The following article is part of an in-depth biography of Sir, the English mathematician and scientist, author of the . It portrays the years after Newton's birth in 1642, his education, as well as his early scientific contributions, before the in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. At the time of Newton's birth, England had not adopted the Gregorian calendar and therefore his date of birth was recorded as Christmas Day, according to the Julian calendar.
Newton was born three months after the death of his father, a prosperous farmer also named Isaac Newton. Isaac Newton, Sr. was described as a "wild and extravagant man." Born prematurely, young Isaac was a small child; his mother Hannah Ayscough reportedly said that he could have fitted inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabus Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough. The young Isaac disliked his stepfather and held some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and the house over them." Later on his mother returned after her husband died.
From the ages of 12 through 17, he was educated at The King's School, Grantham (where his signature can still be seen upon a library window sill). He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, where his mother, widowed by now for a second time, attempted to make a farmer of him. He hated farming. Henry Stokes, master at the King's School, persuaded his mother to send him back to school so that he might complete his education. This he did at the age of eighteen, achieving an admirable final report.
In June 1661, he was admitted to Trinity College, Cambridge as a sizar—a sort of work-study role. At that time, the college's teachings were based on those of Aristotle, whom Newton supplemented with modern philosophers such as Descartes and astronomers such as Copernicus, Galileo, and Kepler. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became infinitesimal calculus. Soon after Newton had obtained his degree in August 1665, the University closed down as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student, Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus, optics and the law of gravitation. In 1667 he returned to Cambridge as a fellow of Trinity.
Newton had stated that when he had purchased a book on astrology at Stourbridge fair, near Cambridge, he was unable, on account of his ignorance of trigonometry, to understand a figure of the heavens which was drawn in the book. He therefore bought an English edition of Euclid's Elements which included an index of propositions, and, having turned to two or three which he thought might be helpful, found them so obvious that he dismissed it "as a trifling book", and applied himself to the study of René Descartes' Geometry. It is reported that in his examination for a scholarship at Trinity, to which he was elected on 28 April 1664, he was examined in Euclid by Dr. Isaac Barrow, who was disappointed in Newton's lack of knowledge on the subject. Newton was convinced to read the again with care, and formed a more favourable estimate of Euclid's merit.