Newton - 17th Century Mathematics - The Story of Mathematics The Story of Mathematics 17TH CENTURY MATHEMATICS - NEWTON Sir Isaac Newton (1643-1727) In the heady atmosphere of 17th Century England, with the expansion of the British empire in full swing, grand old universities like Oxford and Cambridge were producing many great scientists and mathematicians. But the greatest of them all was undoubtedly Sir Isaac Newton. Physicist, mathematician, astronomer, natural philosopher, alchemist and theologian, Newton is considered by many to be one of the most influential men in human history. His 1687 publication, the "Philosophiae Naturalis Principia Mathematica" (usually called simply the "Principia"), is considered to be among the most influential books in the history of science, and it dominated the scientific view of the physical universe for the next three centuries. Although largely synonymous in the minds of the general public today with gravity and the story of the apple tree, Newton remains a giant in the minds of mathematicians everywhere (on a par with the all-time greats like Archimedes and Gauss ), and he greatly influenced the subsequent path of mathematical development.

Over two miraculous years, during the time of the Great Plague of 1665-6, the young Newton developed a new theory of light, discovered and quantified gravitation, and pioneered a revolutionary new approach to mathematics: infinitesimal calculus. His theory of calculus built on earlier work by his fellow Englishmen John Wallis and Isaac Barrow, as well as on work of such Continental mathematicians as Ren� Descartes , Pierre de Fermat , Bonaventura Cavalieri, Johann van Waveren Hudde and Gilles Personne de Roberval. Unlike the static geometry of the Greeks , calculus allowed mathematicians and engineers to make sense of the motion and dynamic change in the changing world around us, such as the orbits of planets, the motion of fluids, etc. Differentiation (derivative) approximates the slope of a curve as the interval approaches zero The initial problem Newton was confronting was that, although it was easy enough to represent and calculate the average slope of a curve (for example, the increasing speed of an object on a time-distance graph), the slope of a curve was constantly varying, and there was no method to give the exact slope at any one individual point on the curve i.e.

effectively the slope of a tangent line to the curve at that point. Intuitively, the slope at a particular point can be approximated by taking the average slope (�rise over run�) of ever smaller segments of the curve. As the segment of the curve being considered approaches zero in size (i.e. an infinitesimal change in x), then the calculation of the slope approaches closer and closer to the exact slope at a point (see image at right). Without going into too much complicated detail, Newton (and his contemporary Gottfried Leibniz independently) calculated a derivative function f �(x) which gives the slope at any point of a function f(x). This process of calculating the slope or derivative of a curve or function is called differential calculus or differentiation (or, in Newton�s terminology, the �method of fluxions� - he called the instantaneous rate of change at a particular point on a curve the "fluxion", and the changing values of x and y the "fluents").

For instance, the derivative of a straight line of the type f(x) = 4x is just 4; the derivative of a squared function f(x) = x2 is 2x; the derivative of cubic function f(x) = x3 is 3x2, etc. Generalizing, the derivative of any power function f(x) = xr is rxr-1. Other derivative functions can be stated, according to certain rules, for exponential and logarithmic functions, trigonometric functions such as sin(x), cos(x), etc, so that a derivative function can be stated for any curve without discontinuities. For example, the derivative of the curve f(x) = x4 - 5x3 + sin(x2) would be f �(x) = 4x3 - 15x2 + 2xcos(x2). Having established the derivative function for a particular curve, it is then an easy matter to calcuate the slope at any particular point on that curve, just by inserting a value for x. In the case of a time-distance graph, for example, this slope represents the speed of the object at a particular point.

Integration approximates the area under a curve as the size of the samples approaches zero The �opposite� of differentiation is integration or integral calculus (or, in Newton�s terminology, the �method of fluents�), and together differentiation and integration are the two main operations of calculus. Newton�s Fundamental Theorem of Calculus states that differentiation and integration are inverse operations, so that, if a function is first integrated and then differentiated (or vice versa), the original function is retrieved. The integral of a curve can be thought of as the formula for calculating the area bounded by the curve and the x axis between two defined boundaries. For example, on a graph of velocity against time, the area �under the curve� would represent the distance travelled. Essentially, integration is based on a limiting procedure which approximates the area of a curvilinear region by breaking it into infinitesimally thin vertical slabs or columns.

In the same way as for differentiation, an integral function can be stated in general terms: the integral of any power f(x) = xr is xr+1⁄r+1, and there are other integral functions for exponential and logarithmic functions, trigonometric functions, etc, so that the area under any continuous curve can be obtained between any two limits. Newton chose not to publish his revolutionary mathematics straight away, worried about being ridiculed for his unconventional ideas, and contented himself with circulating his thoughts among friends. After all, he had many other interests such as philosophy, alchemy and his work at the Royal Mint. However, in 1684, the German Leibniz published his own independent version of the theory, whereas Newton published nothing on the subject until 1693. Although the Royal Society, after due deliberation, gave credit for the first discovery to Newton (and credit for the first publication to Leibniz ), something of a scandal arose when it was made public that the Royal Society�s subsequent accusation of plagiarism against Leibniz was actually authored by none other Newton himself, causing an ongoing controversy which marred the careers of both men.

Newton's Method for approximating the roots of a curve by successive interations after an initial guess Despite being by far his best known contribution to mathematics, calculus was by no means Newton�s only contribution. He is credited with the generalized binomial theorem, which describes the algebraic expansion of powers of a binomial (an algebraic expression with two terms, such as a2 - b2); he made substantial contributions to the theory of finite differences (mathematical expressions of the form f(x�+�b) - f(x�+�a)); he was one of the first to use fractional exponents and coordinate geometry to derive solutions to Diophantine equations (algebraic equations with integer-only variables); he developed the so-called �Newton's method� for finding successively better approximations to the zeroes or roots of a function; he was the first to use infinite power series with any confidence; etc. In 1687, Newton published his �Principia� or �The Mathematical Principles of Natural Philosophy�, generally recognized as the greatest scientific book ever written.

In it, he presented his theories of motion, gravity and mechanics, explained the eccentric orbits of comets, the tides and their variations, the precession of the Earth's axis and the motion of the Moon. Later in life, he wrote a number of religious tracts dealing with the literal interpretation of the Bible, devoted a great deal of time to alchemy, acted as Member of Parliament for some years, and became perhaps the best-known Master of the Royal Mint in 1699, a position he held until his death in 1727. In 1703, he was made President of the Royal Society and, in 1705, became the first scientist ever to be knighted. Mercury poisoning from his alchemical pursuits perhaps explained Newton's eccentricity in later life, and possibly also his eventual death. Isaac Newton Biography | Facts, Quotes & Inventions Isaac Newton Biography March 24, 2016 07:37pm ET MORE Isaac Newton laid the blueprints for his three laws of motion, still recited by physics students, in 1666. Credit: Library of Congress Isaac Netwon is synonymous with apples and gravity.

He rose to become the most influential scientist of the 17th century, his ideas becoming the foundation of modern physics, after very humble beginnings. But first, the big question: Did an apple really fall on Newton's head and spur him to figure out gravity? Historians say there is likely no more than a grain of truth to the story. Sir Isaac Newton was born, premature and tiny, in 1642 in Woolsthorpe, England. His father, wealthy but uneducated, died before Newton was born, and he ended up being raised by his grandmother after his mother remarried. It’s said he didn’t excel at school, but he ended up studying law at Trinity College Cambridge, part of Cambridge University. He worked as a servant to pay his bills. And he kept a journal about his ideas. What got Newton interested in math? He bought a book on the subject and couldn't comprehend it. After getting his bachelor's degree in 1665; he studied math, physics, optics and astronomy on his own (Cambridge was closed for a couple of years due to the plague known as the Black Death). By 1666 he had completed his early work on his three laws of motion .

Later he got his master's degree. Later work focused on the diffraction of light (he used a prism to discover that white light is made of a spectrum of colors ) and the concepts he'd become known for: universal gravitation, centrifugal force, centripetal force, and the effects and characteristics of bodies in motion. His laws are still used by physics students today: An object will remain in a state of inertia unless acted upon by force. The relationship between acceleration and applied force is F=ma. For every action there is an equal and opposite reaction. Isaac Newton quotes Newton said many things worth remembering, including these philosophical gems: "I can calculate the motion of heavenly bodies, but not the madness of people." "To myself I am only a child playing on the beach, while vast oceans of truth lie undiscovered before me." Newton once said that if he had achieved anything in his research, it was "by standing on the shoulders of giants ." The quote was prophetic. A couple of centuries later, Albert Einstein puzzled over how to reconcile Newton's law of gravity with special relativity, which after several years led to Einstein's theory of general relativity .

Isaac Newton inventions While he's best known for his work on gravity, Newton was a tinkerer, too, but more with ideas than physical inventions. He did invent reflecting lenses for telescopes, which produced clearer images in a smaller telescope compared with the refracting models of the time. In his later years, he developed anti-counterfeiting measures for coins, including the ridges you see on quarters today. Among his biggest " inventions " was calculus. Yes, that's right. Mere math and algebra weren't enough to explain the ideas in his head, so he helped invent calculus (German mathematician Gottfried Leibniz is typically credited with developing it independently at about the same time). It's said that Newton invented a cat door so his cats would stop scratching to get in, but the truth of that one is a bit sketchy. He also conceived of an "orbital cannon" that would poke out of a huge mountain, up in space, and with just the right amount of gunpowder could put a cannonball into orbit. This was not something Newton actually imagined building, but rather a way to think about his theories.

Later years Urged by astronomer Edmond Halley (who was studying his now-famous comet), Newton continued to study his notion of gravity and apply it to the motions of the Earth, sun and moon. It all led to his seminal work, published in 1687, called the "Principia" — considered by many as the greatest science book ever written. Newton's research stopped in 1679 when he had a nervous breakdown. Later, recovered, he spoke out against King James II, who wanted only Roman Catholics to be in powerful government and academic positions. When James was later driven out of England, Newton was elected to Parliament. He had a second breakdown in 1693, then retired from research. Isaac Newton died in 1727. Among his more eccentric pastimes, Newton also dabbled (or more than dabbled) in alchemy, also called chymistry, with some historians estimating that he wrote more than a million words of alchemical notes, according to curator of rare books at the Chemical Heritage Foundation, James Voelkel. And in March 2016, researchers announced they had found bought a 17th-century alchemy manuscript written by Newton .

The manuscript, which had been hidden in a private collection for decades and turned up at an auction at Bonhams, provided the recipe for "philosophic" mercury, which was considered a step in the process for concocting a mysterious substance known the philosopher's stone; this material was thought to have supernatural powers — the ability to turn any metal into gold and to grant immortality. The manuscript will be available online for enthusiasts to explore. Further reading ISAAC -- Newton's life Sir Isaac Newton's life Newton's life Newton, Sir Isaac (1643-1727), English mathematician and physicist, considered one of the greatest scientists in history, who made important contributions to many fields of science. His discoveries and theories laid the foundation for much of the progress in science since his time. Newton was one of the inventors of the branch of mathematics called calculus (the other was German mathematician Gottfried Wilhelm Leibniz). He also solved the mysteries of light and optics, formulated the three laws of motion, and derived from them the law of universal gravitation. Newton was born on January 4, 1643, at Woolsthorpe, near Grantham in Lincolnshire.

When he was three years old, his widowed mother remarried, leaving him in the care of his grandmother. Eventually his mother, by then widowed a second time, was persuaded to send him to grammar school in Grantham. Later, in the summer of 1661, he was sent to Trinity College, at the University of Cambridge. Newton received his bachelor's degree in 1665. After an intermission of nearly two years to avoid the plague, Newton returned to Trinity, which elected him to a fellowship in 1667. He received his master's degree in 1668. Newton ignored much of the established curriculum of the university to pursue his own interests: mathematics and natural philosophy. Proceeding entirely on his own, he investigated the latest developments in mathematics and the new natural philosophy that treated nature as a complicated machine. Almost immediately, he made fundamental discoveries that were instrumental in his career in science. The Fluxional Method Newton's first achievement was in mathematics. He generalized the methods that were being used to draw tangents to curves and to calculate the area swept by curves, and he recognized that the two procedures were inverse operations.

By joining them in what he called the fluxional method, Newton developed in the autumn of 1666 a kind of mathematics that is now known as calculus. Calculus was a new and powerful method that carried modern mathematics above the level of Greek geometry. Although Newton was its inventor, he did not introduce calculus into European mathematics. In 1675 Leibniz arrived independently at virtually the same method, which he called differential calculus. Leibniz proceeded to publish his method and received sole credit for its invention until Newton published a detailed exposition of his fluxional method in 1704. Always fearful of publication and criticism, Newton kept his discovery to himself. However, enough was known of his abilities to effect his appointment in 1669 as Lucasian Professor of Mathematics at the University of Cambridge. Optics Optics was another area of Newton's early interests. In trying to explain how colours occur, he arrived at the idea that sunlight is a heterogeneous blend of different rays each of which represents a different colour and that reflections and refractions cause colours to appear by separating the blend into its components.

Newton demonstrated his theory of colours by passing a beam of sunlight through a type of prism, which split the beam into separate colours. In 1672 Newton sent a brief exposition of his theory of colours to the Royal Society in London. Its appearance in the Royal Society's Philosophical Transactions led to a number of criticisms that confirmed his fear of publication, and he subsequently withdrew as much as possible into the solitude of his Cambridge study. In 1704, however, Newton published Opticks, which explained his theories in detail. The Principia In August 1684 Newton's solitude was interrupted by a visit from Edmund Halley, the British astronomer and mathematician, who discussed with Newton the problem of orbital motion. Newton had also pursued the science of mechanics as an undergraduate, and at that time he had already entertained basic notions about universal gravitation. As a result of Halley's visit, Newton returned to these studies. During the following two and a half years, Newton established the modern science of dynamics by formulating his three laws of motion. Newton applied these laws to Kepler's laws of orbital motion formulated by the German astronomer Johannes Kepler and derived the law of universal gravitation.

Newton is probably best known for discovering universal gravitation, which explains that all bodies in space and on earth are affected by the force called gravity. He published this theory in his book Philosophiae Naturalis Principia Mathematica in 1687. This book marked a turning point in the history of science; it also ensured that its author could never regain his privacy. The Principia's appearance also involved Newton in an unpleasant episode with the English philosopher and physicist Robert Hooke. In 1687 Hooke claimed that Newton had stolen from him a central idea of the book: that bodies attract each other with a force that varies inversely as the square of their distance. However, most historians do not accept Hooke's charge of plagiarism. In the same year, 1687, Newton helped lead Cambridge's resistance to the efforts of King James II to make the university a Catholic institution. After the English Revolution in 1688, which drove James from England, the university elected Newton one of its representatives in a special convening of the country's parliament.

The following four years were filled with intense activity for Newton, as, buoyed by the triumph of the Principia, he tried to put all his earlier achievements into a final written form. In the summer of 1693 Newton showed symptoms of a severe emotional disorder. Although he regained his health, his creative period had come to an end. Newton's connections with the leaders of the new regime in England led to his appointment as warden, and later master, of the Royal Mint in London, where he lived after 1696. In 1703 the Royal Society elected him president, an office he held for the rest of his life. As president, he ordered the immediate publication of the astronomical observations of the first Astronomer Royal of England, John Flamsteed. Newton needed these observations to perfect his lunar theory. This matter led to a difficult conflict with Flamsteed. Newton also engaged in a violent dispute with Leibniz over priority in the invention of calculus. Newton used his position as president of the Royal Society to have a committee of that body investigate the question, and he secretly wrote the committee's report, which charged Leibniz with deliberate plagiarism.

Newton also compiled the book of evidence that the society published. The effects of the quarrel lingered nearly until his death in 1727. In addition to science, Newton also showed an interest in alchemy, mysticism, and theology. Many pages of his notes and writings particularly from the later years of his career are devoted to these topics. However, historians have found little connection between these interests and Newton's scientific work. > Isaac Newton 1642 1727 7 German mathematician and philosopher - COE - 2001 View Full Document Isaac Newton (1642-1727) 7 German mathematician and philosopher. Leibniz developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass- produced mechanical calculator.

He also refined the binary number system, which is at the foundation of virtually all digital computers. Gottfried W. v. Leibniz (1646-1716) 8 Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. He extended Newton’s laws to the motion of finite-sized rigid bodies, stating that the resultant of all external forces is equal to the time derivative of its linear momentum, and that the resultant moment of all external forces and couples about a fixed point is equal to the time derivative of the angular momentum about the same point. Leonhard Euler (1707-1783) 9 This is the end of the preview. Sign up to access the rest of the document.

TERM LECTURES+-+12+-+Statics+Overview+-+PDF Georgia Tech Statics Overview Statics Overview 1 Vectors 2 Vectors: Trigonometry Addition, sub LECTURES+-+12+-+Statics+Overview+-+PDF Isaac Newton and his Contributions to Mathematics | 3010tangents Isaac Newton and his Contributions to Mathematics Sir Isaac Newton. Image: Arthur Shuster & Arthur E. Shipley, via Wikimedia Commons.. In class we discussed the Fundamental Theorem of Calculus and how Isaac Newton contributed to it, but what other discoveries did he make? Sir Isacc Newton was born on January 4, 1643, but in England they used the Julian Calender at that time and his birthday was on Christmas Day 1642. He was born in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. His father had already passed prior to his birth and his mother remarried after his birth and left Isaac to live with her mother. He went to The King’s School, Grantham from the time he was twelve until he was seventeen.

His mother removed him from school after the death of her second husband, but later allowed him to return by the encouragement of the school’s headmaster. He rose to be at the top in rankings in his school, mainly motivated to get revenge towards a bully. He began attending Trinity College in Cambridge in 1661. After receiving his degree he developed his theories on calculus over the span of two years during the plague [1] . Newton’s work in calculus intitially started as a way to find the slope at any point on a curve whose slope was constantly varying (the slope of a tangent line to the curve at any point). He calculated the derivative in order to find the slope. He called this the “method of fluxions” rather than differentiation. That is because he termed “fluxion” as the instantaneous rate of change at a point on the curve and “fluents” as the changing values of x and y. He then established that the opposite of differentiation is integration, which he called the “method of fluents”. This allowed him to create the First Fundamental Theorem of Calculus, which states that if a function is integrated and then differentiated the original function can be obtained because differentiation and integration are inverse functions [2] .

Controversy later arose over who developed calculus. Newton didn’t publish anything about calculus until 1693, but German mathematician Leibniz published his own version of the theory in 1684. The Royal Society accused Leibniz of plagiarism in 1699 and the dispute caused a scandal to occur in 1711 when the Royal Society claimed Newton was the real discoverer of calculus. The scandal got worse when it was discovered that the accusations against Leibniz were actually written by Newton. The dispute between Newton and Leibniz went on until the death of Leibniz. It is now believed that both developed the theories of Calculus independently, both with very different notations. It should also be noted that Newton actually developed his Fundamental Theory of Calculus between 1665 and 1667, but waited to publish his works due to fear of being criticized and causing controversy [1] . Newton not only discovered calculus but he is also credited for the discovery of the generalised binomial theorem. This theorem describes the algebraic expansion of powers of a binomial.

He also contributed to the theory of finite differences, he used fractional exponents and coordinate geometry to get solutions to Diophantine equations, he developed a method for finding better approximation to the zeroes or roots of a function, and he was the first to use infinite power series. His work and discoveries were not limited to mathematics; he also developed theories in optics and gravitation. He observed that prisms refract different colors at different angles, which led him to conclude that color is a property intrinsic to light. He developed his theory of color by noting that regardless if colored light was reflected, scattered, or transmitted it remained the same color. Therefore color is the result of objects interacting with colored light and objects do not generate their own colors themselves [1] . Sir Isaac Newton was a truly amazing mathematician and scientist. He achieved so much in his lifetime and the amount of discoveries he made can seem almost impossible. He helped make huge advancements in mathematics and created theorems that we still use heavily to this day. Newton, Isaac | Larson Calculus – Calculus 10e Isaac Newton (1642-1727) Isaac Newton wrote, “. . .

to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” History, of course, sees him very differently. Newton is revered as one of the first to develop the calculus and as the founder of the sciences of dynamics and spectroscopy. He is often credited with inaugurating the Age of Reason. Newton was born prematurely in 1642 in Woolsthorpe, Lincolnshire, in England. His mother claimed that he was so small at birth that he would have fit in a quart mug; in fact, he was not expected to live. Newton’s father died several months before Isaac’s birth. When Newton’s mother remarried two years later, he was sent to live with his grandmother on an isolated farm. The loneliness and ill health that marred Newton’s childhood led to a lifelong interest in intellectual pursuits, to the exclusion of all else. He never married, cared nothing for his appearance, and frequently forgot to eat. His friends were few; his later years were tarnished by bitter quarrels.

Because his physical frailty barred him from participation in the village children’s games, the young Newton occupied himself with solitary pastimes. He particularly enjoyed building miniature working models of carriages, waterwheels, and the like. This skill, developed in childhood, served him well when later in life he sought to construct experimental devices with lenses to prove his theories on the properties of light. Newton was an unremarkable student until the day when he was kicked in the stomach by the school bully. Newton was, surprisingly, able to defeat his opponent, apparently by strength of will if not of body. Having thus tasted victory, Newton determined to surpass his rival, a highranking scholar, at his studies as well. Within a short time Newton rose to the head of his class. This was nearly the end of his academic success. Newton’s mother’s second husband died when Newton was 14 years old, and Newton was withdrawn from school to work on his mother’s farm. It soon became apparent, however, that this was an occupation for which Newton was woefully unsuited. He had no interest in crops or stock, preferring instead to read or dream.

Newton’s mother acknowledged defeat: in 1661, when Newton was 18 years old, she permitted him to enter Trinity College at Cambridge University. While at Cambridge, Newton came to the attention of Isaac Barrow, a professor of mathematics and a gifted scientist and classicist. Newton had done nothing to distinguish himself academically during his first years at the university; nevertheless, Barrow recognized the young man’s “unparalleled genius.” Soon after Newton received his bachelor’s degree in 1665, Barrow relinquished his academic post and was instrumental in securing the professorship for Newton. Thus by the time he was 26 years old, Newton had attained a position of distinction that left him free to pursue his own interests, since his responsibilities were not very taxing. He was required to lecture only once each week on some aspect of mathematics, astronomy, geography, or optics, and to devote two hours per week to consultation with students. The subject on which he chose to lecture that first year was optics. Newton had been drawn to the investigation of light and colors during the previous 18 months, spent at his home in Woolsthorpe when an outbreak of the plague necessitated the temporary closing of Trinity.

During that same period, he also developed the fundamentals of calculus and formulated his law of universal gravitation! It has been suggested that those 18 months were the most productive in all the history of creative imagination. Unfortunately, a fear of criticism restrained Newton from immediately publishing his discoveries. In 1672, Newton submitted his reflecting telescope, an invention arising from his study of light, to the Royal Society of London. This community of scientists immediately recognized the value of Newton’s work and appointed him a Fellow of the Royal Society, England’s highest scientific honor. Thus encouraged, Newton published through the Royal Society a report of his analysis of light and color. The paper failed to win for him the accolade he craved; instead, the Royal Society was besieged with objections. At first, Newton tried to explain his conclusions to his detractors. When his efforts failed to convince them, he grew angry and bitter, and resolved to publish nothing more. For more than a decade Newton labored in relative obscurity at Cambridge, until the day in 1684 when he was visited by Edmund Halley, the celebrated British astronomer and mathematician.

Halley and his associates Robert Hooke and Christian Huygens had been hindered in their research by their inability to apply Johannes Kepler’s laws to determine the orbit of a planet, and sought Newton’s opinion. Newton immediately supplied Halley with the answer, that the orbit was an ellipse. From this, Halley was able to deduce that Newton had discovered the law of gravity, and begged him for his calculations. At Halley’s tactful but insistent urging Newton was persuaded to publish his theorems and proofs, with Halley bearing the cost of printing. The resulting masterpiece, the Philosophiae Naturalis Principia Mathematica, met with instant and virtually universal acclaim upon its release in 1687. The Principia, as it is known, is comprised of three books. The first defines Newton’s three laws of motion and describes the importance of several laws of force; the second concerns motion in various types of fluids; and the third proves the existence of universal gravitation. Taken together, the three books constitute an enormous body of scientific knowledge with extraordinary significance. Newton appears to have suffered some sort of emotional collapse following the publication of the Principia. He grew increasingly suspicious and argumentative, and all scientific inquiry ceased.

In 1696, Newton terminated his position at Cambridge. Through the influence of the English philosopher John Locke, Newton was appointed Warden and later Master of the Royal Mint in London, a lucrative government post. Unfortunately, Newton’s free time was spent not in the pursuit of knowledge, but in acrimony. He used the influence of his position as president of the Royal Society, an honor bestowed on him in 1703, to launch a brutal attack on the German mathematician Gottfried Wilhelm Leibniz, whom Newton unjustly accused of plagiarizing his invention of calculus. History contends that Leibniz arrived at his discovery of calculus independently, using the same sources as Newton. Since Newton had ignored his mentor Isaac Barrow’s suggestion that he publish his notes at the time they were written, there was little substantiation for Newton’s claim of priority. Newton also engaged in bitter and protracted battles with Hooke and the astronomer John Flamsteed. It has been noted that a quarrel accompanied virtually all of Newton’s achievements.

Though the last 30 years of his life were barren of discovery, Newton was knighted by Queen Anne in 1705 in recognition of his inestimable contribution to scientific knowledge. He was buried in Westminster Abbey after his death at the age of 84 in March, 1727. Links Isaac Newton's Life | Isaac Newton Institute for Mathematical Sciences Isaac Newton Institute for Mathematical Sciences Special thanks to the Microsoft Corporation for their contribution to our site. The following information came from Microsoft Encarta. I INTRODUCTION 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. 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. 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 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 and originality he also plunged into chemistry, the early history of Western civilization, and theology; among his special studies was an investigation of the form and dimensions, as described in the Bible, of Solomon's Temple in Jerusalem. II OPTICS In 1664, while still a student, Newton read recent work on optics and light by the English physicists Robert Boyle and Robert Hooke; he also studied both the mathematics and the physics of the French philosopher and scientist René Descartes. He investigated the refraction of light by a glass prism; developing over a few years a series of increasingly elaborate, refined, and 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 and 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 and partially) in public in 1672 and 1675, they provoked hostile criticism, mainly because colours were thought to be modified forms of homogeneous white light. Doubts, and Newton's rejoinders, were printed in the learned journals. Notably, the scepticism of Christiaan Huygens and 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.

III MATHEMATICS 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 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 and 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) and another on the classification of the cubic curves. His Cambridge lectures, delivered from about 1673 to 1683, were published in 1707. The Calculus Priority Dispute 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 and his ideas about God and creation; it was not ended even by Leibniz's death in 1716. The dispute delayed the reception of Newtonian science on the Continent, and dissuaded British mathematicians from sharing the researches of Continental colleagues for a century. IV MECHANICS AND GRAVITATION 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 and 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, and the relation between the length of a pendulum and the time of its swing. These early explorations were not soon exploited by Newton, though he studied astronomy and 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, and 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 and 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, and 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, and the oblateness of Earth and Jupiter, already observed. He explained tidal ebb and flow and the precession of the equinoxes from the forces exerted by the Sun and Moon. All this was done by exact computation. Newton's work in mechanics was accepted at once in Britain, and universally after half a century. Since then it has been ranked among humanity's greatest achievements in abstract thought.

It was extended and perfected by others, notably Pierre Simon de Laplace, without changing its basis and it survived into the late 19th century before it began to show signs of failing. See Quantum Theory; Relativity. V ALCHEMY AND CHEMISTRY Newton left a mass of manuscripts on the subjects of alchemy and chemistry, then closely related topics. Most of these were extracts from books, bibliographies, dictionaries, and so on, but a few are original. He began intensive experimentation in 1669, continuing till he left Cambridge, seeking to unravel the meaning that he hoped was hidden in alchemical obscurity and mysticism. He sought understanding of the nature and structure of all matter, formed from the "solid, massy, hard, impenetrable, movable particles" that he believed God had created. Most importantly in the "Queries" appended to "Opticks" and in the essay "On the Nature of Acids" (1710), Newton published an incomplete theory of chemical force, concealing his exploration of the alchemists, which became known a century after his death.

VI HISTORICAL AND CHRONOLOGICAL STUDIES Newton owned more books on humanistic learning than on mathematics and science; all his life he studied them deeply. His unpublished "classical scholia"explanatory notes intended for use in a future edition of the Principiareveal his knowledge of pre-Socratic philosophy; he read the Fathers of the Church even more deeply. Newton sought to reconcile Greek mythology and record with the Bible, considered the prime authority on the early history of mankind. In his work on chronology he undertook to make Jewish and pagan dates compatible, and to fix them absolutely from an astronomical argument about the earliest constellation figures devised by the Greeks. He put the fall of Troy at 904 BC, about 500 years later than other scholars; this was not well received. VII RELIGIOUS CONVICTIONS AND PERSONALITY Newton also wrote on Judaeo-Christian prophecy, whose decipherment was essential, he thought, to the understanding of God. His book on the subject, which was reprinted well into the Victorian Age, represented lifelong study.

Its message was that Christianity went astray in the 4th century AD, when the first Council of Nicaea propounded erroneous doctrines of the nature of Christ. The full extent of Newton's unorthodoxy was recognized only in the present century: but although a critic of accepted Trinitarian dogmas and the Council of Nicaea, he possessed a deep religious sense, venerated the Bible and accepted its account of creation. In late editions of his scientific works he expressed a strong sense of God's providential role in nature. VIII PUBLICATIONS 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). Contributed By: Alfred Rupert Hall "Sir Isaac Newton" Microsoft® Encarta®. Copyright © 1998 Microsoft Corporation. Newton Isaac Newton 1642 - 1727 Sir Isaac Newton has been described by some as "one of the greatest names in human thought" (Cohen, 1985). Newton was responsible for discovering many outstanding scientific and mathematical concepts. Among those discoveries were his theories of motion and gravitation, the components of light and color and his development of the foundations of calculus. There were many interesting aspects of Newtons life which seemed at times to contradict each other. Newton, was born on Christmas day in 1642 to a family of farmers in the east central portion of England in Linconshire. Surprisingly young Isaac was not an exceptional student.

He enjoyed spending much of his time making contraptions such as a windmill used to grind grain, a clock which was powered by water and other various inventions. Unfortunately because of the time he spent on his projects he did very poorly in school. His teachers described him as "idle" and "inattentive". His father died before he was born and mother remarried leaving him in the care of his grandmother. At the age of fourteen Newton was forced to leave school to help his mother with farming. Isaac spent much of his time on the farm reading and ended up returning to school. At the bidding of an uncle, Newton began furthering his education in June of 1661, when he entered Trinity College, Cambridge. He set out to get a degree in law and this limited his field of study was very during his first few years of college. However, by the third year he was allowed more freedom to pursue other interests. During this time he was able to study new mathematical and scientific methods from such scientists and mathematicians as Galileo, and Wallis. Newton graduated from Cambridge in 1665, without any particular honors.

In the summer of 1665, Newton who had not been an exceptional student and appeared at times very average, seemed to under go a change. During an eighteen month period, in which the school he was at was shut down because of the plague, Newton came up with his theories of motion and gravitation, the components of white light, and calculus. The often told story of how Newton discovered gravity goes as follows: Newton was drinking tea as the British often do, and he observed an apple falling from a tree. He deduced that the same force which caused the apple to fall to the ground causes the moon to orbit the earth (Cohen, 1985). As stated earlier, Newton helped developed what he called fluxions, which is now called calculus ( Burton, 1997). This branch of mathematics Newton discovered, could be used find the answers to such problems as finding the speed of a ball that has been thrown in the air at any moment in the balls flight. During the same time period a German mathematician named Gottfried Leibniz also discovered calculus. With Newtons's and Leibniz's new discoveries mathematicians and scientists were able to enter into new regions of discovery.

As if that wasn't enough Newton made a third important discovery. He used a prism to show that white light is made up of many different colors. Before this scientists had thought that white light was a single entity. While Isaac was looking through a telescope, one day he noted how the light reflected many different colors and led him to this discovery. Newton was very sensitive to negative comments and had to be convinced by another scientist Edmond Halley to publish his findings. After his book Principia Mathematica in which his various discoveries and ideas were presented, Newton enjoyed success in other realms. He became a member of the British Parliament and was a member of various mathematical organizations such as the Royal Society council to which he was later elected president. He died on March 31, 1727 in London. Newton had many interesting characteristics such as his study alchemy. Which is a blend of chemistry, magic and religion. Achlemists' goal was to find a way to produce gold out of different metals and also to find a magic potion which could cure ills and increase ones life. Isaac was modest, and generous to his family and those who helped him along the way.

Some of Newton's discoveries were later refuted by Albert Einstein in reference to his theories of gravitational pull. However, Einstein and others still contend that Newton was indeed a very important force in man's quest for knowledge and is highly regarded for his contributions in many different areas of science. Contributed by Chris Pinaire Burton, D. (1997). The history of mathematics, an introduction, McGraw-Hill New York. Cohen, B. (1985) Sir Isaac Newton.The World Book Encyclopedia, Chicago. Ihde, A. (1985) Alchemy. The World Book Encyclopedia, Chicago. Sir Isaac Newton (1642-1727): - creation.com by Ann Lamont Summary Isaac Newton is well known as one of the greatest scientists who ever lived. Less well known is his deep belief in God and his conviction that scientific investigation leads to a greater knowledge of God the Creator of the universe. Isaac Newton was born at Woolthorpe, Lincolnshire, England on Christmas Day 1642. On that cold winter night, the sick, premature baby seemed unlikely to live. Gradually, however, he gained strength to survive. But Isaac’s first few years were a struggle.

His mother had become a widow two months before Isaac was born. Even with the help of her own mother, she had difficulty caring for Isaac in addition to running their farm while the Civil War in England raged around them. Several years later, his mother married the minister from nearby North Witham, but Isaac remained at Woolthorpe with his grandmother. As he grew, however, he visited his mother frequently. He eagerly read books from his stepfather's well-stocked library, in addition to reading the Bible regularly. Isaac attended school at King’s College in nearby Grantham. Rather than playing outdoor games as a boy, he preferred to make models of such things as windmills and carts. Not only were these in exactly the right proportions, but all of the moving parts actually worked. Isaac’s mother was widowed for the second time when he was 14 years old. Isaac was taken out of school to run the family farm to support his mother and her three younger children. However, Isaac missed his studies greatly and his mother recognized this. When King’s College offered to waive tuition fees because of his ability and poor circumstances, Isaac returned and completed his schooling.

Teachers and other students were impressed with the boy’s knowledge of the Bible. Intended to become a minister Isaac then went to Trinity College at Cambridge University with the intention of becoming a Church of England minister. Again, life was not easy for him. As he was unable to afford the tuition fees, he worked many hours each day serving meals and doing other jobs for the professors in order to pay his way. Isaac’s knowledge of the Bible continued to impress those around him. At that time the ideas of the ancient Greek scholars still dominated what was taught in science, and recent scientific discoveries were largely ignored. This greatly annoyed Isaac Newton who firmly believed that ideas in science should be tested and only accepted if their usefulness could be demonstrated. He was committed to the experimental method of science. Isaac graduated in 1665, shortly before an outbreak of Black Death swept through London. All universities were closed while the plague raged. During this time, Isaac returned to his family’s farm, now run by his young half-brother. He continued his study and research, working on the binomial theorem, light, telescopes, calculus and theology.

After supposedly seeing an apple fall in the garden, he investigated gravity, but was unable to solve the puzzle until some years later. (It should be noted that some authorities question this ‘apple’ story. They say that the first mention of it came through the antireligious French philosopher and skeptic, Voltaire, who reputedly heard it from Newton’s grandniece.) Revolution in Mathematics Newton applied his binomial theorem to infinite series and from there developed calculus, a revolutionary new form of mathematics. For the first time it was possible to accurately calculate the area inside a shape with curved sides, and to calculate the rate of change of one physical quantity with respect to another. A similar system of mathematics was developed by German mathematician Gottfried Leibniz. For a long time there was great confusion, with each being accused of stealing the other’s work. It was a distressing time for both. Many years later, it was established that each had developed calculus independently at roughly the same time. Neither was a cheat. Sir Isaac Newton used prisms to show that sunlight was made up of all the colours of the rainbow. This proved that the ancient Greeks ideas about light were wrong.

Optics When Cambridge University reopened in 1667, Isaac Newton returned to do a Masters Degree, while teaching and doing research. Newton used prisms to show that sunlight was made up of all the colours of the rainbow. This proved that the ancient Greeks’ ideas about light were wrong. In Newton’s time, astronomy was severely hampered because lenses in telescopes broke some of the light into unwanted colours, causing a somewhat unclear view. Although not the first to consider using a curved mirror instead of a lens, Newton was the first to successfully construct a telescope using this principle—a principle still used today in many telescopes. The Royal Society In 1672, Newton became a member of the Royal Society—a group of scientists committed to the experimental method. He presented one of his new telescopes to the Royal Society along with his findings on light. The Royal Society set up a committee led by physicist Robert Hooke to evaluate Newton's findings. Hooke was a scientist employed by the Royal Society to evaluate new inventions. However, Hooke had his own ideas on light and was slow to accept the truth of Newton’s findings. This surprised and disappointed Newton, who even considered not circulating his discoveries in the future.

While it is sometimes said that Newton was too sensitive to critical evaluation of his work, he was merely concerned that the time spent justifying past findings was preventing him from making new discoveries. Political Interference Isaac Newton lived at a time when politics, religion and education were not separated. King Charles II commanded that everyone who taught at places such as Trinity College, where Church of England ministers were trained, must themselves be ordained as Church of England ministers after seven years. This included people such as Newton who taught only mathematics and science, not theology. Although a devout Christian, Newton was not in full agreement with all the doctrines of the Church of England. Thus, his conscience would not allow him to accept ordination. 1 He was also strongly opposed to political involvement in both religious matters and education. The only way for Newton to keep his job was for the king to make an exception in his case. Others who had previously asked for this had been refused. So Newton headed south to London for six weeks to plead his case before the king. During his time in London, he became better acquainted with other scientists in the Royal Society. Those who had known him only through his letters defending his discoveries had mistaken his confidence in his work for arrogance.

His impatience to get on with new work had been mistaken for bad temper. Now the scientists realized what a friendly and considerate person he was and they rallied to his aid. Fortunately, for Newton and for science, the king granted Newton’s request to continue at Trinity College without being ordained. Focused on Gravity In Newton’s day, many people were superstitious or afraid of what they could not understand—such as the appearance of a comet, which was considered a sign of coming disaster. Even scientists generally considered the motion of planets and the motion of bodies on the earth as separate problems. In contrast, Newton reasoned that since the same God created the heavens as well as the earth, the same laws should apply throughout. In 1684, Newton again began to consider gravity. He developed his theory of universal gravitation, which used what is known as the inverse square law. He developed his three laws of motion (movement) and proved mathematically that the same laws did, in fact, apply both to the heavens and the earth. His faith had focused his thoughts in the right direction. When Newton was investigating the movement of the planets, he quite clearly saw the hand of God at work.

He wrote: ‘This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent Being. … This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called “Lord God” Παντοκράτωρ [Pantokratōr cf. 2 Corinthians 6:18], or “Universal Ruler”. … The Supreme God is a Being eternal, infinite, absolutely perfect.’ 2 ‘Opposition to godliness is atheism in profession and idolatry in practice. Atheism is so senseless and odious to mankind that it never had many professors.’ 3 Again Newton encountered difficulties with his old rival Robert Hooke. A number of scientists believed that an inverse square law probably applied, but they had not been able to prove that this would produce the elliptical orbits observed by famous German astronomer Johannes Kepler. Despite Hooke's boasts to the contrary he too failed to be forthcoming with proof. In contrast, Newton succeeded; but Hooke wanted some of the credit. The Royal Society did not wish to be seen to take sides.

This, together with shortage of finances, made the Royal Society reluctant to publish Newton’s landmark book Principia Mathematical. Newton’s friend, astronomer Edmond Halley, came to his aid and privately financed the publication of Newton’s three-part book in 1687. (Halley later used Newton’s laws in his work on comets which, like the planets, move in elliptical orbits around the sun.) Royal Opposition After 1685, Newton again encountered the problem of a monarch who tried to mingle politics, religion and education. The new king, James II, wanted Trinity College to award unearned degrees to those whose religious beliefs agreed with his own. Because they would not do this, Newton and eight other teachers from Trinity College were brought before the High Court on trumped-up charges. Although the charges were rightfully dismissed, the episode had been a great strain on the men. Isaac Newton’s times of hardship and struggle throughout his lifetime did not produce bitterness. Instead, Newton’s own words show that this brought him closer to God. ‘Trials are medicines which our gracious and wise physician gives because we need them; and the proportions the frequency and weight of them to what the case requires.

Let us trust his skill and thank him for the prescription.’ Nervous Breakdown Isaac Newton represented Cambridge University as a Member of Parliament in 1689 and 1690. In 1690, his health failed. This illness was probably a nervous breakdown brought on by many years of working long hours and enduring too much stress. Eventually he fully recovered. For the next few years, Newton pursued his other great love—studying the Bible. The books he wrote included Chronology of Ancient Kingdoms and Observations Upon the Prophecies of Daniel. In 1696, the government appointed Newton to the post of Warden of the Mint. He supervised the replacement of England’s old and damaged coins with those which were new and more durable, and even helped break up a counterfeiting ring. In 1701, Newton began another short term as parliamentarian. Two years later he was elected president of the Royal Society. His re-election to that position every year for the rest of his life showed the high esteem in which he was held by fellow scientists. Now that he had returned to science, Newton published his earlier work on light.

His book, Optiks, contained both his own findings and suggestions for further research. His country officially recognized his work in 1705 when he became the first person to receive a knighthood for scientific achievement. Newton died in 1727, at the age of 84. He was buried in Westminster Abbey. Isaac Newton’s contributions to science were many and varied. They covered revolutionary ideas and practical inventions. His work in physics, mathematics and astronomy is of importance even today. His contributions in any one of these fields would have made him famous; collectively, they make him truly outstanding. But Newton remained a modest man who loved his Lord and Saviour. He loved God and believed God’s Word—all of it. He wrote, ‘I have a fundamental belief in the Bible as the Word of God, written by men who were inspired. I study the Bible daily.’ (Quotes by Newton are taken from the book by J.H.

Tiner, Isaac Newton—Inventor, Scientist and Teacher, Mott Media, Milford (Michigan), 1975.) References (added by editor) Some have accused him of Arianism, but this is rejected by Pfizenmaier, T.C., Was Isaac Newton an Arian? Journal of the History of Ideas 68(1):57–80, 1997. A very detailed defense of Newton’s Trinitarianism is Van Alan Herd, The theology of Sir Isaac Newton , Doctoral Dissertation, University of Oklahoma, 2008. This documents much evidence, including Newton’s words refuting tritheism and affirming Triniarian monotheism: That to say there is but one God, ye father of all things, excludes not the son & Holy ghost from the Godhead becaus they are virtually conteined & implied in the father. … To apply ye name of God to ye Son or holy ghost as distinct persons from the father makes them not divers Gods from ye Father. … Soe there is divinity in ye father, divinity in ye Son, & divinity in ye holy ghost, & yet they are not thre forces but one force.

Return to text . Principia, Book III; cited in; Newton’s Philosophy of Nature: Selections from his writings, p. 42, ed. H.S. Thayer, Hafner Library of Classics, NY, 1953. Return to text . A Short Scheme of the True Religion, manuscript quoted in Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton, p. 347, by Sir David Brewster, Edinburgh, 1855. Return to text . (Also available in Vietnamese )

Question: Which German mathematician developed the theory of calculus at about the same time as, but independently of, Isaac Newton?
Answer: (Gottfried) Liebnitz