Early Modern Philosophy

Gottfried Wilhelm Leibniz

What was the dispute between Leibniz and Newton about the calculus?

Gottfried Leibniz was very sociable intellectually, and welcomed a free and cooperative exchange of ideas. Toward the end of his life, though, he was greatly distressed by the claims of Isaac Newton’s (1643–1727) advocates that he had in effect plagiarized the discovery of the differential calculus from Newton. Leibniz reported that when he was in England in 1637 he was told about Newton’s work on the calculus and wrote to him.

Newton replied through an intermediary, although he wrote about the binomial theory and included only the following sentence, in Latin, about the calculus (“fluxions”). The words of the sentence were presented by Newton, in code, as follows: “aaaaa cc d ae eeeeeeeeeeeee ff iiiiiii lll nnnnnnnnn oooo qqqq rr ssss ttttttttt vvvvvvvvvvvv x.” It meant, “Given equation anywhatsoever, flowing quantities involving, fluxions to find, and vice versa.” No one has ever been able to make sense of what Newton wrote Leibniz, nor has anyone related it to the differential calculus, although the string of letters are sometimes quoted to illustrate how unreasonable Newton was. Leibniz then invented a differential calculus on his own, showed it to Newton’s intermediary, and in 1684 published his method. By 1695, Newton’s followers were accusing him of plagiarism.

Over the centuries, scholars have exonerated Leibniz of plagiarism. The conclusion has been that they each independently invented the calculus and that Newton did so first, although Leibniz published first.


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