Lazare Carnot

French revolutionary politician, military leader, and mathematician

• Born: May 13, 1753
• Birthplace: Nolay, Burgundy, France
• Died: August 2, 1823
• Place of death: Magdeburg, Prussian Saxony (now in Germany)

Carnot is credited with reorganizing the French Republican army so that it could successfully fight the Austrian army. He acted as minister of war during the Napoleonic era and minister of the interior during the Hundred Days. Cofounder of the École Polytechnique, Carnot popularized mathematics education and extended the synthetic geometry developed by Blaise Pascal.

Early Life

Lazare Carnot (lah-zahr kahr-noh), the son of a lawyer, graduated in 1773 from the school of engineering in Mézières, where Gaspard Monge had been one of his instructors. In 1783, Carnot became a captain in the French army corps of engineers. He also published an engineering work, Essai sur les machines en général (1783; essay on machines in general), followed closely by Dissertation sur la théorie de l’infini mathématique (1785; dissertation on the theory of mathematical infinity). Carnot advocated a new geometry, involved with applying the general principles of transformation within geometrical systems to facilitate the design and construction of machines.

Life’s Work

Lazare Carnot’s career may be roughly divided into five parts: his early contributions in the field of mathematics, his political and military career during the French Revolution, his service under Napoleon I, his “retirement”—tutoring his sons and working in the field of mathematics—and his exile in Magdeburg, Germany. After being elected to the national assembly in 1791, Carnot was involved in several military and diplomatic missions. He then became a member of the Committee of General Defense, was placed in charge of armies, and worked at improving their organization and strategies, including the food supply and the armaments of the troops.

Prior to 1793, the French revolutionary armies had been unable to fight effectively against the Austrians. In April, 1793, Carnot took command of the Army of the North and was able to occupy Belgium. He publicly declared that it be “stripped” and exploited on behalf of the French Republic.

Carnot’s efforts in defending the frontiers resulted in the accolade “Organizer of Victory,” as he rejected the “Prussian Military School” traditions, streamlined the delivery of supplies to the armies, and instituted new strategy and tactics. During the winter of 1793-1794, he concentrated on improving discipline among new recruits.

Carnot’s military focus was on recruitment, weaponry, discipline, and tactics. He appointed young generals and advocated taking advantage of numerical superiority, revolutionary ardor, and superior-quality weapons. He also advocated abandoning the system of deployment in line, instead favoring attacks from column formations. He rejected subtlety and long sieges, favoring massive attacks at a single point. Carnot’s approach was employed effectively in the Austrian campaign when the French attacked Vienna at the Main and Danube Rivers.

Carnot became a member of the Committee of Public Safety (1793-1794). He did not take part in the debates concerning King Louis XVI’s execution, but once the debates were over, he voted against an appeal to the people and in favor of executing the king. Carnot bluntly disagreed with Robespierre on several issues, including the concept of the Supreme Being. Robespierre in turn threatened that Carnot would lose his head as soon as he lost his first battle.

Together with Gaspard Monge, Lazare Carnot was cofounder of the École Polytechnique, which was established in 1794 to educate students to serve the republic. The school admitted students via a competitive entrance exam, and it educated many of the political, scientific, and military leaders of France during the next two hundred years. A few of the most famous early graduates of the École Polytechnique include André-Marie Ampère, François Arago, Gustave Gaspard de Coriolis, and Augustin Cauchy.

Continuing to direct the French army, Carnot became one of five members of the Directory (1795-1797). It was Carnot who gave Napoleon I command of the French army at Genoa. In 1796, however, Carnot opposed Napoleon’s appointment as first consul for life, stating, “I am an irreconcilable enemy of all kings.” Carnot left France prior to the coup d’état of September 4, 1797 (Fructidor 18, 1797, in the revolutionary calendar). After his departure, his colleagues stripped him of his chair in geometry, awarding it to Napoleon instead. While in exile, Carnot wrote Réflexions sur la métaphysique du calcul infinitesimal (1797; Reflexions on the Metaphysical Principles of the Infinitesimal Analysis, 1801). This work, a blend of mathematics and philosophy, became very popular and was reprinted in French in numerous editions and translated into a number of foreign languages. Carnot returned to France in 1799.

Carnot was appointed minister of war by Napoleon in early 1800 and accompanied Jean Victor Moreau early in the Rhine campaign. As minister of war, Carnot worked to reduce military expenditures, but he soon tired of the position. In 1801, Napoleon accepted his resignation, and Carnot devoted himself to his mathematical studies and tutoring his sons.

Carnot publicly opposed the monarchist sentiments of Napoleon, but when Carnot’s colonial investments suffered reversals in 1809, he accepted a commission from Napoleon to write a treatise on fortifications. His famous military book De la défense des places fortes (1810; on the defense of strong places) was published the next year. In this book, Carnot suggested a novel defense construct, the “Carnot Wall.” Following Waterloo, some forts were built incorporating Carnot Walls, including the Boyen Fortress in eastern Prussia and the Shoreham and Littlehampton Forts in East Sussex, England.

Carnot maintained his dislike for the Napoleonic monarchy. In 1812, he declared he would fight “for France,” not for the Napoleonic French Empire. He was appointed minister of the interior during the Hundred Days in 1815 and served as governor of Antwerp. In 1816, under Louis XVIII, Carnot’s Republican views forced him into exile at Magdeburg, and he took his young son Lazare Hippolyte Carnot (1801-1888) with him. In 1821, Carnot’s older son Sadi Nicholas Léonard Carnot (1792-1832) visited Magdeburg, where he became interested in steam engines. Carnot himself had become interested in steam engines three years previously, when one had been brought to Magdeburg. For this reason, it is widely believed that the elder Carnot influenced Sadi’s research into thermodynamics, especially the mechanics and efficiency of steam engines.

Significance

Although Lazare Carnot’s leadership roles in the French Revolution and during the Napoleonic era were historically significant, the paradigm shift he and Monge created within mathematics was historic. This paradigm shift was accomplished largely through the education of students at the École Polytechnique, where research and education were intertwined. The graduates of the École Polytechnique shared the ideology of its founders, as well as a new common approach to attacking problems mathematically. The École Polytechnique led to the acceptance of mathematicians and engineers (ingénieurs-savants) as highly respected members of society. This was a radical departure from the classical education of European aristocratic leaders outside France. After more than two hundred years, the École Polytechnique remains among the most internationally esteemed French universities.

Carnot’s ultimate goal was to replace the aristocratic gentleman-scholar with the professional citizen-scientist in a meritocratic environment. His mathematical works, Reflextions on the Metaphysical Principles of the Infinitesimal Analysis, De la corrélation des figures de géométrie (1801; on the correlation of geometrical figures), and Géométrie de position (1803; geometry of position), have been republished periodically during the last two hundred years. Géométrie de position evoked substantial interest among mathematicians. In this work, Carnot initiated the search for “intrinsic coordinates” and introduced a quantity now referred to as “aberrancy” or “angle of deviation.” This work included Carnot’s polygram theorem, which has led to several significant proofs.

Work done by Carnot’s progeny is sometimes attributed to him. They achieved their own places in history, however: His elder son Sadi determined the formula for the efficiency of engines. Hippolyte went into exile in Magdeburg with his father, but in 1823 he returned to France, where he worked with his elder brother Sadi on writing about engines. In 1839, Hippolyte was elected deputy for Paris in the Governing Chamber, sitting with the Radical Left. He was named as a national assembly senator for life in 1875. Hippolyte’s two sons also made significant contributions: Marie François Sadi Carnot (1837-1894) was president of the Third Republic. Under his grandson’s presidency, Hippolyte’s remains were entombed in the Panthéon in 1889. Hippolyte’s younger son Adolphe Marie Carnot (1839-1920) was a prominent analytical chemist and geologist and dean of the École Nationale des Mines (1901-1907) who discovered an ore of uranium subsequently named “carnotite” in his honor. A. M. Carnot authored Traité d’analyse des substances minerals (1898-1904).

Bibliography

Boyer, Carl B. A History of Mathematics. 2d ed. New York: Wiley, 1991. An excellent reference book on great mathematicians that devotes a chapter to Carnot’s contributions to the fields of calculus and geometry.

Carnot, Lazare. Révolution et mathématique. Paris: L’Herne, 1984. A twentieth century French-language publication regarding Lazare Carnot’s contributions to the field of mathematics.

Dhombres, Jean, and Nicole Dhombres. Lazare Carnot. Paris: Fayard, 1997. A 770-page comprehensive work in French, with an excellent portrait of a middle-aged Carnot on the cover.

Glas, Éduard. “Socially Conditioned Mathematical Change: The Case of the French Revolution.” Studies in History and Philosophy of Science, Part A 33 (December, 2002): 709-728. Examines the mathematical accomplishments of Lazare Carnot and Gaspard Monge before, during, and after the French Revolution. Carnot and Monge, as engineers, realized that industrial technology required interchangeable parts, and needed to move to mathematical formulations, rather than “rules of thumb.” Radical changes in political power enabled mathematician-engineer-scientists Carnot and Monge to create a new engineering-oriented mathematics curriculum taught to future French leaders at the École Polytechnique. Carnot’s political prominence led to the wide readership of his mathematical works.

Goubert, Pierre. The Course of French History. Translated by Maarten Ultee. New York: Routledge, 2003. A review of Lazare Carnot’s importance in the French Revolution and his interactions with Napoleon.

McLynn, Frank. Napoleon: A Biography. New York: Arcade, 2002. A good introduction to Carnot’s role under Napoleon.