Newton: The Expert View

Discovering gravity was only part of Isaac Newton's immense contribution to mathematics and science, Robin Wilson and Barbara Allen describe his rise from humble beginnings to national acclaim and pay homage to his genius.

By: Barbara Allen (Mathematics and Statistics Department) , Professor Robin Wilson (Mathematics and Statistics Department)

  • Duration 10 mins
  • Updated Thursday 21st October 2004
  • Introductory level
  • Posted under History of Science
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Isaac Newton was born on Christmas Day 1642, in the tiny hamlet of Woolsthorpe, near Grantham in Lincolnshire. He was born prematurely, apparently "so small that they could have fit him into a quart pot". His father had died three months earlier and when young Isaac was three his mother remarried, and he was brought up by his grandmother. This event was to scar him and could well have led to his rather unpleasant character – although if things had been otherwise, Newton might have ended up as illiterate as his parents, neither of whom were able to sign his birth certificate. When Isaac was eleven his mother's new husband died, and he was soon to be sent away to the Free Grammar School of Edward VI in Grantham.

From the beginning, Newton enjoyed constructing models – for example, he made a small windmill that actually ground flour and was powered by a small mouse in a wheel. In later life he was to construct the apparatus for his research – such as the equipment that enabled him to grind his own lenses for his optics experiments. It is important to remember that Newton was as much a practical scientist as a constructor of grand theories.

At school, his achievements gave no indication as to what would develop later, but he enjoyed mathematics there and probably learned more from his teacher, Mr Stokes, than he would do later from his tutor at Cambridge.

When he was seventeen, Newton returned to Woolsthorpe to manage the estate, but he was an unqualified failure. His mind was so full of problems that he wanted to solve, he had no interest in the matters in hand. Indeed the - probably apocryphal - story is told that he was once leading a horse up a hill when it slipped its bridle. Newton didn’t notice and went on leading the bridle up the hill.

Fortunately both Newton’s uncle and his mathematics master had noticed his talent. They persuaded his uneducated mother that Isaac should return to school and prepare for entrance to Cambridge.

Newton went up to Trinity College, Cambridge in June 1661. Because he was not of gentry sock, he was a subsizar, required to wait on his tutor at table, clean his shoes and do other menial tasks. He did not take to the Aristotelian approach to physics and philosophy and increasingly devoted his time to reading the great scientific works, such as Euclid’s Elements. In particular, Newton spent much time studying Descartes’ Geometry.

Another writer that Newton read avidly was John Wallis. Wallis had been a code-breaker for the Parliamentarians during the Civil War and was to become the greatest English mathematician of his day - after Newton.

Newton’s first researches into mathematics were inspired by Wallis’ work on infinite series. In particular he was concerned to extend the binomial theorem. Newton had an aversion to publishing his results and his generalised binomial theorem did not appear in print until 1704.

Newton graduated from Cambridge in 1665 but soon afterwards, because of the plague that had devastated London, he had to leave. The university was closed for two years and Newton returned to Lincolnshire. He went to Boothby Pagnell where his uncle was rector and where there was a nice orchard of apple trees.

It was during this time that the story of Newton and the apple originated. Seeing an apple fall, Newton realised that the force that draws the apple to earth is the same universal force that keeps the moon in orbit around the earth, and the earth and planets in orbit around the sun. Moreover, as Newton came to realise, this force is governed by a universal law of gravity: that the force of attraction between any two objects is proportional to the product of their masses, and inversely proportional to the distance between them – so if the distance increases ten-fold, the force decreases a hundred-fold. Although his main writings on the subject were not to appear for twenty years, in the Principia, his initial ideas came from these plague years.

Newton’s other mathematical preoccupation at this time was the calculus, later described in his De Analysi of 1669. For many years mathematicians had been working on two, seemingly unrelated, problems: how fast things move or change, and how large they are. The former, now called differentiation, concerns velocities of objects as represented by the slopes of tangents, and was known to Newton as fluxions, while the latter, now called integration, concerns finding areas under and within curves, and was known to Newton as quadrature.

During the 17th Century it was becoming increasingly clear that fluxions and quadrature were intimately related – in fact, they are inverse processes. This inverse relationship seems to have first been noticed in the 1640s by Torricelli, a mathematics student of Galileo and inventor of the barometer. During the plague years, it was Newton who really explained for the first time why these processes are inverse to each other, obtaining what we now call the fundamental theorem of calculus. This work was later, independently, developed by Leibniz, leading to no end of trouble.

Arriving back at Cambridge after the plague years, Newton was elected a fellow of Trinity College, and lectured on mathematics and optics. Within a couple of years he had been appointed to the Lucasian Chair of Mathematics.

In 1669 Newton produced De Analysi, an important mathematical treatise which he circulated to his friends but did not publish. This was followed two years later with his Methods of Fluxions. It is most unfortunate that this was not published until after his death, as it could have prevented the priority disputes on the origin of the calculus.

In 1672 Newton made contact with the Royal Society, presenting his design for a reflecting telescope. Newton had been interested in optics since his time at Boothby Pagnell, when he carried out his important experiment on the refraction of coloured light through prisms. The Royal Society elected him a Fellow in 1672.

Shortly afterwards Newton sent a paper to the Royal Society on the nature of light – essentially that it consists of ‘corpuscles’, rather than Huygens’ view that it consists of waves. This brought him into bitter dispute with Robert Hooke (another disagreeable type) and a lengthy correspondence in the pages of the Society’s Philosophical Transactions. From then on, Newton vowed not to publish, or waste time explaining his discoveries to lesser mortals.

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It was around this time that Leibniz visited London. Leibniz had been working independently on the calculus, being more concerned with the geometry of the situation, rather than any ideas of velocity or motion. In the autumn of 1675, Leibniz introduced the familiar integral sign and the d-notation for differentiation – both of these are still used today.

Newton produced the Principia Mathematica in 1687 but it nearly didn’t appear. Hooke complained that a result of his was not credited, and Newton refused to do so. The main part of the Principia consists of three books.

Book I explains Kepler’s laws of planetary motion. Newton proved Kepler’s law, that the planets orbit in ellipses – and also obtained the converse result, that if a planet under a central law of gravitation travels in an elliptical orbit, then the law of gravity must be an inverse-square one.

Book II is concerned with the movement of objects in resisting media – such as a ball bearing in treacle. Here Newton demolished a rival theory of the universe from Descartes, that all the planets move around the heavens in mini-vortices, or whirlpools.

In Book III, Newton obtains a number of amazing results – these include the calculation of the speed that a projectile needs to travel in order to escape from the Earth’s atmosphere; results on the precession of the equinoxes; the motion of comets; and the shape of the Earth as it rotates.

Newton’s Principia made him famous – few people read it, and even fewer understood it, but everyone knew that it was a great work, rather like Einstein’s Theory of Relativity over two hundred years later.

By 1696 Newton felt the need to move to London, and in that year he was appointed Warden of the Royal Mint, living in the Tower of London.

In 1703 the ailing Robert Hooke died, and with him out of the way, Newton felt happy to become involved again with the Royal Society, which had almost become defunct. It was a good time for Newton. In 1704 with no Hooke to disagree with him, he published his second-greatest book, the Opticks. The next year he was knighted by Queen Anne.

In the 1720s Newton became increasingly ill with gout and other ailments, and he died in March 1727 at the age of 84. He lay in state in Westminster Abbey amidst great pomp and ceremony, for a week preceding his funeral. At the ceremony, his pall was borne by two dukes, three earls and the Lord Chancellor. No previous scientist had ever been so honoured.