Gottfried Wilhelm Leibniz

By Emre Yıldırım

He wanted to calculate everything — not just numbers, but arguments, metaphysics, the whole of human reasoning. Gottfried Wilhelm Leibniz, born in Leipzig in 1646, was the last man who could plausibly claim to know everything: philosopher, mathematician, diplomat, historian, librarian, mining engineer, and inventor, writing some 200,000 pages of manuscripts, most unpublished in his lifetime. He entered the University of Leipzig at fourteen, took a doctorate in law at twenty, and then spent his life in the service of German princes — above all the House of Hanover — as counselor, librarian, and historiographer, scheming for the reunification of the churches and the advancement of science between diplomatic missions.

The mathematics came in a Parisian burst. Sent to Paris in 1672 on a diplomatic scheme to divert Louis XIV from Germany, Leibniz fell in with Christiaan Huygens, who set him mathematical problems; within three years the provincial jurist had invented the differential and integral calculus — with the notation the world still uses. The dy/dx, the elongated S of the integral sign, the rules of differentiation: Leibniz's symbolism was so superior to Newton's fluxions that it conquered the Continent and eventually England too, and it is his notation every student learns. The priority war that followed — Newton accusing him of plagiarism, the Royal Society's rigged 1712 verdict — poisoned British mathematics for a century and embittered Leibniz's last years.

But the calculus was one room in a palace. Leibniz invented the binary system — base-2 arithmetic, the language every computer speaks — and built a calculating machine that could multiply. He dreamed of a characteristica universalis, a symbolic language in which all disputes could be settled by calculation: calculemus — let us compute. His Monadology pictured the universe as infinite windowless monads, each mirroring the whole, harmonized by God in a pre-established harmony; his Theodicy argued this is the best of all possible worlds — the phrase Voltaire would mock in Candide. He founded the Berlin Academy of Sciences, reformed Hanover's coinage, and designed windmills to pump water from the Harz mines. He died in 1716 in Hanover, his funeral attended by almost no one — the court he served had moved to London with George I, who forbade him to follow. The universal genius died unfêted; the binary digits he invented now run the world.

Impact on civilization

Leibniz gave mathematics the calculus in the notation the world still uses — dy/dx and the integral sign — making him, with Newton, the co-founder of modern analysis and thus of all mathematical physics and engineering. His binary arithmetic became, two and a half centuries later, the native language of the digital computer; his stepped reckoner pioneered mechanical calculation. Philosophically, his vision of a universal symbolic language — disputes settled by computation — is the founding dream of symbolic logic and the science of computing. He imagined the computable universe three hundred years before the machine existed.