Antoine Augustin Cournot was a French philosopher and mathematician who also contributed to the development of economics theory.

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Background

Cournot was born on August 28, 1801, in Gray, France. Of Franche-Comté peasant stock, Cournot’s family had belonged for two generations to the petite bourgeoisie of Gray. In his Souvenirs he says very little about his parents but a great deal about his paternal uncle, a notary to whom he apparently owed his early education. Cournot was deeply impressed by the conflict that divided the society in which he lived into the adherents of the ancien régime and the supporters of new ideas, especially in the realm of religion. One of his uncles was a conformist priest, the other a faithful disciple of the Jesuits, having been educated by them.

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Education

Between 1809 and 1816 Cournot received his secondary education at the collège of Gray and showed a precocious interest in politics by attending the meetings of a small royalist club. He spent the next four years idling away his time, working “en amateur” in a lawyer’s office. Influenced by reading Laplace’s Système du monde and the Leibniz-Clarke correspondence, he became interested in mathematics and decided to enroll at the École Normale Supérieure in Paris. In preparation, he attended a course in special mathematics at the Collège Royal in Besançon (1820-1821) and was admitted to the École Normale after competitive examinations in August 1821. However, on 6 September 1822 the abbé Frayssinous, newly appointed grand master of the University of France, closed the École Normale. Cournot found himself without a school and with only a modest allowance for twenty months. He remained in Paris, using this free time - which he called the happiest of his life - to prepare at the Sorbonne for the licence in mathematics (1822-1823). His teachers at the Sorbonne were Lacroix, a disciple of Condorcet, and Hachette, a former colleague of Monge. A fellow student and friend was Dirichlet.

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Career

In October 1823, Cournot was hired by Marshal Gouvion-Saint-Cyr as tutor for his small son. Soon Cournot became his secretary and collaborator in the editing and publishing of his Mémoires Thus, for seven years, until the death of the marshal, Cournot had the opportunity to meet the many important persons around the marshal and to reflect on matters of history and politics. Nevertheless, Cournot was still interested in mathematics. He published eight papers in the baron de Férussac’s Bulletin des sciences, and in 1829 he defended his thesis for the doctorate in science, “Le mouvement d’un corps rigide soutenu par un plan fixe.” The papers attracted the attention of Poisson, who at that time headed the teaching of mathematics in France. When, in the summer of 1833, Cournot left the service of the Gouvion-Saint-Cyr family, Poisson immediately secured him a temporary position with the Academy of Paris. In October 1834 the Faculty of Sciences in Lyons created a chair of analysis, and Poisson saw to it that Cournot was appointed to this post. In between, Cournot translated and adapted John Herschel’s Treatise on Astronomy and Kater and Lardner’s A Treatise on Mechanics, both published, with success, in 1834.

From then on, Cournot was a high official of the French university system. He taught in Lyons for a year. In October 1835 he accepted the post of rector at Grenoble, with a professorship in mathematics at the Faculty of Sciences. Subsequently he was appointed acting inspector general of public education. In September 1838, Cournot married and left Grenoble to become inspector general. In 1839 he was appointed chairman of the Jury d’Agrégation in mathematics, an office he held until 1853. He left the post of inspector general to become rector at Dijon in 1854, after the Fortoul reform, and served there until his retirement in 1862.

At the same time he pursued a career as scientist and philosopher. While rector at Grenoble, he published Recherches sur les prinipes mathématiques de la théorie des richesses (1838). Between 1841 and 1875 he published all his mathematical and philosophical works.

Cournot’s background and his education made him a member of the provincial petite bourgeoisie of the ancien régime. But as a civil servant of the July monarchy and the Second Empire, he became integrated into the new bourgeoisie of the nineteenth century. Of certainly mediocre talents as far as pure mathematics was concerned, he left behind work on the philosophy of science, remarkably forceful and original for its period, that foreshadowed the application of mathematics to the sciences of mankind.

Cournot’s mathematical work amounts to very little: some papers on mechanics without much originality, the draft of his course on analysis, and an essay on the relationship between algebra and geometry. Thus, it is mainly the precise idea of a possible application of mathematics to as yet unexplored fields that constitutes his claim to fame. With the publication in 1838 of his Recherches sur les principes mathématiques de la théorie des rishesses he was a third of a century ahead of Walras and Jevons and must be considered the true founder of mathematical economics. By reducing the problem of price formation in a given market to a question of analysis, he was the first to formulate the data of the diagram of monopolistic competition, thus defining a type of solution that has remained famous as “Cournot’s point.” Since then, his arguments have of course been criticized and amended within a new perspective. Undoubtedly, he remains the first of the important pioneers in this field.

Cournot’s work on the “theory of chance occurrences” contains no mathematical innovation. Nevertheless, it is important in the history of the calculus of probability, since it examines in an original way the interpretation and foundations of this calculus and its applications. According to Cournot, occurrences in our world are always determined by a cause. But in the universe there are independent causal chains. If at a given point in time and space, two of these chains have a common link, this coincidence constitutes the fortuitous character of the event thus engendered. Consequently, there would be an objective chance occurrence that would nevertheless have a cause. This seeming paradox would be no reflection of our ignorance.

More than for his mathematical originality, Cournot is known for his views on scientific knowledge. He defined science as logically organized knowledge, comprising both a classification of the objects with which it deals and an ordered concatenation of the propositions it sets forth. Even though establishing himself as forerunner of a completely modern structural concept of the scientific object, Cournot did not go so far as to propose a reduction of the process of knowledge to the application of logical rules.

## Religion

Cournot's religious opinions seem to have been very conservative.

## Politics

In politics Cournot was an enthusiastic royalist in 1815, only to be disappointed by the restoration of the monarchy. In the presidential elections following the 1848 Revolution, he voted for Louis Eugène Cavaignac, a moderate republican. In 1851, sharply disapproving the organization of public instruction as directed by Louis Napoleon, he decided to become a candidate in the legislative elections in Haute-Saône; this election, however, was prevented by the coup d’état of 2 December.

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Personality

In the course of his long career as administrator, Cournot, who was extremely scrupulous in fulfilling his duties, was able to exert a strong influence on the teaching of mathematics in the secondary schools and published a work on the institution of public instruction in France (1864).

Unassuming and shy, Cournot was considered an exemplary civil servant by his contemporaries.

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Connections

In September 1838, Cournot married, thought the name of his wife is not known.