The Calculus Diaries - Jennifer Ouellette [13]
Leibniz was born in Germany in 1646, and he was a stellar student even as a very young child. “Precocious” could have been his middle name (in reality, it was Wilhelm). His father died when he was six, so Leibniz was raised by his mother, who encouraged her son’s intellectual bent. By eight, he was working his way through his father’s substantial library, teaching himself Latin and Greek so he could read the great works of Aristotle and other philosophers. He entered the University of Leipzig at age fifteen and left two years later with his degree in law. Conspicuously absent from his formal education was any study of mathematics; he was entirely self-taught in that discipline.
A chance meeting with the Dutch scientist Christian Huygens ignited Leibniz’s interest in the study of geometry and the mathematics of motion; he described their meeting as “opening a whole new world” to him. He pursued these interests in his spare time, inventing in 1671 a handy little machine called the step reckoner. A forerunner of the modern calculator, the device could add, subtract, multiply, divide, and even extract square roots. His reasoning: “It is unworthy of excellent men to lose hours like slaves in the labor of calculation, which could be safely relegated to anyone else if machines were used.” Why waste perfectly good brainpower on lowly arithmetic?
At Huygens’s urging, Leibniz read Blaise Pascal’s work on infinitesimals, as well as the work of René François de Sluse, who had made a rule for constructing tangents to a point on a curve. Leibniz realized that Pascal’s approach to infinitesimals could be combined with Sluse’s tangent rule and applied to any geometric curve. That same critical insight—the universality of the method—led him to create his own version of calculus independently of Newton.
Leibniz published his first account of differential calculus in 1684, followed by a discussion of integral calculus two years later. It caused a sensation, which rankled Newton’s pride; he became convinced that Leibniz had stolen his ideas from his earlier unpublished papers that had been circulating privately in academic circles over the years. (He used his new techniques in his scientific work long before the publication of Opticks.) There were rumblings of impending conflict in the ensuing years, as tensions brewed between those in Camp Newton and Camp Leibniz, but things didn’t erupt into outright war until Newton published his essay in Opticks.
The opening volley in the calculus wars was an anonymous review of “On the Quadrature of Curves” that appeared in a European journal early in 1704, implying that Newton had “borrowed” his ideas from Leibniz. While Leibniz denied it for the rest of his life, historians generally accept that he was the author. He also engaged in a form of “sock puppetry”: He penned numerous anonymous attacks on his archrival’s work and then reviewed those attacks (one assumes favorably) in his own signed papers. At the time, Newton was by far the more famous scientist, and a prominent member of the Royal Society of England. While he didn’t engage in sock puppetry, he wasn’t above using his considerable influence to crush the scientific competition. In addition to Leibniz, during his long scientific career he fought with John Flamsteed, with Huygens, and with Robert Hooke, and each proved to be an acrimonious battle. Newton was not a people person; no wonder he purportedly died a virgin.