Isaac Newton's life can be divided into three quite distinct periods. The first is his boyhood days up to his appointment to a chair 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 saw Newton as a highly paid government official in London with little further interest in mathematical research.

Isaac Newton was born on Christmas Day 1642, but according to the corrected Gregorian calendar, this would be January 4, 1643. Early in his schooling, Newton showed little promise in academic work, so was removed from school to manage his mother's estate. He soon showed he had no talent for this either, so he was allowed to return to the Free Grammar School in Grantham in 1660 to complete his school education under Stokes.

Newton entered Trinity College in Cambridge in 1661 to study law. He studied the philosophy of Descartes, Gassendi, Hobbes, and in particular Boyle. He read works of Galileo, Kepler, Descartes, Viète, and Wallis. 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.

When the plague closed the University in the summer of 1665, he had to return to Lincolnshire. There, in a period of less than two years, 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. 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 it did not appear in print until 1736.

When the University reopened in 1667, Newton was awarded his Master's Degree and was elected to a major fellowship in 1668. The following year, he was awarded the Lucasian chair. Newton's first work as Lucasian Professor was on optics. He had reached the conclusion that white light is not a simple entity. When he passed a thin beam of sunlight through a glass prism Newton noted the spectrum of colours that was formed.

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. Newton's relations with Hooke deteriorated further when Hooke claimed that Newton had stolen some of his optical results. Consequently, 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, dealing with investigations of the colours of thin sheets, "Newton's rings", and the diffraction of light.

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. Newton's novel idea 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.

Halley persuaded Newton to write a full treatment of his new physics and its application to astronomy. In 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-fall near the Earth. He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalised that all heavenly bodies mutually attract one another.

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.

After suffering a nervous breakdown in 1693, Newton retired from research. Newton decided to leave Cambridge to take up a government position in London becoming Warden of the Royal Mint in 1696 and Masterof the Mint in 1699. He became very rich. In 1703 he was elected president of the Royal Society and was re-elected each year until his death. He was knighted in 1705 by Queen Anne, the first scientist to be so honoured for his work.

The last portion of his life was dominated in many ways with the controversy with Leibniz over which had invented the calculus. Newton used his position as President of the Royal Society to appoint an "impartial" committee to decide whether he or Leibniz was the inventor of the calculus. He even wrote the official report of the committee.