# Antoine Augustin Cournot

### Quick Info

Gray, Haute-Saône, Franche-Comté, France

Paris, France

**Antoine Cournot**was a French mathematician who was a pioneer of mathematical economics.

### Biography

**Augustin Cournot**was the son of Claude Agapite Cournot (1760-1842) and Claire Eratif. He had siblings Joseph Antoine Cournot, who was born in 1803 but died in the following year, Judith Xavière Cournot (1805-1876) and Eugène Cournot (1810-1880). His parents seem to have had little influence on the young child who lived with a paternal uncle, two maiden aunts and Augustin's grandmother Marguerite Josèphe Cournot. This uncle was a major influence on the young boy. Henry Ludwell Moore (1869-1958) writes [30]:-

This uncle was educated by Jesuits, and remained loyal to them throughout the terrible days of the Revolution and the anxious period that followed. He had a varied reading, a great capacity for work, a still greater capacity for self-sacrifice. In order to help his father bear the burdens of a large family, he remained unmarried, obtained an appointment to a notary's office, - work which he heartily disliked, - and devoted the income to the family support, so that at the age of forty he had not a sou to call his own.As a young boy he was presented with many differing political and religious views from his family. For example one of the aunts he lived with had views completely opposed to those of his favourite uncle and he also received opposing views from his maternal grandfather [30]:-

... a physician, with literary tastes and some knowledge of the world, [who] suggested, on one of the visits of the little Augustin, that he should read, later on, a new book of the day, Chateaubriand's 'Le Genie du Christianisme' Ⓣ. The suggestion scandalised the severe principles of the beloved uncle, who set no store by the romantic Christianity of the time. Instead of the dangerous heresy, the uncle selected for his charge the 'Itinéraire de Jerusalem' Ⓣ.Augustin attended the secondary Collège de Gray between the years 1809 and 1816. He showed an interest in politics at a young age and in a France deeply divided between royalists and republicans, he sided with the royalist cause in his youth. This was despite the fact that his teacher at the Collège de Gray was an extremely enthusiastic supporter of Napoleon and took every opportunity to promote Napoleon to his pupils. He read widely while at the Collège, in particular he read: Bernard de Fontenelle's

*Entretiens sur la pluralité des mondes*Ⓣ (1762), a popular science book explaining the heliocentric model presented by Copernicus; Bernard de Fontenelle's

*Éloges des académiciens de l'Académie royale des sciences morts depuis l'an 1699*Ⓣ (1766); Laplace's

*Exposition du système du monde*Ⓣ (1796), often regarded as the most important book on mechanics after Newton's

*Principia Mathematica*; and

*Port-Royal Logic*by Antoine Arnauld inspired by Blaise Pascal's writings. Cournot wrote in [4]:-

... these were the books which had a decisive influence on all my subsequent ideas and studies.After leaving school he spent four years in a lawyer's office but after he had read the correspondence between Gottfried Leibniz and Samuel Clarke he decided to enter university [26]:-

In [Cournot's] nineteenth year, Poinsot and Andrezel, general inspectors of the University, came, in the course of their tour, to Besançon. Cournot had heard vague reports of the École Normale at Paris, and had determined to take this opportunity to find out from the inspectors the conditions of admission to the scientific department of the famous school. He hurried off to Besançon, but upon his arrival he was ashamed to approach the inspectors, to whom he was an entire stranger, and, instead of addressing them, he obtained the necessary information from friends in the town. He found that in order to enter the desired department at the École Normale it was necessary to complete a special course of higher mathematics, whereas he had not had so much as an adequate elementary course.A preliminary course in mathematics at Collège Royal in Besançon in session 1820-21 prepared him for entry to École Normale Supérieur in Paris. He was taught mathematics at the Collège Royal by Armand Berroyer (1775-1872), an outstanding teacher at the Collège for many years, who went on to become rector of the Academy of Grenoble in 1825. In 1821 Cournot began his studies at the École Normale Supérieur in Paris. However his time there was disrupted when the École Normale Supérieur was closed down on 6 September 1822 by the Abbé Frayssinous, the newly appointed grand master of the University of France. A J Nichol writes [31]:-

The school was abruptly disbanded at the end of his first year. Half the students were immediately appointed to positions in the school system; the others were allowed a very small temporary pension. Cournot found himself in the latter group, being considered lacking in piety. The suspicion was most unjust for Cournot was always a loyal, though unostentatious, son of the Church. Nevertheless, this turn in affairs ultimately proved to be a very favourable one. If he had been sent out into the rural districts at this time to explain "the square on the hypotenuse," he probably would have spent the rest of his life in utter obscurity. As it was, he remained in Paris, and, when his pension expired, found employment as secretary to one of the generals of Napoleon, the Marshal Gouvion Saint-Cyr. Thus he was enabled to continue his studies at the University ...Cournot, along with his fellow student and friend Lejeune Dirichlet, was taught mathematics at the Sorbonne by Sylvestre Lacroix and Jean Hachette. He said this was the happiest time of his life [4]:-

I had nothing to read, nothing to compose, nothing find, nothing to aim at; I had only to listen and to think: this time has been the happiest of my life.The two friends Cournot and Dirichlet would attend meetings of the Academy of Sciences and were particularly interested in observing Laplace, the leading mathematical scientist. Cournot wrote in [4]:-

[Laplace] had a very legitimate pride and, moreover, vanity. He valued his honours, and his noble titles. ... I remember a meeting at the Academy where a discussion took place between him and Ampère about a memoir presented by the latter. "But, Monsieur le Marquis," Monsieur Ampère was saying every moment, and the great man seemed to find the repetition of this ceremonial formula quite natural. One day he had invited Lagrange to dinner: "Shall I put on my senator's robe?" asked Lagrange in a sly tone in which everyone felt the malice except the senator who was the host.In 1823 Cournot had became a secretary to Marshal Gouvion Saint-Cyr, who wanted assistance in writing his military memoirs, and also a tutor to his son. This was not the easiest of occupations for Cournot who was finding difficulties with his vision both in his secretarial work and in his university studies. It was an arrangement that lasted for ten years, however, and it allowed him to continue his work in mathematics receiving his doctorate in 1829 for a thesis

*Le mouvement d'un corps rigide soutenu par un plan fixe*Ⓣ. Poisson was impressed with Cournot and, in 1833, he obtained a position for him with the Academy in Paris. During this time he translated John Herschel's

*Treatise on astronomy*into French; it was published in 1834. Again with Poisson's recommendation, Cournot was appointed to a newly created chair in analysis at Lyon in 1834. In [4] he writes of Poisson's opinion of his first papers in mechanics:-

Poisson discovered in them a philosophical depth - and, I must honestly say, he was not altogether wrong. Furthermore, from then he predicted that I would go far in the field of pure mathematical speculation but (as I have always thought and have never hesitated to say) in this he was wrong.In fact Cournot had begun publishing papers on mechanics before he submitted his thesis. For example

*Sur le calcul des conditions d'inégalité, annoncé par M. Fourier*Ⓣ (1826),

*Extension du principe des vitesses virtuelles au cas ou les conditions de liaison du systeme sont exprimées par des inégalités*Ⓣ (1827), and

*Sur les percussions entre deux corps durs, qui se choquent en plusieurs points*Ⓣ (1827). This last mentioned memoir studied the impact between two rigid bodies which strike each other with more than six points of contact.

On 24 October 1835 Cournot became professor of mathematics at Grenoble and rector there. He replaced Louis Antoine Stanislas Ferriot (1779-1859) who had himself replaced Armand Berroyer, who had taught Cournot mathematics at Besançon. Three years later Cournot became inspector general of public education and, on 10 September 1838, he married Colombe Antoinette Petitguyot in Gray, Franche-Comté; they had one son, Pierre Cournot (1839-1894). In this same year (1838) he published

*Recherches sur les principes mathématiques de la théorie des richesses*Ⓣ in which he discussed mathematical economics, in particular supply-and-demand functions.

You can read an English translation of Cournot's Preface at THIS LINK.

He also considered conditions for equilibrium with monopoly, duopoly and perfect competition. He considered the effect of taxes, treated as changes in production costs, and discussed problems of international trade. He gives a definition of a market which is the basis for that still used in economics:-

Economists understand by the term Market, not any particular market place in which things are bought and sold, but the whole of any region in which buyers and sellers are in such free intercourse with one another that the prices of the same goods tend to equality easily and quickly.This work makes Cournot a pioneer of mathematical economics, 25 years before Stanley Jevons. Jevons had not seen Cournot's work when he wrote

*The Theory of Political Economy*in 1871 but by the time of Jevons' second edition in 1879 he had read Cournot's 1838 book. Jevons writes in the Preface to this second edition:-

Cournot ... [took] the palpable facts known concerning the relations of price, production and consumption of commodities, he investigated these relations analytically and diagraphically with a power and felicity which leaves little to be desired. This work must occupy a remarkable position in the history of the subject. It is strange that it should have remained for me among Englishmen to discover its value.Poisson, a good friend of Courant, died in 1840. In the following year Cournot published

*Traité élémentaire de la théorie des fonctions et du calcul infinitésimal*Ⓣ which included the following dedication:-

In memory of M Poisson, peer of France, member of the Academy of Sciences and of the Royal Council of Public Instruction: Testimony of gratitude and pious attachment.This book contained the lectures he had given when professor in Lyons in 1834. Cournot also worked on probability and, although his investigations into a logical foundation for it were unsuccessful, his work did lead the way to future important developments. He published

*Exposition de la théorie des chances*Ⓣ in 1843, although again he had essentially completed it seven years earlier. He, as Poisson and Condorcet did, applied probability to legal statistics.

We mentioned above Cournot's eyesight problems and over the years these became steadily worse. In 1844 he took a year's leave of absence and visited Italy in an effort to recover. Spending some time in Rome, he had an audience with the Pope, Gregory XVI, who surprised Cournot with his joviality and jokes. When he took up his positions again after the year in Italy he seemed able to carry out his duties but was forced to give up mathematical research [31]:-

It became impossible for him to engage in any long-continued close work with his eyes. He did not give up his companionship with books. Secretaries read aloud to him regularly for hours at a time. He never found any one, however, who could read mathematics to him. Symbols, the meaning and possibilities of which he had once grasped so masterfully through the eye, he was never able to comprehend by ear.He did, however, publish the book

*De l'origine et des limites de la correspondance entre l'algèbre et la géométrie*Ⓣ in 1847. Here is a quotation from that work to give an idea of its contents:-

But once the facts have been conceived and logically assembled, however this might have occurred, it is then necessary for the perfection of the philosophical order - or for that of the idea that one has to have of the system of science and of the subordination of its parts, - to go immediately to the most general facts, which contain the reason of the particular facts and of their several connections. There is no one who does not feel that the demonstrations of Pythagoras' and Thales' theorems by means of the comparison of areas - such as those given by Euclid and Lagrange in their 'Elements' - distort the philosophical order, although they are logically irreproachable. On the one hand, they put Pythagoras' theorem before Thales', whereas the latter contains the reason for the former; on the other hand, they subordinate the proof of the arithmetical relations among lengths to the theory of the measurement of areas, while the former relations should depend neither on the consideration of areas, nor on that of their measures.In 1854 he was offered the position of rector of the Academy at Toulouse, which he refused, but said he would go to Dijon. He was then offered the position of rector of the Academy of Dijon which he accepted. He retired in 1862 and went to Paris where he spent the rest of his life.

Perhaps eyesight was not the only reason for Cournot to give up mathematics for he was clearly saddened by the fact that his mathematical approach to economics was not being taken up. He therefore published the book

*Principes de la Théorie des Richesse*Ⓣ (1863) in which he presented a non-mathematical approach to economics. In 1864 Anne-Paul-Gabriel-Roger de Fontenay (1809-1891) reviewed all of Cournot's work on economics concentrating on his 1838 book. The review was partly positive and partly critical and, in many ways, influenced by Cournot's non-mathematics book of 1863 which, Roger de Fontenay felt, showed him to be an amateur economist when it came to social economy. Cournot reacted badly to the review, concentrating on the negative aspects and ignoring the positive ones. He wrote in 1877 (see, for example, [17]):-

Consider my rotten luck! However much my 1838 work might have gained belated acceptance without my interference, I ruined its prospects in 1863. However much my algebra could be defended in retrospect, according to the publisher, my prose (I am ashamed to say) was less successful. The 'Journal des Economistes' (August 1864) [Roger de Fontenay's review] criticised me for "not having advanced beyond Ricardo," and for ignoring the discoveries of many capable economists of the last twenty-five years: thus the wretched author that none of the orthodox French economists wanted to cite was reproached for not having cited enough other authors.Now although he did not publish any further mathematical works, Cournot did publish several books such as

*Des institutions d'instruction publique en France*Ⓣ (1864),

*Considérations sur la marche des idées et des événements dans les temps modernes*Ⓣ (1872),

*Matérialisme, vitalisme, rationalisme: études sur l'emploi des données de la science en philosophie*Ⓣ (1875) and

*Revue sommaire des doctrines économiques*Ⓣ (1877).

Cournot is also well known for his views on scientific knowledge. He wrote in

*Essai sur les fondements de nos connaissances philosophiques et sur les caractères de la critique philosophique*Ⓣ (1851):-

... scientific knowledge is the sign of great achievement and alone is truly capable of cumulative and indefinitely pursued progress.For further information about this work, including extracts from the

*Essai*and extracts from reviews, see THIS LINK.

After Cournot died at the age of 75, he was buried in Cimetière de Montparnasse in Paris.

We know a considerable amount about Cournot's life because of the autobiographical notes he wrote and were published as [4]. The story of how these survived and came to be published is interesting. Cournot wrote his autobiography on scraps of paper, in tiny, barely legible writing. In 1859 he asked Langeron, his private secretary from 1856 to 1861, to make a fair copy of his notes; he read the copy and then destroyed the original notes. This manuscript was then hidden by Cournot, who did not want it to be published during his lifetime. After his death, his son, Pierre Cournot, did not consider it necessary to publish it either. He contented himself with having three copies made in 1880 of which only one survived, given to Eugène Cournot, Augustin Cournot's younger brother. Finally, in 1913, Cournot's memoirs were published by the Abbé E Paul Bottinelli from this copy which was by then in the hands of Antoinette Donnaud, grandniece and goddaughter of Augustin Cournot. On 10 June 1942 Mme Bouvier Banguillon née Antoinette Donnaud added a handwritten note to one of Bottinelli 1913 published versions, confirming again the above details.

### References (show)

- G Granger, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990).

See THIS LINK - Biography in
*Encyclopaedia Britannica*.

http://www.britannica.com/biography/Antoine-Augustin-Cournot - E P Bottinelli,
*A Cournot, métaphysicien de la conaissance*(Paris, 1913). - E P Bottinelli (ed.),
*A A Cournot, Quelques souvenirs de ma famille et de mon temps*(Paris, 1913). - J Brun and A Robinet (eds.),
*A Cournot: études pour le centenaire de sa mort (1877-1977)*(Paris, 1978). - E Callot,
*La philosophie biologique de Cournot*(Paris, 1959). - A A Cournot,
*Oeuvres Complètes*(10 volumes) (Vrin, Paris, 1973-1989). - R Leroux,
*Antoine-Augustin Cournot as a Sociologist*(Springer, New York, 2019). - Th Martin,
*Probabilités et critique philosophique selon*Cournot (Vrin, Paris, 1996). - Th Martin,
*Bibliographique cournotienne*(Annales littéraires de l'Université de Franche-Comté, Besançon, 1998). - G Milhaud,
*Études sur Cournot*(Paris, 1927). - F Vatin,
*Economie politique et économie naturelle chez Antoine-Augustin Cournot*(Presses Universitaires de France-PUF, 1998). - C P Baloglou, Antoine Augustin Cournot, in
*J Backhaus (ed.), Handbook of the History of Economic Thought, The European Heritage in Economics and the Social Sciences***11**(Springer, New York, 2012), 437-463. - A Béraud, Antoine-Augustin Cournot (1801-1877), in
*G Faccarello and H D Kurz (eds.), Handbook of Economic Thought***1**(Edward Elgar Publishing, 2016). - Cournot, Antoine-Augustin (1801-77), in
*E R A Seligman and A Johnson (eds,), The International Encyclopedia of the Social Sciences***3**(The Macmillan Company, New York, 1923), 511-512. - G H Bousquet, Histoire de l'économie mathématique jusqu'à Cournot,
*Metroecon***10**(1958), 121-135. - R B Ekelund, Jr. and R F Hébert, Cournot and His Contemporaries: Is an Obituary the Only Bad Review?,
*Southern Economic Journal***57**(1) (1990), 139-149. - I Fisher, Irving, Cournot and Mathematical Economics, Quarterly Journal of Economics (January 1898), 119-138; 238-244.
- J W Friedman, The legacy of Augustin Cournot,
*Cahiers d'économie politique***37**(2000), 31-46. - R Gary-Bobo, Cournot, A great forerunner of mathematical economics,
*European Economic Review***33**(1989), 515-522. - H Guitton, Cournot, Antoine-Augustin (1801-77), in
*The International Encyclopaedia of the Social Sciences***3**(Macmillan and Free Press, New York, 1968). - H Guitton, Preface, in
*Antoine Augustin Cournot, Recherches sur les principes mathématiques de la théorie des richesses*(Calmann-Lévy, Paris, 1974). - M Hossain and N M Chowdhury,
*Antoine Augustin Cournot: The Pioneer of Modern Economic Ideas*(24 December 2018).

https://mpra.ub.uni-muenchen.de/90829/ - J Magnan de Bornier, Cournot avant Nash: grandeur et mites d'un modèle unitaire de la concurrence,
*Cahiers d'économie politique***37**(2000), 101-125. - P Mancosu, Bolzano and Cournot on mathematical explanation,
*Revue d'histoire des sciences***52**(3/4) (1999), 429-455. - Th Martin, La valeur objective du calcul des probabilités selon Cournot,
*Math. Inform. Sci. Humaines***127**(1994), 5-17. - Th Martin, Probabilités et philosophie des mathématiques chez Cournot,
*Rev. Histoire Math.***1**(1) (1995), 111-138. - Th Martin, Antoine Augustin Cournot, in
*C C Heyde and Seneta (eds.), Statisticians of the Centuries*(Springer Science-Business Media, New York, 2001), 152-156. - H L Moore, Antoine Augustin Cournot,
*Revue de Métaphysique et de Morale***13**(3) (1905), 521-543. - H L Moore, The personality of Antoine Augustin Cournot,
*The Quarterly Journal of Economics***19**(3) (1905), 370-399. - A J Nichol, Tragedies in the Life of Cournot,
*Econometrica***6**(3) (1938), 193-197. - S Pressman, Antoine Augustin Cournot,
*Fifty Major Economists*(Routledge, 2013), 52-57. - M Shubik, Antoine Augustin Cournot, in
*J Eatwell, M Milgate and P Newman (eds.), Game Theory*(Palgrave Macmillan, 1989), 68-69.

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Last Update November 2020