Leibniz first used the integral sign in calculus
On this day · 29 October 1675
On a single autumn day in 1675, a stretched letter S quietly became one of mathematics' most recognisable symbols.
On 29 October 1675, the German polymath Gottfried Wilhelm Leibniz put pen to paper in an unpublished manuscript titled Analyseos tetragonisticae pars secunda and wrote the symbol ∫ for the very first time. He was working in Paris, wrestling with the problem of summing infinitely many infinitesimal slices to find areas under curves.
The mark was no random flourish. Leibniz drew it as an elongated S, short for the Latin summa (“sum”), to capture the idea of adding up a continuous quantity. Within weeks he paired it with the differential dx, giving the world the compact, expressive notation of calculus that students still learn today.
A single stretched letter, scribbled in a private notebook, outlived empires and now anchors physics, engineering and economics.
Though Isaac Newton developed calculus independently, it was Leibniz’s clear, flexible symbolism—the integral sign and the d notation—that the mathematical world ultimately adopted.
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