he entrapped. Chaloner made himself rich enough to posture as a gentleman. Accusing the mint of providing tools to counterfeiters, he proposed that he be allowed to inspect the mint’s processes to find ways to improve them. He petitioned parliament to adopt his plans for a coinage that could not be counterfeited. All the time, he struck false coins—or so Newton eventually proved to a court of competent jurisdiction. On March 23, 1699, Chaloner was hung, drawn and quartered.
A popular story claims that Newton was inspired to formulate his theory of universal gravitation by the fall of an apple from a tree. Cartoons have gone on to suggest the apple actually hit his head and that its impact made him aware of the force of gravity. There is no basis to that interpretation, but the story of the apple may have something to it. John Conduitt, Newton’s assistant at the Royal Mint and husband of Newton’s niece, described the event when he wrote about Newton’s life:
In the year 1666, he retired again from Cambridge … to his mother in Lincolnshire, & while he was musing in a garden, it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon thought he to himself & that if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a-calculating what would be the effect of that superposition… (Keesing 1998)
The question was not whether gravity existed, but whether it extended so far from Earth that it could also be the force holding the Moon to its orbit. Newton showed that if the force decreased as the inverse square of the distance, one could indeed calculate the Moon’s orbital period and get good agreement. He guessed the same force was responsible for other orbital motions and hence named it universal gravitation.
A contemporary writer, William Stukeley, recorded in his Memoirs of Sir Isaac Newton’s Life a conversation with Newton in Kensington on April 15, 1726. According to that account, Newton recalled “when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth’s centre.” In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), “Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree.” These accounts are variations of Newton’s own tale about sitting by a window in his home (Woolsthorpe Manor) and watching an apple fall from a tree.