Newton's life can be divided into three quite distinct periods. The first is his boyhood days from 1643 up to his graduation in 1669. The second period from 1669 to 1687 was the highly productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematics.
Isaac Newton was born in the manor house of Woolsthorpe, near Grantham in Lincolnshire. Although he was born on Christmas Day 1642, the date given on this card is the Gregorian calendar date. (The Gregorian calendar was not adopted in England until 1752.) Newton came from a family of farmers but never knew his father who died before he was born. His mother remarried, moved to a nearby village, and left him in the care of his grandmother. Upon the death of his stepfather in 1656, Newton's mother removed him from grammar school in Grantham where he had shown little promise in academic work. His school reports described him as 'idle' and 'inattentive'. An uncle decided that he should be prepared for the university, and he entered his uncle's old College, Trinity College, Cambridge, in June 1661.
Newton's aim at Cambridge was a law degree. Instruction at Cambridge was dominated by the philosophy of Aristotle but some freedom of study was allowed in the third year of the course. Newton studied the philosophy of Descartes, Gassendi, and Boyle. The new algebra and analytical geometry of Viète, Descartes, and Wallis; and the mechanics of the Copernican astronomy of Galileo attracted him. Newton's talent began to emerge on the arrival of Barrow to the Lucasian chair at Cambridge.
His scientific genius emerged suddenly when the plague closed the University in the summer of 1665 and he had to return to Lincolnshire. There, in a period of less than two years, while Newton was still under 25 years old, he began revolutionary advances in mathematics, optics, physics, and astronomy.
While Newton remained at home he laid the foundation for differential and integral calculus, several years before its independent discovery by Gottfried Leibniz. The 'method of fluxions', as he termed it, was based on his crucial insight that the integration of a function is merely the inverse procedure to differentiating it. Taking differentiation as the basic operation, Newton produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions. Newton's De Methodis Serierum et Fluxionum was written in 1671 but Newton failed to get it published and it did not appear in print until John Colson produced an English translation in 1736.
Barrow resigned the Lucasian chair in 1669 recommending that Newton (still only 27 years old) be appointed in his place.
Newton's first work as Lucasian Professor was on optics. He had reached the conclusion during the two plague years that white light is not a simple entity. Every scientist since Aristotle had believed that white light was a basic single entity, but the chromatic aberration in a telescope lens convinced Newton otherwise. When he passed a thin beam of sunlight through a glass prism Newton noted the spectrum of colours that was formed.
Newton argued that white light is really a mixture of many different types of rays which are refracted at slightly different angles, and that each different type of ray produces a different spectral colour. Newton was led by this reasoning to the erroneous conclusion that telescopes using refracting lenses would always suffer chromatic aberration. He therefore proposed and constructed a reflecting telescope.
Newton was elected a fellow of the Royal Society in 1672 after donating a reflecting telescope. Also in 1672 Newton published his first scientific paper on light and colour in the Philosophical Transactions of the Royal Society .
Newton's paper was well received but Hooke and Huygens objected to Newton's attempt to prove, by experiment alone, that light consists of the motion of small particles rather than waves. Perhaps because of Newton's already high reputation his corpuscular theory reigned until the wave theory was revived in the 19th C.
Newton's relations with Hooke deteriorated and he turned in on himself and away from the Royal Society. He delayed the publication of a full account of his optical researches until after the death of Hooke in 1703. Newton's Opticks appeared in 1704. It dealt with the theory of light and colour and with (i) investigations of the colours of thin sheets (ii) 'Newton's rings' and (iii) diffraction of light.
To explain some of his observations he had to use a wave theory of light in conjunction to his corpuscular theory.
Newton's greatest achievement was his work in physics and celestial mechanics, which culminated in the theory of universal gravitation. By 1666 Newton had early versions of his three laws of motion. He had also discovered the law giving the centrifugal force on a body moving uniformly in a circular path. However he did not have a correct understanding of the mechanics of circular motion.
Newton's novel idea of 1666 was to imagine that the Earth's gravity influenced the Moon, counter- balancing its centrifugal force. From his law of centrifugal force and Kepler's third law of planetary motion, Newton deduced the inverse- square law.
In 1679 Newton corresponded with Hooke who had written to Newton claiming:-
that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall...
M Nauenberg writes an account of the next events:-
After his 1679 correspondence with Hooke, Newton, by his own account, found a proof that Kepler's areal law was a consequence of centripetal forces, and he also showed that if the orbital curve is an ellipse under the action of central forces then the radial dependence of the force is inverse square with the distance from the centre.
This discovery showed the physical significance of Kepler's second law.
In 1684 Halley, tired of Hooke's boasting:-
asked Newton what orbit a body followed under an inverse square force, and Newton replied immediately that it would be an ellipse. However in De Motu.. he only gave a proof of the converse theorem that if the orbit is an ellipse the force is inverse square. The proof that inverse square forces imply conic section orbits is sketched in Cor. 1 to Prop. 13 in Book 1 of the second and third editons of the Principia, but not in the first edition. [M Nauenberg]
Halley persuaded Newton to write a full treatment of his new physics and its application to astronomy. Over a year later (1687) Newton published the Philosophiae naturalis principia mathematica or Principia as it is always known.
The Principia is recognised as the greatest scientific book ever written. Newton analysed the motion of bodies in resisting and non resisting media under the action of centripetal forces. The results were applied to orbiting bodies, projectiles, pendulums, and free