安托万·奥古斯丁·古诺Antoine Augustin Cournot

安托万·奥古斯丁·古诺是Claude Agapite 古诺（1760-1842）和Claire Eratif的儿子。他有兄弟姐妹Joseph 古诺，生于1803年但次年去世，Judith Xavière 古诺（1805-1876）和Eugène 古诺（1810-1880）。他的父母似乎对年幼的孩子影响甚微，他与一位叔父、两位未婚姑母以及古诺的祖母Marguerite Josèphe 古诺一起生活。这位叔父对小男孩产生了重大影响。Henry Ludwell Moore（1869-1958）写道[30]：-

这位叔父由耶稣会士教育，在大革命的恐怖岁月及随后的焦虑时期始终忠于他们。他阅读广泛，工作能力极强，自我牺牲的能力更强。为了帮助父亲承担大家庭的重担，他保持未婚，获得了一个公证处的职位——他内心非常厌恶这份工作——并将收入用于家庭支持，以至于到了四十岁，他仍一无所有。

他小时候从家人那里接触到许多不同的政治和宗教观点。例如，与他同住的一位姑母的观点与他最喜欢的叔父完全相反，他还从外祖父那里接收到相反的观点[30]：-

……一位医生，有文学品味且略知世事，[他]在小古诺的某次拜访中建议他日后读一本当时的新书，夏多布里昂的《基督教真谛》Ⓣ。这一建议震惊了那位敬爱的叔父的严肃原则，他不看重当时浪漫的基督教。叔父没有选择那危险的异端，而是为他的被监护人挑选了《耶路撒冷行程》Ⓣ。

古诺在1809年至1816年间就读于格雷中学。他年幼时就对政治表现出兴趣，在深深分裂为保皇派和共和派的法国，他年轻时站在保皇派一边。尽管他在格雷中学的老师是拿破仑的极度狂热支持者，一有机会就向学生宣传拿破仑。他在中学期间广泛阅读，特别是读了：贝尔纳·勒布耶·德·丰特奈尔的Entretiens sur la pluralité des mondesⓉ（1762年），一本解释尼古拉·哥白尼提出的日心模型的科普书；贝尔纳·勒布耶·德·丰特奈尔的Éloges des académiciens de l'Académie royale des sciences morts depuis l'an 1699Ⓣ（1766年）；皮埃尔·西蒙·拉普拉斯的Exposition du système du mondeⓉ（1796年），常被视为继艾萨克·牛顿的Principia Mathematica之后最重要的力学著作；以及安托尼·阿尔诺的Port-Royal Logic，受布莱兹·帕斯卡著作的启发。古诺在[4]中写道：-

……这些书对我后来所有的思想和研究产生了决定性的影响。

离开学校后，他在一家律师事务所工作了四年，但在读了哥特弗里德·威廉·莱布尼茨和萨缪尔·克拉克之间的通信后，他决定进入大学[26]：-

在[古诺的]第十九个年头，大学总监路易·普安索和安德烈泽尔在巡视途中来到贝桑松。古诺曾听说过巴黎高等师范学校的模糊传闻，并决定借此机会从总监们那里了解进入这所著名学校科学系的条件。他匆忙赶到贝桑松，但到达后却羞于接近那些总监，对他们来说他完全是个陌生人，他没有与他们交谈，而是从城里的朋友那里获得了必要的信息。他发现，要进入高等师范学校所期望的系，必须完成一门高等数学的专门课程，而他连足够的初等课程都没有学过。

1820-21学年在贝桑松皇家学院的一门数学预备课程为他进入巴黎高等师范学校做了准备。他在皇家学院由Armand Berroyer（1775-1872）教授数学，Berroyer是皇家学院多年的一位杰出教师，后来于1825年成为格勒诺布尔科学院院长。1821年，古诺开始在巴黎高等师范学校学习。然而，他在那里的时光被打断了，因为高等师范学校于1822年9月6日被Abbé Frayssinous关闭，后者是新任命的法国大学大校长。A J Nichol写道[31]：-

学校在他第一年结束时突然解散。一半学生立即被分配到学校系统中任职；其他人则获得了一笔非常少的临时津贴。古诺发现自己属于后一组，被认为缺乏虔诚。这种怀疑极不公正，因为古诺一直是一个忠诚但不张扬的教会之子。然而，事情的这一转折最终证明是非常有利的。如果当时他被派往农村地区去解释“斜边上的正方形”，他很可能在完全默默无闻中度过余生。事实上，他留在了巴黎，当他的津贴到期时，他找到了工作，担任拿破仑的一位将军，Gouvion Saint-Cyr元帅的秘书。因此，他得以继续在大学学习……

古诺和他的同学兼朋友约翰·彼得·古斯塔夫·勒热纳·狄利克雷一起，在索邦大学由西尔维斯特·佛朗索瓦·拉克鲁瓦和Jean Hachette教授数学。他说这是他一生中最快乐的时光[4]：-

我没有什么要读的，没有什么要写的，没有什么要发现的，没有什么要追求的；我只需倾听和思考：这段时间是我一生中最快乐的。

两位朋友古诺和约翰·彼得·古斯塔夫·勒热纳·狄利克雷会参加科学院的会议，并且特别感兴趣地观察皮埃尔·西蒙·拉普拉斯，这位领先的数学科学家。古诺在[4]中写道：-

[皮埃尔·西蒙·拉普拉斯]有一种非常合理的自豪感，而且还有虚荣心。他看重自己的荣誉和贵族头衔。……我记得在科学院的一次会议上，他和安德烈-马里·安培之间就后者提交的一篇论文进行了讨论。“但是，侯爵先生，”安德烈-马里·安培先生每时每刻都在说，这位大人物似乎觉得这种礼节性套话的重复非常自然。有一天他邀请约瑟夫·拉格朗日共进晚餐：“我要穿上我的参议员长袍吗？”约瑟夫·拉格朗日用一种狡黠的语气问道，除了作为主人的参议员之外，每个人都感受到了其中的恶意。

1823年，古诺成为古维翁·圣西尔元帅的秘书，后者希望有人协助撰写其军事回忆录，同时他也担任其子的家庭教师。对古诺而言，这并非最轻松的差事，因为他在秘书工作和大学学业中都遇到了视力方面的困难。然而，这一安排持续了十年，并使他得以继续从事数学研究，于1829年以学位论文Le mouvement d'un corps rigide soutenu par un plan fixe Ⓣ（《被固定平面支撑的刚体运动》）获得博士学位。西莫恩·德尼·泊松对古诺印象深刻，并于1833年为他在巴黎的科学院谋得一个职位。在此期间，他将约翰·赫歇尔的Treatise on astronomy译成法文；该译本于1834年出版。同样在西莫恩·德尼·泊松的推荐下，古诺于1834年被任命到里昂新设立的分析讲席。在[4]中，他写到了西莫恩·德尼·泊松对其最初几篇力学论文的看法：-

西莫恩·德尼·泊松在其中发现了一种哲学深度——而且，我必须诚实地说，他并非完全错误。此外，从那时起他就预言我会在纯数学思辨领域走得很远，但（正如我一直认为并且从不讳言的那样）在这一点上他错了。

事实上，古诺在提交学位论文之前就已开始发表力学论文。例如Sur le calcul des conditions d'inégalité, annoncé par M. Fourier Ⓣ（《论不等条件的计算，由M. Fourier宣布》）（1826年）、Extension du principe des vitesses virtuelles au cas ou les conditions de liaison du systeme sont exprimées par des inégalités Ⓣ（《将虚速度原理推广到系统连接条件由不等式表示的情形》）（1827年）以及Sur les percussions entre deux corps durs, qui se choquent en plusieurs points Ⓣ（《论在两个以上点相遇的两个硬体之间的碰撞》）（1827年）。最后提到的这篇论文研究了两个刚体在超过六个接触点相互撞击时的碰撞。

1835年10月24日，古诺成为格勒诺布尔的数学教授并任该地校长。他接替了路易·安托万 Stanislas Ferriot（1779-1859），后者本人又接替了曾在贝桑松教授古诺数学的Armand Berroyer。三年后，古诺成为公共教育总监，并于1838年9月10日在弗朗什-孔泰的格雷与Colombe Antoinette Petitguyot结婚；他们有一个儿子，Pierre Cournot（1839-1894）。同年（1838年），他出版了Recherches sur les principes mathématiques de la théorie des richesses Ⓣ（《财富理论的数学原理研究》），其中讨论了数学经济学，特别是供求函数。

你可以在THIS LINK读到古诺序言的英译本。

他还考虑了垄断、双寡头和完全竞争下的均衡条件。他考虑了税收的影响，将其视为生产成本的变化，并讨论了国际贸易问题。他给出了市场的定义，这仍然是经济学中所用定义的基础：-

经济学家所说的市场一词，不是指任何特定的买卖商品的场所，而是指买者和卖者彼此之间自由交往，以致相同商品的价格容易而迅速地趋于相等的任何整个区域。

这项工作使古诺成为数学经济学的先驱，比威廉·斯坦利·杰文斯早25年。威廉·斯坦利·杰文斯在1871年写作 The Theory of Political Economy时尚未看到古诺的工作，但到1879年威廉·斯坦利·杰文斯第二版时，他已读过古诺1838年的书。威廉·斯坦利·杰文斯在第二版序言中写道：-

古诺……[掌握]了关于商品的价格、生产和消费之间关系的已知明显事实，他以一种令人几乎无可挑剔的力量和恰当性，对这些关系进行了分析性和图解式的研究。这项工作必定在该学科的历史上占据显著地位。奇怪的是，竟然要由我这个英国人来发现它的价值。

西莫恩·德尼·泊松，理查·科朗特的好友，于1840年去世。次年，古诺出版了Traité élémentaire de la théorie des fonctions et du calcul infinitésimalⓉ（函数论与无穷小分析初论），其中包括如下献词：——

纪念M 西莫恩·德尼·泊松，法国贵族，Academy of Sciences院士及公共教育皇家委员会成员：感激与虔诚依恋之证。

这本书收录了他1834年在里昂任教授时所讲授的课程。古诺还研究过probability，尽管他为该学科寻求逻辑基础的努力未获成功，但他的工作确实为未来的重要发展开辟了道路。他于1843年出版了Exposition de la théorie des chancesⓉ（概率论浅释），尽管他实际上早在七年前就已基本完成此书。他像西莫恩·德尼·泊松和尼古拉·德·孔多塞一样，将概率应用于法律统计。

我们上文提到过古诺的视力问题，多年来这些问题日益恶化。1844年，他休假一年，前往意大利以期康复。他在罗马逗留了一段时间，并觐见了教皇格里高利十六世，教皇的诙谐和玩笑令古诺感到惊讶。在意大利待了一年后重新履职时，他似乎还能履行自己的职责，但被迫放弃了数学研究[31]：——

他已不可能用眼睛从事任何长时间持续的精细工作。他并未放弃与书籍为伴。秘书们定期为他朗读，每次长达数小时。然而，他始终找不到任何能为他朗读数学的人。那些他曾经通过眼睛如此娴熟地把握其含义与可能性的符号，他再也无法通过耳朵来理解了。

然而，他确实在1847年出版了De l'origine et des limites de la correspondance entre l'algèbre et la géométrieⓉ（论代数与几何之间对应关系的起源与界限）一书。以下引自该著作的一段话，可让人了解其内容：-

但一旦事实被构想出来并在逻辑上加以组合，无论这是如何发生的，为了哲学秩序的完善——或者为了人们对科学体系及其各部分从属关系所必须持有的观念的完善——就有必要立即走向最一般的事实，这些事实包含着特殊事实及其各种联系的理由。没有人不感到，通过比较面积来证明毕达哥拉斯'和泰勒斯'定理——如欧几里得和约瑟夫·拉格朗日在《几何原本》中所给出的那样——扭曲了哲学秩序，尽管它们在逻辑上无可指责。一方面，它们把毕达哥拉斯'定理置于泰勒斯'之前，而后者包含着前者的理由；另一方面，它们把长度之间算术关系的证明从属于面积测量理论，而前者既不应当依赖于对面积的考虑，也不应当依赖于对其度量的考虑。

1854年，他获聘图卢兹科学院院长一职，他拒绝了，但表示愿意去第戎。随后他又获聘第戎科学院院长一职，他接受了。他于1862年退休，前往巴黎，在那里度过了余生。

也许视力并不是古诺放弃数学的唯一原因，因为他显然因自己用数学方法研究经济学未被人采纳而感到悲伤。因此，他出版了Principes de la Théorie des RichesseⓉ（财富理论原理）（1863年）一书，在书中他提出了一种非数学的经济学研究方法。1864年，Anne-Paul-Gabriel-Roger de Fontenay（1809-1891）评述了古诺关于经济学的全部工作，集中于他1838年的著作。这篇评论既有肯定也有批评，并且在许多方面受到古诺1863年那本非数学著作的影响，Roger de Fontenay觉得，那本书表明，就社会经济而言，他不过是个业余经济学家。古诺对这篇评论反应很差，专注于负面方面而忽略了正面方面。他在1877年写道（例如，见[17]）：-

想想我有多倒霉！无论我1838年的著作在没有我干预的情况下本可能多么迟来地被接受，我却在1863年毁掉了它的前景。无论我的代数在事后看来多么站得住脚，据出版商说，我的散文（我羞于承认）却不那么成功。《经济学家杂志》（1864年8月）[Roger de Fontenay的评论]批评我“没有超越⟦N5⟧”，并忽视了过去二十五年许多有能力的经济学家的发现：于是，这个法国正统经济学家中没有人愿意引用的可怜作者，竟被指责没有引用足够多的其他作者。

现在，尽管他没有再出版任何数学著作，古诺确实出版了几本书，如Des institutions d'instruction publique en FranceⓉ（法国公共教育机构）（1864年）、Considérations sur la marche des idées et des événements dans les temps modernesⓉ（关于近代思想与事件进程的思考）（1872年）、Matérialisme, vitalisme, rationalisme: études sur l'emploi des données de la science en philosophieⓉ（唯物主义、活力论、理性主义：关于在哲学中使用科学数据的研究）（1875年）以及Revue sommaire des doctrines économiquesⓉ（经济学说概要）（1877年）。

古诺也因其关于科学知识的观点而闻名。他在Essai sur les fondements de nos connaissances philosophiques et sur les caractères de la critique philosophiqueⓉ（《论我们哲学知识的基础及哲学批判的特征》
）（1851年）中写道：-

……科学知识是伟大成就的标志，并且唯有它真正能够实现累积的、无限追求进步。

关于这部作品的更多信息，包括Essai 的摘录和评论摘录，见THIS LINK。

古诺去世时享年75岁，他被安葬在巴黎的蒙帕纳斯公墓。

我们对古诺的生平了解相当多，因为他写了自传笔记，并以[4]出版。这些笔记如何保存下来并得以出版的故事很有趣。古诺在碎纸片上用微小、几乎难以辨认的字迹写下了他的自传。1859年，他请1856年至1861年间的私人秘书Langeron将他的笔记誊清；他阅读了副本，然后销毁了原始笔记。这份手稿随后被古诺藏了起来，他不想在其有生之年出版。他去世后，他的儿子Pierre Cournot也不认为有必要出版它。他满足于在1880年制作了三份副本，其中只有一份幸存下来，交给了Eugène 古诺，古诺的弟弟。最后，在1913年，古诺的回忆录由Abbé E Paul Bottinelli从这份副本出版，当时这份副本在Antoinette Donnaud手中，她是古诺的侄孙女和教女。1942年6月10日，Mme Bouvier Banguillon née Antoinette Donnaud在Bottinelli 1913年出版的一个版本上添加了手写注释，再次确认了上述细节。

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.