让·勒朗·达朗贝尔Jean Le Rond d'Alembert

让·勒朗·达朗贝尔 的父亲是一名炮兵军官，路易-夏尔·艾蒂安·路易·加缪 德图什，他的母亲是德唐辛夫人。她曾是一名修女，但在1714年获得了教皇的豁免，允许她开始 [4]：-

……一段辉煌的社交生涯，其中政治阴谋和爱情纠葛争夺首位；及时参与著名的 弗瑞兹·约翰 法律计划使她能够在完全财务安全的情况下追求这些活动。

[约翰 法律是一位苏格兰货币改革家，他于1716年在巴黎创办了一家银行，有权发行纸币。起初非常成功，正是德唐辛夫人赚钱的时候，但在1720年崩溃了。]

德达朗贝尔是德唐辛夫人一段风流韵事所生的私生子。他的父亲路易-加缪·德图什在达朗贝尔出生时不在国内，他的母亲把刚出生的孩子放在圣达朗贝尔勒达朗贝尔教堂的台阶上。孩子很快被发现并送到无家可归儿童收容所。他受洗时取名达朗贝尔勒达朗贝尔，以发现他的台阶所在的那座教堂命名。

当他的父亲回到巴黎时，他与年幼的儿子取得了联系，并安排由玻璃匠的妻子Mme Rousseau照顾他。在他自己眼中，她永远是达朗贝尔的母亲，特别是因为他的亲生母亲从未承认他是她的儿子，他一直住在Mme Rousseau的房子里直到中年。

达朗贝尔上的第一所学校是一所私立学校，他的教育由他的父亲安排。他的父亲于1726年去世，当时达朗贝尔九岁，他给他留下了刚好足够给他安全感的钱。德图什家族继续照顾达朗贝尔的教育，他们安排他进入詹森派的四国学院。他以达朗贝尔-巴蒂斯特·达朗贝尔的名字注册，但很快改名为达朗贝尔。

Collège des Quatre Nations是达朗贝尔学习数学的绝佳场所，尽管课程是初级的。由Carron教授讲授的数学课程基于皮埃尔·伐里农的讲座，达朗贝尔能够利用学院优秀的数学图书馆。除了数学训练，他在学院还了解了勒内·笛卡儿的物理思想，但当他后来形成自己的思想时，他对勒内·笛卡儿的观点几乎没有尊重。

Jansenist Collège des Quatre Nations的主要目标是培养能够成为神学专家并论证Jansenist反对Jesuits的学者。然而，达朗贝尔在学院对神学研究失去了兴趣。1735年毕业后，他决定从事法律职业，但他真正的热情是数学，他继续在业余时间研究这个主题。1738年，达朗贝尔取得了律师资格，但他似乎已经决定这不是他的职业。第二年，达朗贝尔学习了医学，但这是他发现比神学更糟糕的科目。在他学习的所有科目中，他真正热衷的是数学，他在这方面的进步相当显著，特别是考虑到他几乎完全自学，而且在他本应为其他资格学习的时候。

1739年7月，达朗贝尔向巴黎科学院宣读了他的第一篇论文，内容是关于他在Reyneau的标准教材Analyse démontréeⓉ（《分析论证》）中发现的一些错误，这些错误并不十分重要，但标志着他数学生涯的开端。1740年，他提交了第二篇关于流体力学的工作，受到了亚历克西斯·克劳德·克莱罗的赞扬。1741年5月，凭借这些工作以及关于积分学的论文，达朗贝尔被接纳为巴黎科学院成员。他接连提交了三次申请均未成功，之后才获得任命，这需要他下相当大的决心。

在讨论达朗贝尔的贡献之前，先讨论一下他的个性是有益的，因为这对他的科学工作的发展方式产生了重大影响。从某种意义上说，达朗贝尔的一生平淡无奇。他很少旅行，一生都在巴黎科学院和法国科学院工作。从另一个层面看，他的一生充满戏剧性，因为他几乎与身边的每一个人都发生过争论。正如[5]中所说：——

达朗贝尔总是被争议所包围。……他是一根避雷针，从所有哲学家的敌人那里引来火花。……不幸的是，他把这种……好斗带入了他的科学研究中，一旦卷入争议，他便以活力和固执为自己的事业辩护。他对可能出错的可能性闭目塞听……

尽管有与周围所有人争吵的倾向，他的贡献确实非常杰出。德达朗贝尔通过在他1743年出版的Traité de dynamiqueⓉ（《动力学论》）中改进艾萨克·牛顿对力的定义，帮助解决了数学物理中关于动能守恒的争议。这部著作还包含了达朗贝尔的力学原理。这是一部重要著作，其序言包含了达朗贝尔对为力学奠定坚实基础的尝试的明确陈述。在[5]中，达朗贝尔在这篇序言中提出的思想被描述为：——

……达朗贝尔是一位数学家，不是物理学家，他认为力学和几何学或代数学一样，都是数学的一部分。理性力学是一门基于简单必然原理的科学，所有具体现象都可以通过严格的数学方法从中推导出来。……达朗贝尔认为力学应该成为一个完全理性主义的数学体系。

D'达朗贝尔在1742年末开始向科学院宣读他的Traité de dynamique的部分内容，但不久之后亚历克西斯·克劳德·克莱罗开始向科学院宣读他自己关于动力学的工作。显然，竞争很快出现，达朗贝尔停止向科学院宣读该工作，并匆忙将该论著付印。这两位数学家得出了相似的想法，事实上，这种竞争在接下来的几年里变得严重得多。

D'达朗贝尔明确表明了他的立场，即他认为力学基于形而上学原理，而非实验证据。他在阅读艾萨克·牛顿的Principia时似乎没有意识到，艾萨克·牛顿的运动定律在多大程度上基于实验证据。对达朗贝尔来说，这些运动定律是逻辑必然。

1744年，达朗贝尔将其结果应用于流体的平衡和运动，并出版了Traité de l'équilibre et du mouvement des fluidesⓉ（《流体平衡与运动论》）。这部著作给出了与丹尼尔·伯努利所出版的流体处理不同的另一种处理方式。D'达朗贝尔认为这是一种更好的方法，当然，正如人们可能预料的那样，丹尼尔·伯努利并不认同这一观点。

达朗贝尔在巴黎科学院变得不快乐，几乎可以肯定是因为他与亚历克西斯·克劳德·克莱罗的竞争以及与他人的分歧。1745年，当皮埃尔·莫佩尔蒂离开巴黎去担任柏林科学院负责人一职时，他的处境变得更加不快乐，当时莱昂哈德·欧拉正在那里工作。

大约在1746年，达朗贝尔的生活发生了相当突然的变化。这在[4]中描述如下：——

直到[1746年]，他一直满足于在其养母家中过着隐居但思维活跃的生活。1746年，他被介绍给Geoffrin夫人，这位富有、专横、缺乏学识但慷慨的沙龙创始人，达朗贝尔突然被邀请参加她的沙龙。他很快进入了一种社交生活，令人惊讶的是，他在其中开始享有巨大的成功和声望。

大约在同一时期，达朗贝尔开始参与一个重大项目，即与Diderot一起编辑Encyclopédie。他签约担任编辑，负责数学和物理天文学，但他的工作涵盖了更广泛的领域。当第一卷于1751年出版时，其中包含一篇由达朗贝尔撰写的序言，该序言被广泛誉为天才之作。布丰说：——

这是人类知识的精华……

达朗贝尔为Encyclopédie工作了许多年。事实上，这部28卷著作中的大部分数学文章都是他写的。然而，他在为Encyclopédie工作的同时继续着自己的数学工作。他是偏微分方程研究的先驱，并开创了它们在物理学中的应用。他关于这一主题的工作最早出现在他为1747年柏林科学院Réflexions sur la cause générale des ventsⓉ（《关于风的普遍原因的思考》）的征文而提交的一篇文章中，他确实赢得了该奖。然而，莱昂哈德·欧拉看到了达朗贝尔所引入的方法的力量，并很快将这些方法发展得远远超过了达朗贝尔。事实上，达朗贝尔关于风的这项工作存在一个缺陷，这一缺陷是他所有工作的典型特征，即它在数学上非常严谨，但所依据的物理证据却相当薄弱。例如，在这种情况下，达朗贝尔假设风是由潮汐对大气的作用产生的，而大气的加热只起了很小的作用。亚历克西斯·克劳德·克莱罗攻击了达朗贝尔的方法[5]：-

为了避免精细的实验或漫长乏味的计算，为了代之以麻烦较少的分析方法，他们常常提出自然界中并不存在的假设；他们追求与目标无关的理论，而只要在实施一种极其简单的方法时稍加坚持，就必定能达到目标。

达朗贝尔与亚历克西斯·克劳德·克莱罗之间的一场激烈争论，导致这两位优秀的数学家在当时的科学期刊上互相辱骂。

1747年对达朗贝尔来说是重要的一年，因为那一年他的第二部重要著作问世，即他关于振动弦的文章。这篇文章首次在印刷品中出现了波动方程，但同样存在缺陷，即他使用了某些boundary conditions在数学上令人愉悦的简化，导致结果与观察不符。

莱昂哈德·欧拉大约在1743年通过丹尼尔·伯努利的来信得知了达朗贝尔的工作。然而，丹尼尔·伯努利在阅读了他的Traité de l'équilibre et du mouvement des fluides Ⓣ（关于流体的平衡和运动的论文）后，由于我们上面提到的原因，对达朗贝尔变得非常挑剔。当达朗贝尔凭借他关于风的论文赢得柏林科学院的奖项时，他创作了一部莱昂哈德·欧拉认为优于丹尼尔·伯努利的作品。当然，此时莱昂哈德·欧拉和达朗贝尔与莱昂哈德·欧拉关系非常好，高度尊重达朗贝尔的工作，两人就许多共同感兴趣的话题通信。

然而，在涉及约翰·萨穆埃尔·柯尼希的柏林科学院争论于1751年开始后，莱昂哈德·欧拉和达朗贝尔之间的关系很快恶化。1752年，当达朗贝尔被邀请成为柏林科学院的主席时，情况变得更加相关。达朗贝尔对莱昂哈德·欧拉感到愤怒的另一个原因是他觉得莱昂哈德·欧拉在窃取他的想法，没有给予他应有的荣誉。从某种意义上说，达朗贝尔是有道理的，但另一方面，他的工作通常如此混乱，以至于莱昂哈德·欧拉无法理解，只能从头开始来澄清正在解决的问题。

Paris Academy不是达朗贝尔在与那里同事闹翻后发表文章的地方，他在1750年代将他的数学论文寄给了柏林科学院。然而，莱昂哈德·欧拉不愿意发表这些作品，达朗贝尔停止发表他的数学文章，将它们收集起来并出版为Opuscules mathématiques Ⓣ（数学小册子），于1761年至1780年间出版了八卷。

普鲁士国王腓特烈二世再次试图说服达朗贝尔接受柏林科学院院长一职。莱昂哈德·欧拉对此强烈反对，并写信给约瑟夫·拉格朗日（见[5]）：-

……达朗贝尔试图用各种吹毛求疵来贬低[我对振动弦问题的解答]，而唯一的理由就是他自己没有得出这个解答。……他以为凭自己的雄辩就能欺骗半吊子学者。……他想在我们的期刊上发表的不是一个证明，而只是宣称我的解答有缺陷的赤裸裸的断言。……由此你可以判断，如果他成为我们的院长，他会掀起怎样的轩然大波。

然而莱昂哈德·欧拉不必担心，因为达朗贝尔于1764年拜访了腓特烈二世三个月，再次拒绝了院长一职的邀请，并试图说服腓特烈二世让莱昂哈德·欧拉担任院长。这并不是达朗贝尔拒绝的唯一邀请。他还拒绝了叶卡捷琳娜二世邀请他去俄国担任她儿子家庭教师的邀请。

D'达朗贝尔 对数学还做出了我们尚未提及的其他重要贡献。在1754年发表于Encyclopédie第4卷的一篇题为Différentiel的文章中，他提出应当把极限理论建立在牢固的基础之上。他是最早理解函数重要性的人之一，并在这篇文章中把函数的导数定义为增量之商的极限。他在极限方面的思想使他得出了收敛性判别法，即今天所称的达朗贝尔比值判别法，它出现在Opuscules mathématiques第5卷Ⓣ（数学小册子）中。

在他生命的后期，达朗贝尔更多地转向了文学和哲学。D'达朗贝尔的哲学著作主要出现在五卷本著作Mélanges de littérature et de philosophie Ⓣ（文学与哲学的混合物）中，该书于1753年至1767年间问世。在这部著作中，他阐述了对形而上学问题的怀疑论。他接受支持上帝存在的论证，其依据是认为智慧不可能仅仅是物质的产物。然而，尽管他在书中持这种公开观点，来自他朋友的证据表明，在1770年之前，他被狄德罗说服转向了唯物主义。

达朗贝尔于1754年11月28日当选为法兰西科学院院士。1772年，他当选为法兰西科学院终身秘书，并花费大量时间为该科学院撰写讣告[1]：-

他成为该科学院最有影响力的成员，但尽管他努力，该机构在他的主导时期未能产生任何值得注意的文学作品。

达朗贝尔从1765年起，在一次疾病发作后抱怨他的头脑不再能够专注于数学。1777年，在给约瑟夫·拉格朗日的一封信中，他表达了他对此的遗憾：-

最让我烦恼的是，几何学，这是唯一真正让我感兴趣的工作，却是我无法做的事情。我在文学方面所做的一切，尽管在法兰西科学院的公开会议上很受欢迎，但对我来说只是填补时间的方式，因为没有更好的事情可做。

他多年来健康状况不佳，他的死亡是膀胱疾病的结果。作为一个已知的不信者，达朗贝尔被埋葬在一个普通的无标记坟墓中。

Jean d'Alembert's father was an artillery officer, Louis-Camus Destouches and his mother was Mme de Tencin. She had been a nun but had received a papal dispensation in 1714 which allowed her to begin [4]:-

... a brilliant social career in which political intrigues and amorous liaisons contended for first place; a timely participation in the famous John Law Scheme allowed her to pursue these activities in complete financial security.

[John Law was a Scottish monetary reformer who founded a bank in Paris in 1716 with authority to issue notes. It was highly successful at first, the time when Mme de Tencin made her money, but collapsed in 1720.]

D'Alembert was the illegitimate son from one of Mme de Tencin 'amorous liaisons'. His father, Louis-Camus Destouches, was out of the country at the time of d'Alembert's birth and his mother left the newly born child on the steps of the church of St Jean Le Rond. The child was quickly found and taken to a home for homeless children. He was baptised Jean Le Rond, named after the church on whose steps he had been found.

When his father returned to Paris he made contact with his young son and arranged for him to be cared for by the wife of a glazier, Mme Rousseau. She would always be d'Alembert's mother in his own eyes, particularly since his real mother never recognised him as her son, and he lived in Mme Rousseau's house until he was middle-aged.

The first school that d'Alembert attended was a private school, his education being arranged by his father. His father died in 1726 when d'Alembert was nine years old and he left him just enough money to give him security. The Destouches family continued to look after d'Alembert's education and they arranged for him to enter the Jansenist Collège des Quatre Nations. He enrolled in the name of Jean-Baptiste Daremberg but soon changed his name to Jean d'Alembert.

The Collège des Quatre Nations was an excellent place for d'Alembert to study mathematics even though the course was elementary. The mathematics course, given by Professor Carron, was based on Varignon's lectures and d'Alembert was able to make use of the excellent mathematics library at the Collège. As well as the mathematical training, he learnt about Descartes' physical ideas at the Collège but, when he formed his own ideas later in his life, he would have little respect for the views of Descartes.

The main aim of the Jansenist Collège des Quatre Nations was to produce scholars who could become experts in theology and argue the Jansenist case against the Jesuits. However, d'Alembert was turned off the study of theology at the Collège. After graduating in 1735 he decided that he would make a career in law but his real passion was for mathematics and he continued to work in his spare time on that subject. In 1738 d'Alembert qualified as an advocate but he seems to have decided that this was not the career for him. The following year d'Alembert studied medicine but this was a topic that he found even worse than theology. Of all the topics he had studied the one that he had real enthusiasm for was mathematics and his progress in this was quite remarkable, particularly given that he had studied almost exclusively on his own and at a time when he was supposed to be studying for other qualifications.

In July 1739 d'Alembert read his first paper to the Paris Academy of Science on some errors he had found in Reyneau's standard text Analyse démontrée Ⓣ which were not of great significance but marked the start of his mathematical career. In 1740 he submitted a second work on the mechanics of fluids which was praised by Clairaut. In May 1741 d'Alembert was admitted to the Paris Academy of Science, on the strength of these and papers on the integral calculus. It took some determination on his part, submitting three unsuccessful applications in quick succession, before his appointment.

Before discussing d'Alembert's contributions it is useful to discuss his personality, which was to have a major effect on the way his scientific work was to develop. In one sense d'Alembert's life was uneventful. He travelled little and worked at the Paris Academy of Science and the French Academy all his life. On another level his life was one of great drama as he argued with almost everyone around him. As stated in [5]:-

D'Alembert was always surrounded by controversy. ... he was a lightning rod which drew sparks from all the foes of the philosophes. ... Unfortunately he carried this... pugnacity into his scientific research and once he had entered a controversy, he argued his cause with vigour and stubbornness. He closed his mind to the possibility that he might be wrong...

Despite this tendency to quarrel with all around him, his contributions were truly outstanding. D'Alembert helped to resolve the controversy in mathematical physics over the conservation of kinetic energy by improving Newton's definition of force in his Traité de dynamique Ⓣ which he published in 1743. This also contains d'Alembert's principle of mechanics. This is an important work and the preface contains a clear statement by d'Alembert of an attempt to lay a firm foundation for mechanics. In [5] d'Alembert's ideas, as presented in this preface, are described:-

... d'Alembert was a mathematician, not a physicist, and he believed mechanics was just as much a part of mathematics as geometry or algebra. Rational mechanics was a science based on simple necessary principles from which all particular phenomenon could be deduced by rigorous mathematical methods. ... d'Alembert thought mechanics should be made into a completely rationalistic mathematical system.

D'Alembert had begun to read parts of his Traité de dynamique to the Academy in late 1742 but soon afterwards Clairaut began to read his own work on dynamics to the Academy. Clearly a rivalry quickly sprung up and d'Alembert stopped reading the work to the Academy and rushed into print with the treatise. The two mathematicians had come up with similar ideas and indeed the rivalry was to become considerably worse in the next few years.

D'Alembert stated his position clearly that he believed mechanics to be based on metaphysical principles and not on experimental evidence. He seems not to have realised in his reading of Newton's Principia how strongly Newton based his laws of motion on experimental evidence. For d'Alembert these laws of motion were logical necessities.

In 1744 d'Alembert applied his results to the equilibrium and motion of fluids and published Traité de l'équilibre et du mouvement des fluides Ⓣ. This work gave an alternative treatment of fluids to the one published by Daniel Bernoulli. D'Alembert thought it a better approach, of course, as one might expect, Daniel Bernoulli did not share this view.

D'Alembert became unhappy at the Paris Academy, almost certainly because of his rivalry with Clairaut and disagreements with others. His position became even less happy in 1745 when Maupertuis left Paris to take up the post of head of the Berlin Academy where, at that time, Euler was working.

In around 1746 d'Alembert's life took a rather sudden change. This is described in [4] as follows:-

Until [1746] he had been satisfied to lead a retired but mentally active existence at the house of his foster-mother. In 1746 he was introduced to Mme Geoffrin, the rich, imperious, unintellectual but generous founder of a salon to which d'Alembert was suddenly invited. He soon entered a social life in which, surprisingly enough, he began to enjoy great success and popularity.

Around the same time d'Alembert began to become involved in a major project, namely editing the Encyclopédie with Diderot. He was contracted as an editor to cover mathematics and physical astronomy but his work covered a wider field. When the first volume appeared in 1751 it contained a Preface written by d'Alembert which was widely acclaimed as a work of great genius. Buffon said that:-

It is the quintessence of human knowledge...

D'Alembert worked on the Encyclopédie for many years. In fact he wrote most of the mathematical articles in this 28 volume work. However, he continued his mathematical work while working on the Encyclopédie. He was a pioneer in the study of partial differential equations and he pioneered their use in physics. His work on this topic first appeared in an article which he submitted for the 1747 prize of the Berlin Academy Réflexions sur la cause générale des vents Ⓣ which indeed he won the prize. Euler, however, saw the power of the methods introduced by d'Alembert and soon developed these far further than had d'Alembert. In fact this work by d'Alembert on the winds suffers from a defect which was typical of all of his work, namely it was mathematically very sound but was based on rather poor physical evidence. In this case, for example, d'Alembert assumed that the winds were generated by tidal effects on the atmosphere and heating of the atmosphere played only a very minor role. Clairaut attacked d'Alembert's methods [5]:-

In order to avoid delicate experiments or long tedious calculations, in order to substitute analytical methods which cost them less trouble, they often make hypotheses which have no place in nature; they pursue theories that are foreign to their object, whereas a little constancy in the execution of a perfectly simple method would have surely brought them to their goal.

A heated argument between d'Alembert and Clairaut resulted in the two fine mathematicians trading insults in the scientific journals of the day.

The year 1747 was an important one for d'Alembert in that a second important work of his appeared in that year, namely his article on vibrating strings. The article contains the first appearance of the wave equation in print but again suffers from the defect that he used mathematically pleasing simplifications of certain boundary conditions which led to results which were at odds with observation.

Euler had learnt of d'Alembert's work in around 1743 through letters from Daniel Bernoulli. However, Daniel Bernoulli became highly critical of d'Alembert after reading his Traité de l'équilibre et du mouvement des fluides Ⓣ for reasons we noted above. When d'Alembert won the prize of the Berlin Academy of Sciences with his essay on winds he produced a work which Euler considered superior to that of Daniel Bernoulli. Certainly at this time Euler and d'Alembert were on very good terms with Euler having high respect for d'Alembert's work and the two corresponded on many topics of mutual interest.

However relations between Euler and d'Alembert soon took a turn for the worse after the dispute in the Berlin Academy involving Samuel König which began in 1751. The situation became more relevant to d'Alembert in 1752 when he was invited to became President of the Berlin Academy. Another reason for d'Alembert to feel angry with Euler was that he felt that Euler was stealing his ideas and not giving him due credit. In one sense d'Alembert was justified but on the other hand his work was usually so muddled that Euler could not follow it and resorted to starting from scratch to clarify the problem being solved.

The Paris Academy had not been a place for d'Alembert to publish after he fell out with colleagues there and he was sending his mathematical papers to the Berlin Academy during the 1750s. However Euler was unhappy to publish these works and d'Alembert stopped publishing his mathematical articles, collecting them together and publishing them as Opuscules mathématiques Ⓣ which appeared in eight volumes between 1761 and 1780.

Again Frederick II, the King of Prussia, tried to persuade d'Alembert to accept the presidency of the Berlin Academy. Euler was strongly opposed to this and wrote to Lagrange (see [5]):-

... d'Alembert has tried to undermine [my solution to the vibrating strings problem] by various cavils, and that for the sole reason that he did not get it himself. ... He thinks he can deceive the semi-learned by his eloquence. ... He wished to publish in our journal not a proof, but a bare statement that my solution is defective. ... From this you can judge what an uproar he would let loose if he were to become our president.

Euler need not have feared however, for d'Alembert visited Frederick II for three months in 1764, turned down the offer of the presidency again, and tried to persuade Frederick II to made Euler president. This was not the only offer d'Alembert turned down. He also turned down an invitation from Catherine II to go to Russia as a tutor for her son.

D'Alembert made other important contributions to mathematics which we have not yet mentioned. In an article entitled Différentiel in volume 4 of Encyclopédie written in 1754, he suggested that the theory of limits be put on a firm foundation. He was one of the first to understand the importance of functions and, in this article, he defined the derivative of a function as the limit of a quotient of increments. His ideas on limits led him to the test for convergence, known today as d'Alembert's ratio test, which appears in Volume 5 of Opuscules mathématiques Ⓣ.

In the latter part of his life d'Alembert turned more towards literature and philosophy. D'Alembert's philosophical works appear mainly in the five volume work Mélanges de littérature et de philosophie Ⓣ which appeared between 1753 and 1767. In this work he sets out his skepticism concerning metaphysical problems. He accepts the argument in favour of the existence of God, based on the belief that intelligence cannot be a product of matter alone. However, although he took this public view in his books, evidence from his friends showed that he was persuaded by Diderot towards materialism before 1770.

D'Alembert was elected to the French Academy on 28 November 1754. In 1772 he was elected perpetual secretary of the French Academy and spent much time writing obituaries for the academy [1]:-

He became the academy's most influential member, but, in spite of his efforts, that body failed to produce anything noteworthy in the way of literature during his pre-eminence.

D'Alembert complained from 1765, after a bout of illness, that his mind was no longer able to concentrate on mathematics. In 1777, in a letter to Lagrange, he showed how much he regretted this:-

What annoys me the most is the fact that geometry, which is the only occupation that truly interests me, is the one thing that I cannot do. All that I do in literature, although very well received in our public sessions of the French Academy, is for me only a way to fill the time for lack of anything better to do.

He suffered bad health for many years and his death was as the result of a bladder illness. As a known unbeliever, d'Alembert was buried in a common unmarked grave.