German philosopher, physicist, and mathematician whose mechanical studies included forces and weights. He believed in a deterministic universe which followed a "pre-established harmony." He extended the work of his mentor Huygens from kinematics to include dynamics. He was self-taught in mathematics, but nonetheless developed calculus independently of Newton. Although he published his results slightly after Newton, his notation was by far superior (including the integral sign and derivative notation), and is still in use today. It is unfortunate that continental and English mathematicians remained embroiled for decades in a heated and pointless priority dispute over the discovery of calculus.

Leibniz made many contributions to the study of differential equations, discovering the method of separation of variables, reduction of homogeneous equations to separable ones, and the procedure for solving first order linear equations. He used the idea of the determinant 50 years before Cramer, and did work on the multinomial theorem.

Leibniz combined the Scala Naturae with his plenum (continuous) view of nature, and called the result the Law of Continuity. He believed that it was not possible to put organisms into discrete categories, stating "Natura non facit saltus" (Nature does nothing in leaps).

Leibniz was a strong believer in the importance of the product of mass times velocity squared which had been originally investigated by Huygens and which Leibniz called vis viva, the living force. He believed the vis viva to be the real measure of force, as opposed to Descartes's force of motion (equivalent to mass times velocity, or momentum ). It is not entirely clear why Leibniz should have chosen mv² as this quantity rather than Descartes' mv, but he was apparently led to the conclusion that his quantity was the more fundamental by mechanical arguments. Leibniz's contention that vis visa, not Descartes's quantity, was the most fundamental conserved quantity comes extremely close to an early statement of the Law of Conservation of Energy in mechanics. Since, however, the conservation of quantity of motion had become one of the pillars of Cartesian natural philosophy, Leibniz's suggestion that the fundamental quantity of motion was different from the one Descartes had proposed was rejected out of hand by all good Cartesians. A great controversy ensued between the German school of physical thought, which naturally supported Leibniz, and the French and English schools, whose Cartesians and Newtonians opposed him. In identifying vis viva as the fundamental quantity of motion, Leibniz was searching for some active principle that was conserved and kept the universe from "running down."

Leibniz believed that his vis viva, which described the "force" of a body in motion, would fit the bill. He further realized that this quantity could never increase, since this would produce perpetual motion, a notion which he summarily dismissed as "absurd." On the other hand, Leibniz also maintained that vis viva could never decrease, since this would contradict his belief that it was equivalent to the eternity of God's creation. In fact, Leibniz vigorously clung to his concept of universal conservation of living force, which had nothing but his metaphysical beliefs to support it, even though it appeared to be violated for inelastic collision and was bitterly opposed by a large segment of the scientific community. Thus, Leibniz serves as the first example of a scientist who vehemently argued the existence of a fundamental conservation quantity based not on experimental evidence, but rather from a belief in the order and continuity of the universe. Leibniz's dispute with the Cartesians eventually died down and was forgotten. However, nearly one and a half centuries passed before conservation laws and energy would once again dominate the realm of scientific inquiry and philosophical speculation.

Additional biographies: MacTutor (St. Andrews), Dublin Trinity College, Bonn