The rate of change of the rate of change/the area under a curve.

November 11, 2008, 3:32 pm

Below the historians debate which American Presidents count as intellectual. Here I sing of math and the man, Gottfried Leibniz, German polymath, the smartest man that ever lived. I could sing out long and loud, but today I sing only one verse to make the case:*

In 1672, the Elector of Mainz sent the young diplomat Leibniz to Paris. The young diplomat Leibniz did little in the service of diplomacy, but instead met all of the intellectuals that he could find, including the Dutch mathematician Christian Huygens, and to his chagrin, the young Leibniz learned that his mathematical knowledge was quite deficient. So he decided to rectify the situation.

Three years later, on this day in 1675, he invented the calculus.


Of course, the claim that he invented the calculus was not (is not?) uncontroversial. Newton claimed to have developed his method of fluxions in 1666 or so, and thus Leibniz’s contribution, at most, was developing a better notation system for someone else’s discovery.

Historians of science sometimes speak of the calculus as ready to be discovered, and so, like the question of who discovered the New World, it’s simply a matter of who did it, when, and whether he did it on his own.** And the evidence at best is mixed. It’s clear that Newton did not publish his method of fluxions until 1693; Leibniz first publishes his differentials in 1684. But the intellectual currency of the day was manuscripts and letters, mostly undated, and it is not clear whether Leibniz saw Newton’s manuscripts prior to 1677, when he sent a note to Newton detailing some of the principles of his system.

Complicating the issue further is rabid partisanship. In 1687, Newton claims that he invented the calculus independently some twenty years earlier, but acknowledged Leibniz as a skilled geometer who had shared his own independently developed method ten years earlier. It was not until the early 1700s when charges of plagiarism began to appear on both sides. Neither man acquitted himself well:

All-out war began in 1710, when an English writer published an article bluntly accusing Leibniz of plagiarism. Understandably outraged, Leibniz demanded an independent inquiry from the Royal Society. In 1712, the Society duly organized a commission, which delivered its verdict: the accusation of plagiarism stands. The de facto chairman of the inquiry and author of its report on Leibniz was Isaac Newton.

An anonymous article appeared in the German press defending Leibniz and reversing the charge: Newton, the unnamed author declaims, plagiarized Leibniz. Leibniz was forced to disown the article, claiming it had been put out by a “zealous friend.” But it soon became clear to all parties that the “zealous friend” in question was Leibniz himself. In England, meanwhile, appeared an anonymous review of the dispute, according to which Newton was the innocent victim of Leibniz’s chicanery. The “anonymous” author, it turns out, was Newton himself.

The dispute resolved solomonically: We say they both independently invented the calculus. Newton invented it first. Leibniz invented it…. better.

*Diderot sings it shorter: “When one compares the talents one has with those of a Leibniz, one is tempted to throw away one’s books and go die quietly in the dark of some forgotten corner.”

** I heart the locution “discovered.” As if the calculus were behind the sofa all along!

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