[6] His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, achieved the first great unification in physics and established classical mechanics.

He used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity.

Newton's inference that the Earth is an oblate spheroid was later confirmed by the geodetic measurements of Maupertuis, La Condamine, and others, thereby convincing most European scientists of the superiority of Newtonian mechanics over earlier systems.

[22] In addition to his creation of calculus, as a mathematician, he generalized the binomial theorem to any real number, contributed to the study of power series, developed a method for approximating the roots of a function, classified most of the cubic plane curves, and also originated the Newton-Cotes formulas for numerical integration.

Isaac Newton was born (according to the Julian calendar in use in England at the time) on Christmas Day, 25 December 1642 (NS 4 January 1643[a]) at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire.

[29] When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough (née Blythe).

[31] From the age of about twelve until he was seventeen, Newton was educated at The King's School in Grantham, which taught Latin and Ancient Greek and probably imparted a significant foundation of mathematics.

At Cambridge, Newton started as a subsizar, paying his way by performing valet duties until he was awarded a scholarship in 1664, which covered his university costs for four more years until the completion of his MA.

[36] At the time, Cambridge's teachings were based on those of Aristotle, whom Newton read along with then more modern philosophers, including Descartes and astronomers such as Galileo Galilei and Thomas Street.

His books showed his interests to be wide-ranging, with Newton himself described as a "Janusian thinker, someone who could mix and combine seemingly disparate fields to stimulate creative breakthroughs.

[48] The Geographia Generalis is viewed by some as the dividing line between ancient and modern traditions in the history of geography, and Newton's involvement in the subsequent editions is thought to be a large part of the reason for this enduring legacy.

[106] After the exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector.

[17] In the same work, Newton presented a calculus-like method of geometrical analysis using 'first and last ratios', gave the first analytical determination (based on Boyle's law) of the speed of sound in air, inferred the oblateness of Earth's spheroidal figure, accounted for the precession of the equinoxes as a result of the Moon's gravitational attraction on the Earth's oblateness, initiated the gravitational study of the irregularities in the motion of the Moon, provided a theory for the determination of the orbits of comets, and much more.

[121] Newton moved to London to take up the post of warden of the Royal Mint during the reign of King William III in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer.

He took charge of England's great recoining, trod on the toes of Lord Lucas, Governor of the Tower, and secured the job of deputy comptroller of the temporary Chester branch for Edmond Halley.

Starting in 1707, Newton introduced the practice of testing a small sample of coins, a pound in weight, in the trial of the pyx, which helped to reduce the size of admissible error.

[153][154] Their relationship came to an abrupt and unexplained end in 1693, and at the same time Newton suffered a nervous breakdown,[155] which included sending wild accusatory letters to his friends Samuel Pepys and John Locke.

[176] The contrast between Laplace's mechanistic worldview and Newton's one is the most strident considering the famous answer which the French scientist gave Napoleon, who had criticised him for the absence of the Creator in the Mécanique céleste: "Sire, j'ai pu me passer de cette hypothèse" ("Sir, I didn't need this hypothesis").

[180] The clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism,[181] and at the same time, the second wave of English deists used Newton's discoveries to demonstrate the possibility of a "Natural Religion".

[188] Newton's fundamental contributions to science include the quantification of gravitational attraction, the discovery that white light is actually a mixture of immutable spectral colors, and the formulation of the calculus.

"[187]In June 2020, two unpublished pages of Newton's notes on Jan Baptist van Helmont's book on plague, De Peste,[189] were being auctioned online by Bonhams.

As far as the therapy is concerned, Newton writes that "the best is a toad suspended by the legs in a chimney for three days, which at last vomited up earth with various insects in it, on to a dish of yellow wax, and shortly after died.

The epitaph added is as follows:[193] H. S. E. ISAACUS NEWTON Eques Auratus, / Qui, animi vi prope divinâ, / Planetarum Motus, Figuras, / Cometarum semitas, Oceanique Aestus.

Suâ Mathesi facem praeferente / Primus demonstravit: / Radiorum Lucis dissimilitudines, / Colorumque inde nascentium proprietates, / Quas nemo antea vel suspicatus erat, pervestigavit.

MDCCXXVI,which can be translated as follows:[193] Here is buried Isaac Newton, Knight, who by a strength of mind almost divine, and mathematical principles peculiarly his own, explored the course and figures of the planets, the paths of comets, the tides of the sea, the dissimilarities in rays of light, and, what no other scholar has previously imagined, the properties of the colours thus produced.

Diligent, sagacious and faithful, in his expositions of nature, antiquity and the holy Scriptures, he vindicated by his philosophy the majesty of God mighty and good, and expressed the simplicity of the Gospel in his manners.

[197] In his home of Monticello, Thomas Jefferson, a Founding Father and President of the United States, kept portraits of John Locke, Sir Francis Bacon, and Newton, whom he described as "the three greatest men that have ever lived, without any exception", and who he credited with laying "the foundation of those superstructures which have been raised in the Physical and Moral sciences".

[228] Voltaire then wrote in his Essay on Epic Poetry (1727), "Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree.

[239] The monument features a figure of Newton reclining on top of a sarcophagus, his right elbow resting on several of his great books and his left hand pointing to a scroll with a mathematical design.

The still-surviving farmhouse at Woolsthorpe By Colsterworth is a Grade I listed building by Historic England through being his birthplace and "where he discovered gravity and developed his theories regarding the refraction of light".