Newton's pure math: Arithmetica Universalis
Newton was lifelong neurotically reluctant to publish his scientific and mathematical discoveries, an obsessive dread of controvery which nonetheless fueled his bitter, lengthy public dispute over the invention of the calculus with Leibniz. Most modern scholars agree the invention was simultaneous and independent. Leibniz' simpler and more logical notation prevailed and is the one taught and used today.
In the Arithmetica, Newton reveals his discovery of the Binomial Theorem, the algebraic foundation of the differential calculus.
Newton held Cambridge's Lucasian Chair of Mathematics, which Stephen Hawking holds today.
You can read every page of this edition of the Arithmetica, including about 20 pages of Newton's geometrical diagrams, in FlipBook format (just click on the right-hand page to turn to the next two pages).
After a paranoid depressive episode -- a nervous breakdown -- Newton's friends and admirers urged him to leave Cambridge for London. With his brilliant, charming and beautiful niece Catherine Barton (admired by, among others, Jonathan Swift) as hostess, Newton pursued government and political ambitions and eventually became Master of the Mint, foiling the schemes of counterfeiters and overseeing a major coinage conversion, for which he invented "milling" -- the ribbing around a coin's edge which prevents "snipping" bits of precious metal from the circumference. Though his government achievements are of little lasting significance compared to his scientific achievements, they showed hard-headed, immensely practical aspects of his character. One dispute with a flamboyant counterfeiter ended up with the counterfeiter convicted, drawn and quartered.
Newton devoted most of his intellectual energies to alchemy and to investigations to reveal the truths of the early Christian church (and the doctrines he believed were subsequent historical falsehoods). He was deeply religious, apparently secretly an early Unitarian -- i.e., he rejected the Trinity -- and his personality was more comfortable in the Middle Ages than in the scientific Enlightenment he was credited with creating.
Mathematics was taught at Cambridge, but was outside the standard curriculum for undergraduates. He bought his first math book, a trigonometry text, when he had trouble understanding the trigonometric concepts in the astrology books he was trying to master.
John Maynard Keynes ended his biographical lecture about Newton by asking if the world would be better if there were more Newtons. It would not, he concluded; a world full of Newtons would be a world full of monsters.
But a great monster now and then makes for a much greater world than a world with no monsters at all.