**Isaac Newton** was the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.

- 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 mathematical research.
- Isaac Newton was born in the manor house of Woolsthorpe, near Grantham in Lincolnshire.
- From shortly after this time Isaac began attending the Free Grammar School in Grantham.
- Isaac was taken away from school but soon showed that he had no talent, or interest, in managing an estate.
- This time he lodged with Stokes, who was the headmaster of the school, and it would appear that, despite suggestions that he had previously shown no academic promise, Isaac must have convinced some of those around him that he had academic promise.
- Another piece of evidence comes from Isaac's list of sins referred to above.
- We know nothing about what Isaac learnt in preparation for university, but Stokes was an able man and almost certainly gave Isaac private coaching and a good grounding.
- There is no evidence that he learnt any mathematics, but we cannot rule out Stokes introducing him to Euclid's Elements which he was well capable of teaching (although there is evidence mentioned below that Newton did not read Euclid before 1663).
- Anecdotes abound about a mechanical ability which Isaac displayed at the school and stories are told of his skill in making models of machines, in particular of clocks and windmills.
- Newton's aim at Cambridge was a law degree.
- Newton studied the philosophy of Descartes, Gassendi, Hobbes, and in particular Boyle.
- It is a fascinating account of how Newton's ideas were already forming around 1664.
- How Newton was introduced to the most advanced mathematical texts of his day is slightly less clear.
- According to de Moivre, Newton's interest in mathematics began in the autumn of 1663 when he bought an astrology book at a fair in Cambridge and found that he could not understand the mathematics in it.
- Returning to the beginning, Newton read the whole book with a new respect.
- The new algebra and analytical geometry of Viète was read by Newton from Frans van Schooten's edition of Viète's collected works published in 1646.
- Newton also studied Wallis's Algebra and it appears that his first original mathematical work came from his study of this text.
- It would be easy to think that Newton's talent began to emerge on the arrival of Barrow to the Lucasian chair at Cambridge in 1663 when he became a Fellow at Trinity College.
- Certainly the date matches the beginnings of Newton's deep mathematical studies.
- Despite some evidence that his progress had not been particularly good, Newton was elected a scholar on 28 April 1664 and received his bachelor's degree in April 1665.
- 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 foundations for differential and integral calculus, several years before its independent discovery by Leibniz.
- 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 Ⓣ(On methods of series and on fluxions) 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.
- When the University of Cambridge reopened after the plague in 1667, Newton put himself forward as a candidate for a fellowship.
- In July 1669 Barrow tried to ensure that Newton's mathematical achievements became known to the world.
- Collins showed Brouncker, the President of the Royal Society, Newton's results (with the author's permission) but after this Newton requested that his manuscript be returned.
- Collins could not give a detailed account but de Sluze and Gregory learnt something of Newton's work through Collins.
- Barrow resigned the Lucasian chair in 1669 to devote himself to divinity, recommending that Newton (still only 27 years old) be appointed in his place.
- Newton's first work as Lucasian Professor was on optics and this was the topic of his first lecture course begun in January 1670.
- 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 was led by this reasoning to the erroneous conclusion that telescopes using refracting lenses would always suffer chromatic aberration.
- In 1672 Newton was elected a fellow of the Royal Society 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.
- The paper was generally 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.
- The reception that his publication received did nothing to improve Newton's attitude to making his results known to the world.
- However, perhaps because of Newton's already high reputation, his corpuscular theory reigned until the wave theory was revived in the 19th century.
- Newton's relations with Hooke deteriorated further when, in 1675, Hooke claimed that Newton had stolen some of his optical results.
- Although the two men made their peace with an exchange of polite letters, Newton turned in on himself and away from the Royal Society which he associated with Hooke as one of its leaders.
- Newton's Opticks appeared in 1704.
- Another argument, this time with the English Jesuits in Liège over his theory of colour, led to a violent exchange of letters, then in 1678 Newton appears to have suffered a nervous breakdown.
- 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.
- 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.
- asked Newton what orbit a body followed under an inverse square force, and Newton replied immediately that it would be an ellipse.
- 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 Ⓣ(Mathematical Principles of Natural Philosophy) or Principia as it is always known.
- Newton analysed the motion of bodies in resisting and non-resisting media under the action of centripetal forces.
- Newton explained a wide range of previously unrelated phenomena: the eccentric orbits of comets, the tides and their variations, the precession of the Earth's axis, and motion of the Moon as perturbed by the gravity of the Sun.
- This work made Newton an international leader in scientific research.
- However this did not stop the universal admiration for Newton's technical expertise.
- Newton was a staunch Protestant and strongly opposed to what he saw as an attack on the University of Cambridge.
- The Vice-Chancellor took Newton's advice and was dismissed from his post.
- However Newton continued to argue the case strongly preparing documents to be used by the University in its defence.
- The University of Cambridge elected Newton, now famous for his strong defence of the university, as one of their two members to the Convention Parliament on 15 January 1689.
- Newton was at the height of his standing - seen as a leader of the university and one of the most eminent mathematicians in the world.
- After suffering a second nervous breakdown in 1693, Newton retired from research.
- Newton himself blamed lack of sleep but this was almost certainly a symptom of the illness rather than the cause of it.
- Newton decided to leave Cambridge to take up a government position in London becoming Warden of the Royal Mint in 1696 and Master in 1699.
- As Master of the Mint, adding the income from his estates, we see that Newton became a very rich man.
- Newton did not treat it as such and he made a strong contribution to the work of the Mint.
- Given the rage that Newton had shown throughout his life when criticised, it is not surprising that he flew into an irrational temper directed against Leibniz.
- Perhaps all that is worth relating here is how Newton used his position as President of the Royal Society.
- Newton's assistant Whiston had seen his rage at first hand.

Born 4 January 1643, Woolsthorpe, Lincolnshire, England. Died 31 March 1727, London, England.

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