Lazare Nicolas Marguerite, Count Carnot (French: [lazaʁ nikɔla maʁɡəʁit kaʁno]; 13 May 1753 – 2 August 1823) was a French mathematician, physicist, military officer, politician, and a key member of the Committee of Public Safety during the French Revolution. His military reforms, including the introduction of mass conscription (levée en masse), helped transform the French Revolutionary Army into a strong and effective fighting force.

Carnot was elected to the National Convention in 1792. A year later, he joined the Committee of Public Safety, where he directed France’s war efforts as one of the Ministers of War during the War of the First Coalition. He reorganized the army, enforced discipline, and greatly increased France’s military strength through mass conscription. His work led to France’s military successes from 1793 to 1794, earning him the nickname “Organizer of Victory.”

As he became more unhappy with the extreme political actions of the Montagnards, Carnot left the group led by Maximilien Robespierre. He helped remove Robespierre from power on 9 Thermidor and later saw him executed. Carnot was one of the first five members of the Directory but was removed after the Coup of 18 Fructidor in 1797 and went into exile.

After Napoleon rose to power, Carnot returned to France and briefly served as Minister of War in 1800. A strong supporter of the Republic, he left public life after Napoleon became Emperor. In 1812, he returned to work under Napoleon and managed the defense of Antwerp against the Sixth Coalition. During the Hundred Days, he served as Napoleon’s Minister of the Interior. Carnot was exiled again after the second Bourbon Restoration and died in Magdeburg, Prussia, in 1823.

In addition to his political work, Carnot was a respected mathematician. His 1803 book Géométrie de position was an important early work in the field of projective geometry. He is also known for designing the Carnot wall, a type of fortification widely used in Europe during the 19th century.

Education and early life

Lazare Carnot was born on May 13, 1753, in the village of Nolay, Burgundy, as the son of a local judge and royal notary, Claude Carnot, and his wife, Marguerite Pothier. He was the second oldest of seven children. At age fourteen, Lazare and his brother began attending the Collège d'Autun, where Lazare focused on studying philosophy and the classics. He believed in stoic philosophy and was deeply influenced by Roman civilization. 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. During his time with them, he studied logic, mathematics, and theology under the Abbé Bison.

Impressed by Lazare's scholarly work, the duc d'Aumont (Marquis de Nolay) suggested a military career for him. Carnot was sent by his father to the Aumont residence to continue his education. There, he attended M. de Longpré's pension school in 1770 until he was ready to enter one of two prestigious engineering and artillery schools in Paris. In February 1771, he ranked third among twelve students chosen from a class of over one hundred who took entrance exams. At this time, he entered the École royale du génie de Mézières, where he was appointed as a second lieutenant. His studies at Mézières included geometry, mechanics, geometrical designing, geography, hydraulics, and material preparation. On January 1, 1773, he graduated the school, ranked as a first lieutenant. He was eighteen years old.

Carnot obtained a commission as a lieutenant in Louis Joseph, Prince of Condé's engineer corps. At this time, he gained recognition for his work in theoretical engineering and for his contributions to fortifications. While stationed in Calais, Cherbourg, and Béthune, he continued studying mathematics. In December 1783, he was promoted to the rank of captain.

In 1784, he published his first work, Essay on Machines, which included a statement that introduced early ideas about energy related to falling objects and the earliest proof that kinetic energy is lost in collisions between imperfectly elastic bodies. This publication earned him the honor of the Académie des Sciences, Arts et Belles-Lettres de Dijon. Another important event was his essay on Vauban, in which he praised the engineer's work while also advancing his own career as a writer and engineer. Vauban's work greatly influenced Carnot's later work as a general and engineer. In 1786, he met Robespierre, a lawyer in Arras, at a local literary club. In 1788, he returned to Béthune, where he was imprisoned with a lettre de cachet due to a broken promise to marry a woman from Dijon. After his release, he was stationed in Aire-sur-la-Lys and married Sophie Dupont from Saint-Omer in May 1791. For two months, he served as president of the local literary society.

Political career

In September 1791, he became a representative for Pas-de-Calais to the Legislature. While part of the Legislative Assembly, Carnot was chosen to serve on the Committee of Public Instruction. He believed that all people should have access to education. As a member of that committee, he created plans to improve teaching and education systems, but these plans were not carried out because of the difficult and dangerous conditions during the Revolution.

After the Legislative Assembly was shut down, Carnot was elected to the National Convention in September 1792. In the last months of 1792, he traveled to Bayonne to help organize the military defense against possible attacks from Spain. When he returned to Paris, he voted for the execution of Louis XVI, even though he had not been present during the debates about the king’s trial. By mid-February, Carnot suggested that France should take control of certain areas, regardless of whether the people living there agreed. After the king refused to support efforts to remove priests who refused to swear loyalty to the Revolution on May 27, Carnot and Servan proposed creating a permanent group of volunteer soldiers on June 8. This happened after the dismissal of Brissotin ministers on June 18. These events led to a failed protest on June 20.

On August 14, 1793, Carnot was elected to the Committee of Public Safety, where he managed military matters as one of the Ministers of War. He had a friendly relationship with Johan Valckenaer, who worked to speed up the invasion of the Dutch Republic.

When the Directory was formed in 1795, Carnot became one of the five initial directors. At first, the directors worked well together and with the councils. However, differences in political views caused a split between Carnot and Étienne-François Letourneur, followed by François de Barthélemy, and the group of Paul François Jean Nicolas, vicomte de Barras, Jean-François Rewbell, and Louis Marie de La Révellière-Lépeaux. Carnot and Barthélemy supported ending the war through compromises and wanted to replace the triumvirate with more conservative leaders. After Letourneur was replaced by Barthélemy, both Carnot and Barthélemy, along with many deputies in the Council of Five Hundred, were removed from power in the Coup of 18 Fructidor (September 4, 1797), led by Generals Napoleon Bonaparte (once Carnot’s student) and Charles-Pierre Augereau. Carnot fled to Geneva, where he published his book La métaphysique du calcul infinitésimal in 1797.

The creation of the French Revolutionary Army was largely due to Carnot’s ability to organize and enforce discipline. To raise more soldiers for the war, Carnot introduced conscription, a system called levée en masse approved by the National Convention. This system increased France’s army from 645,000 troops in mid-1793 to 1.5 million by September 1794. Carnot was the first to use modern methods of war with large armies and careful planning during the Revolution. As a military engineer, he preferred forts and defensive strategies. He designed new defensive structures for forts, including the Carnot wall, named after him. However, due to constant attacks, he shifted to offensive strategies. His plans and organization helped change the course of the war from 1793 to 1794.

Carnot’s main idea was to create a large army divided into smaller units that could move faster than the enemy and attack from the sides rather than head-on, a tactic that had previously caused defeats. This strategy was very effective against traditional European armies. He also trained new soldiers by pairing them with experienced soldiers instead of relying on large groups of untrained volunteers.

After solving the problem of having enough soldiers, Carnot focused on organizing supplies for the army. Materials like copper for guns, saltpeter for gunpowder, and leather for boots were in short supply. To address these shortages, he ordered church bells to be melted for copper, used chemistry to produce saltpeter, and found new ways to tan leather for boots. His quick organization helped turn the war’s tide. This effort caused anger in areas still loyal to the Bourbon monarchy, like the Vendée, which had started a rebellion five months earlier. However, the government at the time saw it as a success, and Carnot earned the nickname “Organizer of Victory.” In autumn 1793, he led French forces on the Northern Front and helped Jean-Baptiste Jourdan win the Battle of Wattignies.

Carnot first met Robespierre in Arras, where he was assigned military duties and shortly after Robespierre finished his legal studies. Both were members of a literary club called the Societe des Rosati, which was founded in 1778 and inspired by the works of Chapelle, La Fontaine, and Chaulieu. They became friends through this group. Robespierre joined the Academy of Arras in April 1784, while Carnot joined in 1786.

While both were members of the Committee of Public Safety in 1794, tensions between Carnot and Robespierre grew. During his time on the committee, Carnot signed 43 decrees and drafted 18 of them, most related to military tactics and education. Though he shared some Jacobin beliefs, he was seen as the more conservative member of his group. He was not an official Jacobin and had his own views on issues like Robespierre’s plan for an equal society, which Carnot strongly opposed.

Although Carnot did not actively oppose the Reign of Terror, he and other technocrats, including Robert Lindet and Louis-Bernard Guyton de Morveau, turned against Robespierre and his allies during the Thermidorian Reaction. Robespierre was arrested and later killed along with 21 followers. After Robespierre’s fall, Carnot was accused of his role but the charges were dropped when he joined the Directory.

In 1795, Carnot appointed Napoleon Bonaparte as general in chief of the Army of Italy. He was the only member of the Directory to support Napoleon during this time.

In 1800, Bonaparte made Carnot Minister of War, and he held this position during the Battle of Marengo. In 1802, Carnot voted against giving Napoleon lifelong power and the right to pass it to his children. He argued that power tied to a family would become tyrannical.

After Napoleon became emperor on December 2, 1804, Carnot refused to accept high office under the First French Empire because of his republican beliefs. He left public life. Later, in response to the British capturing the fortress of Vlissingen during the Walcheren Campaign in 1809, Napoleon asked Carnot to write a guide on improving fort

Retirement and legacy

In 1803, Carnot wrote a book called Géométrie de position. This work focused on projective geometry, not descriptive geometry. Carnot introduced the use of cross-ratios, which are a way to measure the relationship between four points on a line. He showed that this measurement stays the same even when the line is transformed, helping to explain the properties of shapes like the complete quadrilateral. This method influenced later mathematicians, including Karl von Staudt, who used it to create new ideas in mathematics about 40 years later.

Several important ideas in math are named after Carnot. These include the Borda–Carnot equation, which describes how water moves, and theorems about triangles, conic sections, and lines that are perpendicular to triangle sides.

In 1810, Carnot published a book titled Traité de la Défense des Places Fortes, which explained how to build strong fortifications. A new version of this book was published in 1812, and an English version called A Treatise on the Defence of Fortified Places came out in 1814. Although many engineers did not use his ideas, the Carnot wall, a type of defensive structure, became widely used in fortifications built in the mid-1800s.

Carnot lived in Warsaw, Congress Poland, and later moved to the Kingdom of Prussia, where he died in Magdeburg. His remains were buried in the Panthéon in 1889, along with those of Théophile Corret de la Tour d'Auvergne, Jean-Baptiste Baudin, and François Séverin Marceau-Desgraviers.

Carnot lived through all major events of the French Revolution, from its start in 1789 until Napoleon’s defeat in 1815. He worked to improve society and proposed reforms, including free public education for all citizens. He also wrote a plan for a new French Constitution that included a statement requiring all citizens aged 20 to 25 to receive education and serve in the military.

Work in mathematics and theoretical engineering

• 1801: De la Corrélation des Figures de Géométrie, a book that includes several geometry rules now called Carnot's theorem.
• Principes fondamentaux de l'équilibre et du mouvement (in French). Published in Paris by Jean-François-Pierre Deterville in 1803.
• 1832: Reflexions on the Metaphysical Principles of the Infinitesimal Analysis

He also wrote essays about engineering theory. His work Essai sur les machines en général received an honorable mention from the Académie des Sciences of Paris in 1780. It was revised and published again in 1783. In this work, he described a mathematical way to explain how power moves in mechanical systems. His later work, Principes fondamentaux de l'équilibre et du mouvement (1803), was an updated and expanded version of the earlier essay.

Carnot’s son, Sadi, was influenced by his father’s research when he studied how steam engines use heat to produce work.

Carnot’s name is one of the 72 names listed on the Eiffel Tower.

Famous offspring

• His son Sadi Carnot helped create the study of thermodynamics and developed ideas about heat engines (see Carnot cycle).
• His second son Lazare Hippolyte Carnot worked in the French government.
• His grandson Marie François Sadi Carnot (son of Lazare Hippolyte Carnot) served as President of the French Republic from 1887 until he was killed in 1894.