Lazare Nicolas Marguerite Carnot (Nolay, May 13, 1753 - Magdeburg, August 22, 1823) was a French politician and mathematician. He is best know for his role as "Organizer of Victory" in the French Revolutionary Wars, and for a special property of the second law of thermodynamics, called Carnot's rule, which says essentially, that there must be a degradation of energy in any machine which outputs free energy.
Born at Nolay, he was educated in Burgundy, and obtained a commission in the engineer corps of the Prince de Condé. Although in the army, he continued his mathematical studies in which he felt great interest. His first work, published in 1784, was on machines; it contains a statement which foreshadows the principle of energy as applied to a falling weight, and the earliest proof of the fact that kinetic energy is lost in the collision of imperfectly elastic bodies.
On the outbreak of the French Revolution in 1789, Carnot threw himself into politics. He became a delegate to the National Convention in 1792, and in 1793 he was elected to the Committee of Public Safety, and the victories of the French army were largely due to his powers of organization and enforcing discipline. Due to this he became known as the "Organizer of Victory." He had taken no steps to oppose the Reign of Terror, but he, along with other technocrats on the committee like Robert Lindet and Prieur of the Côte d'Or, turned on Robespierre and his allies after 9 Thermidor. With the establishment of the Directory in 1795, Carnot became one of the initial directors. His moderation proved his undoing, however, and he was one of the two directors ousted in the Fructidor coup of 1797. He took refuge in Geneva, and there in 1797 issued his La métaphysique du calcul infinitésimal.
In 1800 he was appointed Minister of War by Bonaparte (originally his protégé), and served in that office at the time of the Battle of Marengo, but his sincere republican convictions were inconsistent with the retention of office, and he resigned from public life, although he was later made a Count by Napoleon as Lazare Nicolas Marguerite, comte Carnot.
In 1803 he produced his Géométrie de position. This work deals with projective rather than descriptive geometry, it also contains an elaborate discussion of the geometrical meaning of negative roots of an algebraic equation.
During the Hundred Days, he served as Minister of the Interior for Napoleon, and was exiled after the Second Restoration. He died at Magdeburg in Prussia.