Isaac Newton

In 1687 Isaac Newton published Philosophiae Naturalis Principia Mathematica, usually known simply as the Principia, at the urging and expense of the astronomer Edmond Halley. The book set out three laws of motion, an object at rest or in uniform motion stays that way unless a force acts on it, force equals mass times acceleration, and every action has an equal and opposite reaction, together with the law of universal gravitation: every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

What made the Principia extraordinary was not any single law but the demonstration that one set of rules governed motion everywhere, an apple falling in an English orchard and a planet tracing its orbit around the sun answered to the same equation. Newton derived Johannes Kepler's earlier empirical laws of planetary motion as consequences of his own gravitational law, showing that Kepler's careful cataloguing of how the planets moved followed necessarily from a deeper physical cause. He wrote the whole argument in the geometric style of classical mathematics rather than the calculus he had developed to find it, a choice that made the proofs harder to follow but easier for contemporary readers trained in Euclid to accept.

The Principia's authority held for more than two centuries, and its core predictions still hold today at the scales of everyday engineering and ordinary astronomy, only at speeds near light or in very strong gravitational fields does Einstein's general relativity supersede it. Newton himself considered the work unfinished business rather than a final word, revising it twice more in his lifetime, and its method, stating a small number of general laws and showing that the observed world follows from them, became the template for physical science that followed.

Newton's reputation rests overwhelmingly on the Principia, but two other threads of his working life reveal a stranger and more contested figure. His 1704 book Opticks, published in English rather than the era's usual scholarly Latin, reported years of experiments showing that white light is not pure but a mixture of colors that a prism separates and a second prism can recombine, overturning the older idea that prisms themselves added color to light. Alongside this public science, Newton spent decades on alchemy, filling more than a million words of private manuscripts with attempts to transmute metals and recover what he believed was an ancient, lost body of natural knowledge. He kept almost none of it published in his lifetime, and historians now treat it as a genuine, serious part of his intellectual project rather than an embarrassing sideline, even though it produced no results resembling the chemistry that followed.

The most bitter episode of Newton's career was his dispute with the German philosopher and mathematician Gottfried Wilhelm Leibniz over who had invented calculus. Newton had developed his method of fluxions in the 1660s but published almost nothing about it for decades, Leibniz developed an independent version in the 1670s and published first, in 1684, with a notation that proved easier to use and is largely what is taught today. When the priority question became a public accusation of plagiarism, the Royal Society, of which Newton was president, appointed a supposedly independent committee to investigate, Newton wrote much of its 1712 report himself without disclosing his authorship, and it ruled in his favor. The two men never reconciled, and the fight split British and continental mathematics into rival camps for a generation, with British mathematicians clinging to Newton's clumsier notation partly out of loyalty and falling behind continental developments as a result. Modern historians of mathematics regard the two as having reached calculus independently, by different routes, at nearly the same time.