SIR ISAAC NEWTON 1642 – 1727 (PART – I) By: VIVEK JOSEPH DEPARTMENT OF MATHEMATICS BBDNIIT

"Nature and Nature's laws lay hid in the night; God said, Let Newton be! And all was light." Alexander Pope

Talk on Isaac Newton Early Life Life in Cambridge University Conflict with Robert Hooke and Leibniz Principia End Days of Isaac Newton

BIRTH OF ISAAC NEWTON A year later after Galileo’s death, Isaac Newton was born prematurely on Christmas day 1642 in Woolsthorpe, a hamlet near Grantham in Lincolnshire (U.K.). His father, died shortly before Newton was born. When he was barely three years old Newton's mother, Hanna (Ayscough), placed her first born with his grandmother in order to remarry and raise a second family with Barnabas Smith, a wealthy rector from nearby North Witham.

PICTURE OF BIRTHPLACE OF NEWTON

PICTURE OF MOTHER OF ISAAC NEWTON

EARLY LIFE OF NEWTON (Enter in School, Hanna’s Return, Return of Newton) Isaac Newton was sent to King’s school at Grantham (7 miles from Woolthrope), were his learning and mechanical proficiency excited some attention. Hanna returned to Woolsthorpe in 1653 after the death of her second husband. In 1656 Newton returned home to learn the business of a farmer, but spent most of his time solving problems, making experiments, or devising mechanical models.

Photo of King’s School in Grantham

PICTURE OF THE NEWTON IN SCHOOL

EARLY LIFE OF NEWTON (Recommendation by Newton’s Uncle for Cambridge) With the bending interest of Isaac Newton in Science, Isaac Newton uncle (Hanna’s Brother) having been himself educated at Trinity College, Cambridge, recommended that he should be sent there. On 5/15 June, 1661 Newton entered as a student at Trinity College, Cambridge.

TRINITY COLLEGE, CAMBRIDGE

Department of Mathematics, Cambridge University

LIFE OF ISAAC NEWTON IN CAMBRIDGE (Newton Did not get Scholarship) Isaac Newton initially did not got any scholarship in Trinity College during his Graduation. Isaac paid his way through college for the first three years by waiting tables and cleaning rooms for the fellows (faculty) and the wealthier students. In fact for the first time he found himself among surroundings which were likely to develop his powers.

LIFE OF ISAAC NEWTON IN CAMBRIDGE (INTEREST OF NEWTON IN MATHEMATICS) Isaac Newton had not read any mathematics before coming into residence, but was acquainted with Sanderson's Logic, which was then frequently read as preliminary to mathematics. At the beginning of his first October term he happened to stroll down to Stourbridge Fair, and there picked up a book on astrology, but could not understand it on account of the geometry and trigonometry.

PHOTO OF Sanderson's Logic BOOK

Bending Interest Towards Mathematics (Read Discarte Geometry, Elements, study privately) Now to Understand the concept of Geometry and Trigonometry Isaac Newton bought a book of Euclid, Descartes's Géométrie, Oughted's Clavis. During his undergraduate years Newton was deeply engrossed in private study, that he privately mastered the works of René Descartes, Pierre Gassendi, Thomas Hobbes, and other major figures of the scientific revolution. By 1664 Newton had begun to master Descartes' Géométrie and other forms of mathematics far in advance of Euclid's Elements.  

PICTURE OF EUCLID

COVER PAGE OF EUCLID’S BOOK ELEMENT

Rinni Descarte

Descartes's Géométrie

Attention of Isaac Barrow towards Isaac Newton (Introduction of Isaac Barrow) During his undergraduate period Newton was founded to work on Kepler's Optics, the works of Vieta, van Schooten's Miscellanies, Descartes's Géométrie, and Wallis's Arithmetica Infinitorum. He also attended Barrow's lecture Isaac Barrow a gifted Mathematician and Lucasian Professor of Mathematics at Cambridge seeing all this and bound to appreciate Newton's genius.

Isaac Barraow

Completing Graduation Isaac Newton graduated BA in 1664/5 in a class of twenty-six from Trinity without honors or distinction. In 1665 the university was closed for the next two years because of plague, Newton returned to Woolsthorpe in midyear.

Photo of Isaac Newton During the Degree of Graduation

Contribution of Isaac Newton During the period of Plague in Cambridge There, in the following 18 months, he made a series of original contributions to science. He wrote later that during this time he first understood the theory of gravitation, and the theory of optics. He also worked out the fluxional calculus. Newton said 'All this was in the two plague years of 1665 and 1666, for in those days I as in my prime of age for invention, and minded mathematics and philosophy more than at any time since”.

Work of Isaac Newton during 18 Months Period Newton was the first to understand that white light was made up of seven colour i.e. Rainbow. Newton conducted most of the optical experiment on his own eye making himself almost blind. In 1666 Newton observed the fall of an apple in his garden at Woolsthorpe, later recalling, 'In the same year I began to think of gravity extending to the orbit of the Moon.‘ In fact, all evidence suggests that the concept of universal gravitation did not spring full-blown from Newton's head in 1666 but was nearly 20 years in gestation. In 1666 Newton developed Binomial Theorem.

Newton working on Optics

Handwritten Paper of Newton on Optics

Picture of Falling Apple in Newton’s Garden

Reputed descendants of Newton's apple tree, at the Cambridge University Botanic Garden

The Apple Tree in Newton’s Garden

Calculus Who is the considered to be the mathematician to developed calculus? One of the biggest and controversial question in Mathematics. Today in the world of Mathematics Newton and Leibniz were given credit for the development of Calculus.

Development of Calculus before Newton Much of the work on Calculus had been done before Newton. Fermat defined his own concept of Maxima and Minima. Isaac Barrow developed a concept of tangent at any point on the curve. Isaac Newton contributions provided the leap from the possible to the actual. Newton started thinking on Calculus with the Problem of describing a path of an object as it travelled in either straight line or a curved line.

Past Concept on Calculus The straight line had been long understood, but the curved path was merely described by the use of many small, straight lines. The more small lines, the more accurate the calculation. Even Galileo had worked to understand the curved path of an object, showing the need to find a means to describe this path. Descartes invented analytical geometry in response to Galileo's work, so now algebraic equations could be used to solve the problems.

Newton’s Concept on Calculus Newton made a subtle change in the existing understanding of the curved path that resulted in great advances. Newton considered the path as created by one point moving through space for a period of time. This moving point was called a fluent , and its velocity was called fluxion . Changes in the fluxion was acceleration.   Finally in 1734 James Smith published his work as Newton Treatise of Fluxions.

Return of Isaac Newton to Cambridge (Return to Cambridge, Elected fellowship, Revised Isaac Barrow Lecture) On his return to Cambridge in 1667 Newton was elected to a fellowship at his college. In the early part of 1669, or perhaps in 1668, he revised Barrow's lectures for him. The end of the fourteenth lecture is known to have been written by Newton, but how much of the rest is due to his suggestions cannot now be determined.

Newton House in Cambridge

Lucansian Chair of Professorship in Mathematics (Isaac Barrow Resigned, Newton Lecture’s in optics) In October 1669, Barrow resigned the Lucasian chair in favour of Newton. During his tenure of the professorship, it was Newton's practice to lecture publicly once a week, for from half-an-hour to an hour at a time, in one term of each year. Newton used to give four or five hours at the end of the week to those students who wished to come to his rooms to discuss the results of the previous lecture.

Lucasian Chair of Professorship in Mathematics The Lucasian Professorship of Mathematics is the most famous academic chair in the world. This is due in no small part to the current holder of the chair, Professor Stephen Hawking, who is a well known theoretical physicist, and Sir Isaac Newton who was the second holder of the chair. What is not so commonly known is that the chair has been held by others who represent the best and most influential minds in science and technology the world has known. As a group, the seventeen men who have held the chair have made a unique contribution to the world. The three hundred thirty years that have passed since its founding have seen a dramatic evolution of science. Michael Green (Mathematcian) hold the Chair after Stephen Hawking in 2009. 

Micheal B. Green (Present Professor of Lucasian Chair)

Topic of the Lecture from 1669 to 1671 When first appointed Newton chose optics for the subject of his lectures and Before the end of 1669 he had worked out the details of his discovery of the decomposition of a ray of white light into rays of different colours by means of a prism. The complete explanation of the theory of the rainbow followed from this discovery. These discoveries formed the subject-matter of the lectures which he delivered as Lucasian professor in the years 1669, 1670 and 1671.

Elected to the Royal Society In 1672 Isaac Newton elected to the Royal Society. The chief new results were embodied in a paper communicated to the Royal Society in February, 1672, and subsequently published in the Philosophical Transactions. On December 10, Newton sends letter to John Collins on method of tangents. The manuscript of his original lectures was printed in 1729 under the title Lectiones Opticae.

Image of the Paper of Newton in Philosophical Transaction

Lectiones Opticae

Reflecting Microscope (Newton Theory of Light as Corpuscular Theory) In 1672 he invented a reflecting microscope, and some years later he invented the sextant which was rediscovered by J. Hadley in 1731. Newton studied on the question as how the effect of light were really produced. By the end of 1675 Newton formed a corpuscular or emission theory and with this he explained various phenomenon of geometrical optics, reflection, refraction, diffraction etc. Newton's corpuscular theory was expounded in memoirs communicated to the Royal Society in December 1675, which are substantially reproduced in his Optics, published in 1704.

Newton’s Reflecting Microscope

Conflict Between Newton & Robert Hooke In February, 1672 when Isaac Newton presented a paper his first paper to the Royal Society, detailing his work on the nature of light and advancing his theory that white light was a composite of all the colours of the spectrum. Hooke had his own ideas about the nature of light--ideas that contradicted Newton's suggestion that light was composed of particles; Hooke himself believed that light travelled in waves. Thus he quickly damned Newton's paper by praising it only in condescending terms--he noted its "niceness and curiousity"--and then proceeding to attack Newton's methodology and conclusions.

Conflict between Isaac Newton & Robert Hooke Newton was so depressed and hurt with this situation that in March 1673 he threaten to withdraw from Royal Society. He only remained at the pressing of the Secretary, Henry Oldenburg, who assured him that the Fellows indeed held him in high esteem. The conflict between Newton and Hooke again raised up on Gravitational Law.

Robert Hooke

Period from 1673- 1680 Newton professorial lectures from 1673 to 1683 were on algebra and the theory of equations. One of the work was on Theory of Equation in which he classified the second degree equation as Parabola, Ellipse and Hyperbola. In next step he classified the cubic equation in 78 different curves.

One Page Image of Newton Book on Algebra

Newton & Leibniz (Fluxion development when Leibniz was 20, Systematic presentation of Calculus by Leibniz) In 1665 -1666 when Newton developed the concept of fluent and fluxion Leibnitz was at the age of 20 and didn’t no anything about mathematics. Inspite of this Leibniz was given a credit for a systematic presentation of Calculus which were known today. Leibniz independently developed the theory of calculus in which he gave the notation of differential coefficient as and integration

Gottfried Wilhelm von Leibniz

Controversy between Newton and Leibnitz Leibnitz, who had been in London in 1673, had communicated some results to the Royal Society which he had supposed to be new, but which it was pointed out to him had been previously proved by Mouton. During two month visit of London Leibniz made contact with several English mathematician and purchased Barrow’s Lectiones opticæand Lectiones geometricæ.

He also started working on the nature of series and their summations. Controversy between Newton and Leibnitz (Leibniz neither met collin, start studying work of Gregory, Start working on Infinite series) However, Leibniz neither met Collins nor gained access to Newton’s De analysi before returning to Paris. Once Leibniz got back to Paris, he started studying the mathematical works of Cavalieri, James Gregory, Pascal, Sluse and others. He also started working on the nature of series and their summations. By the end of 1673 Leibniz had obtained his celebrated series

Exchange of Letter between Leibniz and Oldenberg In 1674 Leibniz wrote saying that he possessed ``general analytical methods depending on infinite series.'' Oldenburg, in reply, told him that Newton and Gregory had used such series in their work. With the request from Leibniz, Oldenburg sent a report containing Newton series of sinx and arcsinx as well as James Gregory’s series tanx and arctanx . Leibniz reply to Odenberg was not fair and clear he professed to have found no time to compare these expansions with formulas he claimed to have obtained several years earlier.

Exchange of Letter between Newton and Leibniz In in 1675, he used the ∫dx notation for the first time in his first manuscript on calculus.  Leibniz also published the product rule for derivatives in this manuscript. Till that time Leibniz didn’t know that Newton had already hit upon the calculus. In 1676 Leibniz asked for a further explanation of the methods Newton employed in the calculation of series. Newton wrote a letter on June 13, 1676, giving a brief account of his method, but adding the expansions of a binomial (that is, the binomial theorem) and of  ; from the latter of which he deduced that of sin x

Leibniz paper of product of Differentiation

Newton and Leibniz With the request of Leibniz, Newton wrote a letter the Epistola posterior of 24 October 1676 in context with the series, tangent and differential calculus. Newton in the cover letter for Oldenburg in Epistola posterior declared his intention to terminate his correpondense. Newton now became worried of stealing of his work on calculus. Newton directed Oldenburg, “Pray let none of my mathematical papers be printed without my special licence.”

Newton and Leibniz (Leibniz own concept on tangent, Newton’s Mother Death) Leibniz in dated June 21, 1677, explains his method of drawing tangents to curves, which he says proceeds ``not by fluxions of lines, but by the differences of numbers'‘. Leibniz introduces his notation of dx and dy for the infinitesimal differences between the co-ordinates of two consecutive points on a curve. In 1678, Newton suffered a serious emotional breakdown, and in the following year his mother died.

Rift between Newton and Leibniz began In October 1684 when Leibniz staked his claim to calculus by publishing his Nova methodus pro maximis et minimis [18, pp. 121–131]. With this paper, which did not allude to Newton, the seeds of a poisonous priority dispute were sown. With all the above incidents a case of plagiarism build against Leibniz.

Gravitational Law (Hooke initiation on planetary motion, Robert Hooke view point) In November 1679, Hooke initiated an exchange of letters that bore on the question of planetary motion. Although Newton hastily broke off the correspondence, Hooke's letters provided a conceptual link between central attraction and a force falling off with the square of distance. Robert Hooke proposed his view point to Newton about the gravitational law that force of attraction holding planets in their orbits varied inversely with the square of their distance from the sun Sometime in early 1680, Newton appears to have quietly drawn his own conclusions.

Gravitational Law In August 1684, Halley paid a legendary visit to Newton in Cambridge, hoping for an answer to his riddle:  What type of curve does a planet describe in its orbit around the sun, assuming an inverse square law of attraction? When Halley posed the question, Newton's ready response was 'an ellipse.‘ When asked how he knew it was an ellipse Newton replied that he had already calculated it.

Gravitational Law After further discussion he promised to send Halley a fresh calculation forthwith. In partial fulfilment of his promise Newton produced his De Motu of 1684.  From that seed, after nearly two years of intense labour, the Philosophiae Naturalis Principia Mathematica appeared. After publishing the Principia, Newton became more involved in public affairs.

Principia

Another point of Conflict between Newton and Robert Hooke Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. When Newton's book was presented in 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him.

Severe Nervous Breakdown In 1689 he was elected to represent Cambridge in Parliament. In 1693, however, Newton suffered a severe nervous disorder, not unlike his breakdown of 1677-1678. The cause is open to interpretation: overwork; the stress of controversy; the unexplained loss of friendship with Fatio; or perhaps chronic mercury poisoning, the result of nearly three decades of alchemical research.

Warden and Master of the Mint (Death of Robert Hooke) In 1696, with the help of Charles Montague, a fellow of Trinity and later earl of Halifax, Newton was appointed Warden and then Master of the Mint. His new position proved 'most proper,' and he left Cambridge for London without regret. After the death of Hooke in 1703, Newton was elected president of the Royal Society and was annually re-elected until his death.

Isaac Newton in his old age

Newton’s Death In 1704 he published his second major work, the Opticks, based largely on work completed decades before. In old age Newton's health began to deteriorate: when he was eighty he began to suffer from incontinence, due to a weakness in the bladder, and his movement and diet became restricted. He ate mainly vegetables and broth, and was plagued by a stone in the bladder. In 1725 he fell ill with gout, and endured haemorrhoids the following year. Meanwhile, the pain from his bladder stones grew worse, and on March 19, 1727, he blacked out, never to regain consciousness. He died on 31st March, 1727, at the age of eighty-five, and was buried in Westminster Abbey; his funeral attended by all of England's eminent figures, and his coffin carried by noblemen. It was, a contemporary noted, a funeral fit for a king.

Isaac Newton Grave

Dr. Robert Hooke Robert Hooke was an English inventor, microscopist, physicist, surveyor, astronomer, biologist and artist, who played an important role in the scientific revolution, through both theoretical and experimental work. In 1660, he discovered Hooke's law of elasticity, which describes the linear variation of tension with extension in an elastic spring. In 1662 Hooke was named Curator of Experiments of the newly formed Royal Society of London -- meaning that he was responsible for experiments performed at the Society's weekly meetings.  In 1665, he published a book entitled Micrographia. Hooke devised the compound microscope and illumination system - one of the best such microscopes of his time, and used it in his demonstrations at the Royal Society's meetings.

Henry Oldenburg Henry Oldenburg (1619 – 1677) was a German theologian known as a diplomat and a natural philosopher.

Thank You To myself I am only a Child playing on the beach, while vast Ocean of truth lie undiscovered before me.