Beyond Genius by Bulent Atalay

Author:Bulent Atalay
Language: eng
Format: epub
Publisher: Pegasus Books
Published: 2023-11-07T00:00:00+00:00

THE CALCULUS WARS

In a manuscript dated November 1665, it is clear that Newton had insight into the method of fluxions, differential calculus, to determine the instantaneous slope at a specified point on a smooth curve, and from the equation of a tangent at that point, the radius of curvature. He was already using the binomial theorem and the elements of infinitesimal calculus—both his own creations—to solve problems regarding change and motion by 1666, but he was keeping it all close to the vest. By the late 1670s Newton and Leibniz communicated on mathematical issues and Newton, uncharacteristically, shared his ideas with his rival, including the mathematical expression known as the fundamental theorem of calculus, demonstrating that the integral is the anti-derivative of a function. The fundamental theorem of calculus forms the backbone of calculus and links its two main ideas, the concept of the integral, the infinite summation of vanishingly small elements, and the concept of the derivative, the infinitesimal dissembling of a continuous distribution.

Newton had numerous feuds with other great men, and when he did not see critics as nonthreatening puppies nipping at his ankles, he saw them as mortal enemies. A rare rival in his own intellectual weight class was the German polymath Gottfried Wilhelm Leibniz. Four years his junior, Leibniz was trained in mathematics, philosophy, law, ethics, theology, politics, history, philology, and mechanical engineering. He could write scholarly works on each of these subjects in Latin, French, English, and German. Without ever coming face-to-face, Newton and Leibniz engaged each other in mortal combat in the Calculus Wars that lasted longer than the Hundred Years’ War and the War of the Roses combined. The issue concerned the provenance of infinitesimal calculus.

In 1684, the same year that Newton began formulating the Principia, Leibniz published his version of infinitesimal calculus. Meanwhile, fearing that the use of calculus in the formulations in his book would not be comprehended by other scholars, Newton decided instead to use only plane geometry familiar to all. However, when Leibniz’s publication of the calculus appeared first, Newton was left fuming. He publicly accused Leibniz of plagiarizing. When Leibniz countersued Newton over the primacy of calculus he had no idea that the system was rigged against him. By then Newton was president of the Royal Society, the one passing judgment on Leibniz’s claim, and so he was the one writing the final judgment posing as a “fair arbitrator!”

The Calculus Wars never quite came to an end, although 330 years after they began, most scholars regard the two surpassing geniuses, one English, the other German, as the coinventors of calculus. As modern mathematicians readily admit, Leibniz’s notation was the superior of the two, and is the one now used universally. The war never had to be fought! There was more than enough credit to go around. Leibniz, very much the more gracious of the two, when asked his opinion of Newton by the queen of Prussia, replied, “Taking mathematicians from the beginning of the world to the time when Sir Isaac lived, what he had done was much the better half.

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