🇩🇪Gottfried
Leibniz

Gottfried Wilhelm Leibniz was eight years old when he gained access to his late father's library and began reading it systematically. His father, a professor of moral philosophy at Leipzig, had died when Leibniz was six, leaving behind a substantial collection of classical and scholarly texts. The boy worked through Latin and Greek largely on his own, using the books themselves as his teachers, and by twelve he had a command of both languages sufficient to compose verse and engage in formal argument. By fifteen he had mastered the classical curriculum, the scholastic philosophers, the works of Descartes and Bacon, and had begun his own philosophical investigations. He entered the University of Leipzig in 1661. He was fifteen years old. He was already, by almost any reasonable definition, an educated man.

Born on July 1, 1646, in Leipzig, Leibniz grew up in the intellectual atmosphere of Protestant Germany in the decades after the Thirty Years' War — a period of intense scholarly activity as European thought began the long transition from scholasticism to what we now call the Scientific Revolution. He completed his undergraduate degree in philosophy in two years, then began studying law. He was refused a doctorate in law at Leipzig — accounts suggest the faculty thought him too young — and transferred to the University of Altdorf, where he submitted a dissertation of such quality that the faculty offered him a professorship on the spot. He was twenty years old. He declined the professorship: he had other plans.

Those other plans involved essentially everything. Leibniz is one of the very few thinkers in history who can be said, without exaggeration, to have made foundational contributions to multiple distinct fields. In mathematics, he independently developed the infinitesimal calculus, producing the notation — the integral sign, the d for differential — that mathematicians still use today, while Newton's notation fell out of use. He invented the stepped reckoner, a calculating machine that could perform multiplication and division mechanically. He developed binary arithmetic — the representation of numbers using only 0 and 1 — and saw its potential for logical computation, though the world would not catch up to that insight for two centuries. He founded symbolic logic, anticipating the work of Boole and Frege by a century and a half.

In physics, he developed the concept of vis viva — what we now call kinetic energy — and argued, against Newton, that space and time are not absolute substances but relational properties of objects. This debate, which consumed much of the intellectual energy of both men's final decades, was settled definitively in Einstein's favour of Leibniz in 1905, with special relativity. In philosophy, he developed a complete metaphysical system — the monadology — arguing that reality is ultimately composed of simple, indivisible, perception-bearing substances called monads. He also articulated the principle of sufficient reason (nothing exists without a reason), the principle of the identity of indiscernibles (no two things are exactly alike), and the principle of pre-established harmony (God created the universe so that all substances unfold in perfect coordination without causally interacting). These are not fringe positions; they remain central topics in metaphysics.

He spent much of his adult life in the service of the House of Hanover, working as librarian, diplomatic adviser, genealogist, and engineer — designing mining machinery, water pumps, and wind turbines for the Harz Mountains, none of which worked quite as planned, but all of which occupied a mind that seemed constitutionally incapable of staying within any discipline. He corresponded with over a thousand individuals across Europe — scientists, philosophers, theologians, rulers, merchants — in a network of intellectual exchange unprecedented in breadth. He worked continuously on a project he called the characteristica universalis: a universal symbolic language in which all human knowledge could be expressed and all disputes resolved by calculation. He never completed it. The project was, in retrospect, about three centuries premature.

The calculus priority dispute with Newton — one of the most bitter and consequential controversies in the history of mathematics — consumed the last decade of his life. Both men had independently developed the calculus: Newton first in unpublished manuscripts (c. 1666), Leibniz independently in published form (1684). The Royal Society, heavily influenced by Newton, ruled against Leibniz in 1712, accusing him of plagiarism. The accusation was false. Modern historians are unanimous that both discoveries were independent. But the dispute damaged Leibniz's reputation and embittered his final years. He died in Hanover on November 14, 1716, largely forgotten by the court that had employed him. His secretary was the only person who attended his funeral. The notation he invented is used by every mathematics student in the world every day.