Lazare Nicolas Marguerite Carnot (Nolay, May 13, 1753 - Magdeburg, August 22, 1823) was a French mathematician and politician. He is best know 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. 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. He continued to occupy a prominent place in every successive form of government till 1796 when, having opposed Napoleon's coup d'état, he had to flee from France. He took refuge in Geneva, and there in 1797 issued his La métaphysique du calcul infinitésimal. In 1802 he assisted Napoleon, but his sincere republican convictions were inconsistent with the retention of office.
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.
He was the father of Nicolas Léonard Sadi Carnot.