The German mathematician and scientist Gottfried Wilhelm Leibniz is one of the great thinkers of the Scientific Enlightenment >.Leibniz, with Isaac Newton >, is now credited as the inventor of differential calculus. His work, which at times contradicted Newton’s, greatly inspired and influenced Émilie du Châtelet >.
According to Leibniz’s notebooks, a critical breakthrough occurred Nov. 11, 1675, when he employed integral calculus for the first time to find the area under a function y = ƒ(x).He introduced several notations still used to this day, such as the integral sign representing an elongated S, from the Latin word summa, and the d used for differentials, from the Latin word differentia. This ingenious and suggestive notation for the calculus is probably his most enduring mathematical legacy. These ideas were later outlined by Newton in 1677. In 1684, Leibniz published his first paper on calculus. A small group of mathematicians took up his ideas and became Leibniz supporters.
Though Leibniz’s approach to the calculus was ingenious, he generated controversy with his work. Leibniz freely associated calculus with determining how the universe works, causing theologians to ridicule his work as “a big leap of faith” that undermined God and Christianity. By the 1690s, Newton and Leibniz became entangled in serious debate over whether Leibniz had invented calculus independently of Newton or whether he had merely invented another notation for ideas that were fundamentally Newton’s. Supporters of Leibniz asserted that he had communicated the differential method to Newton, although Leibniz had claimed no such thing. Newtonians then asserted that Leibniz had seen papers of Newton’s during a London visit in 1676. A violent dispute sprang up, part public, part private, with Leibniz attacking Newton on his theory of universal gravitation and his ideas about God and Creation. This dispute continued until Leibniz’s death in 1716. The dispute delayed the reception of Newtonian science on the Continent and dissuaded British mathematicians from sharing the research with their Continental colleagues for more than a century.
Modern, rigorous calculus based on the foundations of Leibniz’s work emerged in the 19th century in Germany and traveled across Europe and America. Then, beginning in 1960, American mathematician Abraham Robinson brought Leibniz’s calculus back into the mainstream. Today, Leibniz’s calculus is used in classrooms around the world.
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