October 29, 1675

Leibniz's notation

Leibniz first writes the integral sign in a private manuscript

The integral sign began as a private replacement for three letters and a period: the "omn." Leibniz had been writing to mean "all of them."

29 October 1675: a dated page in Paris

In Paris, Gottfried Wilhelm Leibniz dated a manuscript — Analyseos tetragonisticae pars secunda, "Second Part of Analytical Quadrature" — 29 October 1675. It was not published at the time; the memorandum remained private.

On it he proposed replacing his existing abbreviation "omn." with ∫, writing in effect that ∫l meant the sum of all the l's. The new sign was an elongated S, taken from the Latin summa.

Not a character, an operator

Leibniz had been writing "omn." for omnia — "all" — in summation expressions, and his increasingly elaborate calculations made a shorter operational sign desirable.

He did not stop at the abbreviation. In the same memorandum he explored the inverse relationship between summation and taking differences, and worked through an identity recognizable as an early form of integration by parts.

From working page to print

In his manuscript of 11 November, Leibniz advanced the notation by placing dx after an integral sign, producing an ancestor of the modern ∫…dx form.

None of it was announced. The page sits in the critical edition at Sämtliche Schriften und Briefe, series VII, volume 5, pages 288–295, and the integral sign did not reach print until June 1686.

Sources

Researched 23 Aug 2026 5 sources 2 audit passes, 1 issue open

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