Monthly Archives: June 2013

The Calculus Wars

Jason Socrates Bardi’s The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time describes the “priority dispute” between Britain’s favorite scientist Isaac Newton and German mathematician and philosopher Gottfried Leibniz over credit for the invention of differential and integral (infinitesimal) calculus.

Newton developed his “method of fluxions and fluents” (geometric calculus) in 1666 but chose not to publish his work and so expose himself to the rigorous scrutiny involved. Leibniz developed an alternate approach with superior notation (differential calculus) beginning in 1674 and published it in 1684. Initially, the minimal interaction between the two was tentative, cordial and appreciative of the other’s work. However, when Leibniz implied anonymously but transparently that Newton had taken credit for some of Leibniz’s work, Newton employed the wide range of resources at his disposal as Britain’s pre-eminent intellectual–primarily the Royal Society, of which he was president–to turn the tables and accuse Leibniz of plagiarism instead. Newton’s prominence helped him gain the upper hand in the debate in the near term–certainly in Great Britain–but fortunately, for history’s sake, both are now universally given credit for the original aspects of their work, and each is recognized for his contribution to the foundations of calculus.

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Reluctant Genius

Everyone knows Alexander Graham Bell as the inventor of the telephone, but Charlotte Gray’s book, “Reluctant Genius” reveals much more about him.

Among the greatest American inventors, Bell is contrasted with Thomas Edison for his modesty and his insistence on perfecting his advancements before promoting them prematurely in order to gain a commercial advantage. Indeed, without the legal work of his father-in-law, Gardiner Hubbard, he would surely not have received and retained the patents that supported him and his family throughout their lives.

Bell enjoyed a remarkable love affair with his wife Mabel, a “warm-hearted, clever woman” who devoted herself to her “brilliantly intuitive” but often “demanding and insensitive” husband and allowed him the freedom to pursue his ideas.

Bell’s creative impulses continued throughout his life and he was granted a total of 31 patents—13 relating to the “electric speaking telephone” and 18 more for:

Bell said, “An inventor is a man who looks around the world and is not content with things the way they are; he wants to improve what he sees; he wants to benefit the world.”

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