October 29

1675: Leibniz ∫ums It All Up, Seriesly

Gottfried Leibniz writes the integral signin an unpublished manuscript, introducing the calculus notation that’s still in use today.

Leibniz was a German mathematician, philosopher, lawyer, and alchemist who fancied himself a poet. He also conducted diplomatic missions. In London he showed an unfinished calculating machine to the Royal Society, which elected him a fellow. Leibniz discussed with his English colleagues his interest in summing series and the geometry of infinitesimals, and corresponded with them from France. They apprised him of the latest books and also told him about Isaac Newton’s unpublished work on the subject.

Newton wrote to Leibniz through an intermediary, and they exchanged letters that took weeks or even months to reach the recipient. The muddled back-and-forth led to bad blood, with Newton claiming that Leibniz had stolen his work in founding calculus. Newton’s letters, however, described results, not methods. Leibniz’s legal and philosophical formalism let him create his own symbolic system: the integral sign and the notation of differentials we still use today. Newton published slightly before Leibniz, but the German’s notation was superior.

It’s another example of simultaneous discovery (see here). The scientists were of the same era, associated with the same circles, read the work of the same precursors, and shared some of their own ideas. It should amaze no one that they reached the same results in slightly different language at nearly the same time.

Does Newton deserve credit? Maybe, but it’s Leibniz’s language you learn in calculus class. And ol’ Isaac gets his props for many other discoveries (see here), so don’t overestimate the gravity of the situation. Happy Integral Day, Gottfried!—RA