born: July 1, 1646 at Leipzig

died: Nov 14, 1716 at Hanover

**If Leibniz was not as penetrating a mathematician as Newton, he was perhaps a broader one, and while inferior to his English rival as an analyst and mathematical physicist, he probably had a keener mathematical imagination and a superior instinct for mathematical form.**

(Howard Eves)

Co-inventor of calculus. Introduced the dy/dx and notations. Invented combinatorial analysis and made important initial contributions to symbolic logic. Lawyer. Diplomat.

Leibniz was born into the moderately well-off family of a scholar and professor. His father died when Leibniz was only six and the boy mostly educated himself by constant reading. By the time he entered college, at 15, to study law, he had already mastered Latin and Greek and the mathematics available in books. By 1666, at 20, he was ready to receive a doctorate in law at the University of Leipzig, but the school refused to grant him the degree because of his young age, so he moved to the University of Altdorf in Nuremburg. There he was quickly granted his degree and even offered a position on the law faculty, but he turned it down to help revise some of the local legal codes and to serve on several commissions. At 20 he was already thinking of quite new mathematics, and, in his essay “De arte combinatoria,” he proposed to reduce reasoning to mere calculation on an appropriate set of symbols — a formal logic well before its time. In it he invented the ideas of class union, intersection and negation, as well as the null class and class inclusion, ideas now fundamental to set theory.

During his diplomatic duties in Paris in 1672, Leibniz met Christian Huygens, a physicist who knew a lot of mathematics, and Huygens agreed to teach Leibniz some of the ‘newer’ mathematics. By 1676, Leibniz had discovered many of the formulas of calculus as well as the Fundamental Theorem of Calculus, 11 years after Newton’s unpublished discovery. He introduced and used much of the notation commonly encountered in elementary calculus including the ratio dy/dx to denote a derivative and the familiar (at least to calculus students) (an elongated “S” for the Latin word summa or sum), to denote an integral. He devoted most of the rest of his life to diplomacy and work as the librarian for the Duke of Hanover, but he did find time to start one journal and to found the Berlin Academy of Science.

His greatest diplomatic attempt, a conference in 1683, was to reunite the Protestant and Catholic churches after their recent split, but “neither party could agree which was to be swallowed by the other.” He followed this failure with the Protestant Conference, an attempt to simply reunite the 2 Protestant factions of the day. That also failed.

During the last seven years of his life, the controversy about who discovered calculus broke out among his followers and those of Newton. Despite his relative fame and secure position in life, it is said that his funeral was attended only by his secretary.

Condensed from Men of Mathematics by E.T. Bell (1937, Simon and Schuster) and An Introduction to the History of Mathematics, 4th ed., by H. Eves (1976, Holt, Rinehart and Winston). DTH

Last Updated September 22, 2022