It was at Cambridge that Newton first learned mathematics. Most of the books (many containing handwritten marginal notes) in Newton's library have been reassembled; from these and other sources, it is known that Newton backtracked from contemporary mathematical works he was trying to read, all the way back to Euclid. He then mastered each work in the forward direction. Isaac Barrow, Newton's teacher at Cambridge, was a competent and creative mathematician, who must have helped to raise Newton's interests. It is known that Barrow made contributions to the Fundamental Theorem of Calculus.

Newton completed his undergraduate studies in 1665, the same year as the onset of the great plague in London; consequently, he returned to Woolsthorpe. The next two years were the most productive two years in the history of science and mathematics, a true anni mirabiles. During these two years Newton built on his last year of work at Cambridge to make the revolutionary discoveries whose elaboration was to occupy him for the rest of his academic life. He discovered the `method of fluxions' (the differential calculus) together with its applications to mechanics, the fact that integration is the inverse procedure to differentiation (hence the Fundamental Theorem of Calculus), the compostion of white light, and started many of his other investigations.

Throughout his life, Newton was always very reluctant to publish. Many of his papers were only published years after they were written; his full account of the calculus was only to be published after his death and his Opticks didn't appear until 1704. Some of his manusripts containing results on the calculus were circulated to other mathematicians as early as 1669, but Newton requested that they be returned. There are many reasons for Newton's tardiness in publication, including distrust of others. Late in his life Newton was involved in a bitter priority dispute with Leibniz over the invention of the calculus. Part of the conflict over priority for the calculus is concerned with how much knowledge Leibniz had of Newton's unpublished manuscripts and how much of Leibniz's motivation came from them. There is no doubt that Newton's manuscripts predate Leibniz's work, nor is there doubt that Leibniz published first.

The dispute between Newton and Leibniz and their respective followers was a long one with both Newton and Leibniz showing their worst attributes during the conflict. By strongly following Newton, avoiding Leibniz's notation, and isolating themselves from continental mathematicians, the next few generations of British mathematicians severely hindered their own progress.

Newton returned to Cambridge in 1667 when it reopened after the plague. He received his Master's Degree in 1668 and was elected to a fellowship. In 1669 Barrow resigned the Lucasian chair to turn to religion, and he recommended that Newton be appointed in his place. Hence Newton was the second to hold the Lucasian chair (the current holder is Stephen Hawking). In 1687 Newton, with Halley's encouragement and financial support, published his masterpiece Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy),} and Newton soon became as famous as a scientist-mathematician can be, both among his peers and the general public; he was elected to the Royal Society and to serve as president from 1703 until his death, and he was even subject to Hogarth's jabs in one of his prints. An appreciation of Newton's discoveries and his role in the scientific community of the time cannot be given here. An excellent source is the biography [W] by Westfall. The description of Newton's life and work at Cambridge from 1669- 1696 makes fascinating reading.

Since the Principia contains no direct application of the calculus, and since many of its arguments, while geometric, seem motivated by the calculus, many have suspected that Newton obtained much of what is in the {\it Principia} using calculus, and then rewrote it giving only geometric arguments, possibly with a motive of keeping details of the calculus private. In letters Newton acknowledged that he did sometimes, but not universally, obtain results in this manner. The geometric recasting, however, was for the purposes of rigor; the calculus was not put on a rigorous foundation for another two centuries, and Newton did not want to unnecessarily open his work to criticism.

In 1696 Newton left Cambridge to live in London and serve as Warden of the Royal Mint, and he became Master of the Mint in 1699. He served capably in both positions, even becoming wealthy, but he ceased any creative scientific or mathematical work when he left Cambridge. Newton was knighted by Queen Anne and buried in Westminister Abbey.

Here are two, possibly true, stories about Newton. Newton was elected to parliament to represent Cambridge. It is reported that the only time Newton spoke in parliament was to give the speech, "The window needs closing." It is often reported that Newton had little sense of humor; his assistant, Humphrey Newton (no relation) said that the only time he saw Newton laugh was when he was asked, "Of what practical use is geometry?"

Here are four stamps issued by Great Britain in honor of Newton.