He oversaw the reorganization of the army, imposed discipline, and significantly expanded the French force through the imposition of mass conscription.

Increasingly disillusioned with the radical politics of the Montagnards, Carnot broke with Maximilien Robespierre and played a role in the latter's overthrow on 9 Thermidor and subsequent execution.

When he turned fifteen, he left school in Autun to strengthen his philosophical knowledge and study under the Society of the Priests of Saint Sulpice.

Impressed with Lazare's work as a scholar, the duc d'Aumont [fr] (Marquis de Nolay) recommended a military career for the youngster.

As a member of that committee, he wrote a series of reforms for the teaching and educational systems, but they were not implemented due to the violent social and economic climate of the Revolution.

He spent the last few months of 1792 on a mission to Bayonne, organizing the military defense effort in an attempt to ward off any possible attacks from Spain.

Upon returning to Paris, Carnot voted for the death of Louis XVI, although he had been absent for the debates surrounding his trial.

[7] On 14 August 1793 Carnot was elected to the Committee of Public Safety, where he took charge of the military situation as one of the Ministers of War.

Carnot and Barthélemy supported concessions to end the war, and hoped to oust the triumvirate and replace them with more conservative men.

After Letourneur had been replaced by another close collaborator of Carnot, François de Barthélemy, both of them, alongside many deputies in the Council of Five Hundred, were ousted in the Coup of 18 Fructidor (4 September 1797), engineered by Generals Napoleon Bonaparte (originally, Carnot's protégé) and Pierre François Charles Augereau.

[9] The basic idea was to have a massive army separated into several units that could move more quickly than the enemy and attack from the flanks rather than head on, which had led to resounding defeats before Carnot was elected to the Committee of Public Safety.

It was his initiative to train the conscripts in the art of war and to place new recruits with experienced soldiers rather than having a massive volunteer army without any real idea of how to wage battle.

Once the problem of troop numbers had been solved, Carnot turned his administrative skills to the supplies that this massive army would need.

It added significantly to discontent with the course of the Revolution in still Bourbon-loyalist areas—such as the Vendée, which had broken out in open revolt five months earlier—but the government of the time considered it a success, and Carnot became known as the Organizer of Victory.

[4] In autumn 1793, he took charge of French columns on the Northern Front, and contributed to Jean-Baptiste Jourdan's victory in the Battle of Wattignies.

[10] While they were active members of the Committee of Public Safety in 1794, tensions between Carnot and Robespierre began to rise massively.

[13] Although he had taken no steps to oppose the Reign of Terror, he and some other technocrats on the committee, including Robert Lindet and Louis-Bernard Guyton de Morveau, turned on Maximilien Robespierre and his allies during the Thermidorian Reaction by having him arrested.

"[citation needed] After Napoleon crowned himself emperor on 2 December 1804, Carnot's republican convictions precluded his acceptance of high office under the First French Empire, and he resigned from public life.

Probably in response to the fall of the fortress of Vlissingen to the British during the Walcheren Campaign in 1809, Napoleon employed Carnot to write a treatise describing how fortifications could be improved, for the use of the École militaire de Metz [fr].

Building on the theories of the controversial engineer Montalembert, Carnot advanced ideas on how the long-established bastioned system of fortification could be modified for close defense and to allow for counter attack by the besieged garrison.

During the Hundred Days, Carnot served as Minister of the Interior for Napoleon, and was exiled as a regicide during the White Terror after the Second Restoration during the reign of Louis XVIII.

Carnot is responsible for initiating the use of cross-ratios: "He was the first to introduce the cross (anharmonic) ratio of four points of a line taking account of its sign, thereby sharpening Pappus's concept.

Carnot's remains were interred at the Panthéon in 1889, at the same time as those of Théophile Corret de la Tour d'Auvergne, Jean-Baptiste Baudin and François Séverin Marceau-Desgraviers.

Carnot's son, Nicolas, was influenced by his father's work when he undertook his research into the thermal efficiency of steam engines.