皮埃尔·莫佩尔蒂Pierre-Louis Moreau de Maupertuis

皮埃尔·莫佩尔蒂的父亲M 莫佩尔蒂是商业委员会的成员，他还代表布列塔尼州。他在莫佩尔蒂出生前不久获得了他的头衔，莫佩尔蒂是他的长子。莫佩尔蒂的母亲过度保护，在塑造他的性格方面起了很大作用。皮埃尔·萨米埃尔 Formey在柏林科学院上为莫佩尔蒂写的讣告中写道（例如见[1]）：-

莫佩尔蒂夫人崇拜她的儿子而不是爱他。她无法拒绝他任何事。

这种待遇的一个后果是，莫佩尔蒂的弟弟莫佩尔蒂 de Saint Ellier 非常嫉妒他的哥哥受到比他好得多的待遇，因此他开始憎恨莫佩尔蒂。

1714年，莫佩尔蒂被送到巴黎的马什学院学习。尼古拉斯‧马勒伯朗士六十年前曾在这所著名的学院学习，现在莫佩尔蒂在勒布隆指导下学习哲学。然而，在巴黎两年后，莫佩尔蒂的母亲坚持要他回到圣马洛的家中。他于1717年开始学习音乐，但很快对数学产生了浓厚的兴趣。

海军对莫佩尔蒂来说似乎是一条有吸引力的职业道路，但他的母亲觉得太危险，因此他被禁止选择这条路。他的父亲为他谋得了火枪手团中尉的职位，1718年他加入了驻扎在里尔的拉罗什吉永团。尽管这是当时大多数年轻人只能梦想的职位，但它并不适合莫佩尔蒂。到1722年，他已经放弃了骑兵军官的职业生涯，住在巴黎享受咖啡馆的知识生活。他与剧作家、小说家和记者马里沃、剧作家拉莫特以及数学家约瑟夫Saurin、妮科尔和泰拉松成为朋友。他对数学的早期兴趣现在蓬勃发展，在这些人的指导下学习该学科更高深的内容，他很快获得了深刻的理解。

莫佩尔蒂于1723年成为Académie des Sciences的助理，次年他发表了他的第一篇论文Sur la forme des instruments de musique，研究乐器形状对其所产生音符特性的影响。随后又有更多论文：1726年关于极大值和极小值，1727年关于摆线，以及1727年、1728年和1729年关于曲线的更多论文。然而在此期间，莫佩尔蒂也对生物学感兴趣。他担任博物学家比尼翁的秘书，并撰写了一篇关于蝾螈的重要论文，显示了他作为自然界优秀观察者的才能。1728年，莫佩尔蒂访问了伦敦，在这次短暂访问期间，他当选为皇家学会会士。

为了扩展他的数学和科学知识范围，莫佩尔蒂前往巴塞尔师从约翰·伯努利。他于1729年9月30日在巴塞尔注册入学，并在整个学期住在约翰·伯努利家中。在巴塞尔大学，他接受了出色的教育和训练。他从他的老师约翰·伯努利那里了解到勒内·笛卡儿的太阳系涡旋理论模型以及哥特弗里德·威廉·莱布尼茨的力学观点，约翰·伯努利也许是这些理论最坚定的支持者。然而与此同时，莫佩尔蒂从约翰·伯努利那里了解到艾萨克·牛顿的物理学，约翰·伯努利接受万有引力的结果，但指望哥特弗里德·威廉·莱布尼茨的理论为这些结果提供解释，而艾萨克·牛顿对此完全没有解释。两个物体被真空隔开时，它们如何能相互影响？

1730年7月回到巴黎后，莫佩尔蒂开始撰写力学论文，在其中运用了他已在曲线方面发展出的专长。到1731年，他已写出第一篇天文学论文和另一篇微分方程论文，并迅速赢得了作为全面数学家和科学家的声誉。1732年，他在Philosophical Transactions of the Royal Society of London上发表了一篇论文，讨论旋转体，特别讨论了土星环的性质（他认为那是被捕获的彗星尾巴）以及旋转体所呈现的形状。这是一篇有趣的论文，但其中有一些错误，并表明莫佩尔蒂尚未完全理解艾萨克·牛顿的平方反比定律以及由此在固体内部产生的引力。1732年11月，他通过出版一部重要论著Figures des astres Ⓣ（《恒星的形状》），在法国宣称自己支持艾萨克·牛顿的引力理论。该论著宣告了莫佩尔蒂在当时最大问题之一，即地球形状问题上的立场。

1735年5月，Paris Academy派遣一支远征队前往秘鲁测量地球。这支远征队由夏尔·马里·德·拉孔达米纳率领，成员有皮埃尔·布格和Godin。另一支远征队被派往拉普兰，由莫佩尔蒂率领，同样是为了测量子午线上一个弧度的长度。它于1736年5月2日离开敦刻尔克，科学家亚历克西斯·克劳德·克莱罗和夏尔·艾蒂安·路易·加缪在莫佩尔蒂带领下随行。他们在芬兰北部的托尔尼奥建立基地，尽管夏天受到昆虫袭击，冬天又遭受难以忍受的严寒，他们还是设法完成了测量。返程途中他们在波罗的海遭遇海难，但设法使观测记录完好无损。相当奇怪的是，莫佩尔蒂带回了两个芬兰本地女孩。回到巴黎后，他出席了1737年8月20日的科学院会议，报告他的结果证实地球是扁的。他在11月13日向科学院作了完整报告。

莫佩尔蒂因这次远征而声名鹊起，但他通过发表一些对其对手的恶毒攻击来强固自己的优势，尤其是对雅克·卡西尼的攻击。就连他的朋友也对他表现出的个人怨恨感到震惊。他与亚历克西斯·克劳德·克莱罗和约翰·伯努利的关系在此前不久已经有些破裂。1739年，他与沙特莱侯爵夫人和伏尔泰交好，在他们位于西雷的家中住了一段时间。他试图修复与约翰·伯努利的关系，访问了巴塞尔，并与约翰·伯努利二世日益友好。到1739年底，他已获得一份优厚薪水，从事航海问题研究。

1740年，普鲁士国王腓特烈大帝邀请他前往德国，这是腓特烈将顶尖哲学家和科学家带到柏林的目标的一部分。腓特烈告知莫佩尔蒂，他将建立柏林科学院，并邀请他担任院长。在柏林逗留一段时间，而腓特烈忙于军事事务之后，他于1741年4月随普鲁士军队与国王会合，参加莫尔维茨战役。腓特烈因担心战败而早早离开战场，莫佩尔蒂被奥地利人俘虏。他受到善待，被带到维也纳，但很快获释并返回柏林。到6月，他已回到巴黎，多少因这些经历而受到震动。

回到巴黎后，莫佩尔蒂被任命为Académie des Sciences副院长，次年成为院长。1743年6月27日，他获选进入法兰西学术院。1744年秋，他前往巴塞尔，又从那里前往法国军营，参加弗赖堡围城战。随后他带着法国胜利的消息回到普鲁士，并将消息呈报给腓特烈。Berlin Academy此时正在成形，腓特烈再次敦促莫佩尔蒂担任其首任院长。他决定接受这一职位，并于1745年春返回巴黎处理事务，然后履新。在柏林期间，他已安排与Eleonor Borck结婚，在短暂访问巴黎之后，他于1745年8月25日在柏林与她结婚。

莫佩尔蒂此时已投身柏林，而巴黎科学院在雅克·卡西尼领导的一场反对他的运动之后，于1745年9月取消了他的会员资格。1746年5月12日，莫佩尔蒂被正式任命为柏林科学院院长，这一职位他将担任八年。然而，他的院长任期开局并不顺利，因为6月他的父亲去世，他返回巴黎，一直待到9月。尽管他非常努力地想要成功履行柏林科学院院长的职责，但情况对他相当不利。一方面，他不会说德语，虽然科学院的正式事务用法语或拉丁语进行，但莫佩尔蒂与用德语进行的日常管理相当隔绝。他的另一个问题是，腓特烈希望他的科学院成为世界一流，但他不愿拿出必要的资金来吸引顶尖人才。莫佩尔蒂试图通过任命不在科学院工作的外国科学家为通讯院士来克服这一点。当然，科学院中确实有一位最高水准的人物，即莱昂哈德·欧拉。

莫佩尔蒂发表了许多主题的著作，包括数学、地理学、道德哲学、生物学、天文学和宇宙论。我们在上文已经提到了他的一些贡献，但现在让我们提及其他一些。1745年，一部关于自然史的重要出版物是Vénus physique Ⓣ（尘世的维纳斯），他在其中讨论了胚胎形成的生物学理论。这部著作，以及莫佩尔蒂关于遗传的其他工作，提出了一系列猜想，有些人将其视为进化论的早期版本。事实上，如果他进一步推进这些猜想并将其发展成更完整的理论，他如今可能会被认为提出了进化论的基础。实际情况是，尽管他提出了一个物种发展为另一个物种的机制，但他未能假设出驱动机制，即自然选择。

我们在本文中直到很晚才讨论莫佩尔蒂最为人所知的主题，即最小作用量原理。一个原因是，他确实是在职业生涯的后期才提出这一原理的。那是在1746年，他刚成为柏林科学院院长后不久，首次阐述了Principle of Least Action，四年后他在Essai de cosmologie Ⓣ（论宇宙学）中发表了它。莫佩尔蒂希望这一原理能统一宇宙的定律，并将其与试图证明上帝存在的尝试结合起来。他写道（例如见[1]）：-

由此[从最小作用量原理]推导出的运动定律，被发现与自然界中观察到的完全相同，我们可以赞叹它适用于所有现象，在动物的运动中，在植物的生长中，在天体的运行中：宇宙的景象因此变得更加宏大，更加美丽，更加配得上它的创造者……

这些定律，如此美丽又如此简单，也许是事物的创造者和组织者在物质中建立的唯一定律，用以实现可见世界的一切现象……

将最小作用量原理的讨论留到现在的另一个原因是，它在他生命末期的悲伤事件中起了很大作用。

约翰·萨穆埃尔·柯尼希是一位莫佩尔蒂认识很久的数学家。两人都曾是约翰·伯努利的学生，都教过沙特莱侯爵夫人，都研究过地球的形状，而莫佩尔蒂曾提名约翰·萨穆埃尔·柯尼希竞选柏林科学院。这件奇怪的事始于1751年，当时约翰·萨穆埃尔·柯尼希访问柏林，并给莫佩尔蒂一篇论文以供考虑发表。显然，莫佩尔蒂从未读过它，只是第二天就归还并推荐发表。它确实于1751年3月发表，直到那时莫佩尔蒂才读到它，并发现一方面它论证最小作用量原理是错误的，另一方面它论证哥特弗里德·威廉·莱布尼茨是第一个提出该理论的人。为支持这一主张而提出的证据是1707年哥特弗里德·威廉·莱布尼茨写给Jacob 雅各布·赫尔曼的一封信。

公平地说，此时莫佩尔蒂已有严重的健康问题。而且他对批评从未反应良好，随着健康衰退变得越来越敏感，我们已经描述过许多年前在地球形状的争论中他对对手进行的恶毒人身攻击。然而，也许最相关的是，他觉得最小作用量原理是他最伟大的成就，是他将因此名垂青史的成就。莫佩尔蒂得到了莱昂哈德·欧拉的大力支持，但他利用自己作为科学院院长的职位，让科学院公开宣布约翰·萨穆埃尔·柯尼希伪造了引文。这使得约翰·萨穆埃尔·柯尼希别无选择，只能从科学院辞职。伏尔泰曾一度是莫佩尔蒂的密友，但在这件悲伤的事之前多年，两人已经闹翻。伏尔泰现在利用他高超的文学技巧来诋毁莫佩尔蒂的思想、他的拉普兰之旅，并且他[1]：-

……讽刺了莫佩尔蒂在北方的情色冒险。

弗雷德里克试图支持他科学院的院长，但莫佩尔蒂的健康状况在压力下崩溃，于1753年离开柏林前往巴黎。他在那里待了一年多，弗雷德里克催促他回柏林，声称院长缺席后科学院已失控。莫佩尔蒂于1754年照办，但随后他显然被一个女孩勒索，那女孩声称他是她孩子的父亲。

1756年雅克·卡西尼去世。此后不久，莫佩尔蒂的Académie des Sciences会籍得以续期，他还获得了巴黎科学院颁发的年金。他于1756年7月返回巴黎，但到9月时已回到家乡圣马洛。因健康原因，有人建议他去意大利旅行，他便于1757年6月启程。此时法国人正与普鲁士人交战，他的处境变得更加艰难。他在波尔多逗留了七个月，最终于1758年10月抵达巴塞尔，在那里他做客于约翰·伯努利家中。到次年夏天，他意识到自己的生命即将走到尽头，他的妻子便启程前往巴塞尔与他相聚。她尚未抵达巴塞尔，他便去世了，被安葬在多纳赫。

Beeson写道[4]：-

他所做的大部分工作的辉煌，因他倾向于留下未完成的工作、未能意识到自己的潜力而受到削弱：正是天才的洞察力引导他得出最小作用量原理，但缺乏智力上的精力或严谨性，使他未能为其提供约瑟夫·拉格朗日将会提供的数学基础。……他在遗传学、在理解物种发展的机制方面，甚至在免疫学方面，都展现出非凡的洞察力，但没有完全阐发的理论。他的哲学著作最为引人入胜：大胆、激动人心、论证充分。

Pierre-Louis Moreau de Maupertuis's father, M Moreau, was a member of the Council of Commerce and he also represented the state of Brittany. He had received his title shortly before the birth of Pierre-Louis who was his eldest son. Pierre-Louis's mother played a large part in forming his character by being excessively protective. Samuel Formey, in his obituary of Maupertuis for the Berlin Academy, wrote (see for example [1]):-

Madame Moreau idolized her son rather than loved him. She could not refuse him anything.

One effect of this treatment was that Maupertuis' younger brother, Moreau de Saint Ellier, was very jealous of the fact that his older brother was treated so much more favourably than he was, and he came to hate Maupertuis because of this.

In 1714 Maupertuis was sent to study at the Collège de la Marche in Paris. Malebranche had studied at this famous college sixty years earlier and now Maupertuis studied philosophy under Le Blond. After two years in Paris, however, Maupertuis' mother insisted that he come home to Saint Malo. He began to study music in 1717 but soon he developed a strong interest in mathematics.

The navy seemed like an attractive career to Maupertuis but his mother felt it was too dangerous so he was forbidden from pursuing this choice. His father was able to obtain for him the position of lieutenant in the Musketeers and in 1718 he joined the regiment of La Roche Guyon stationed at Lille. Although this was the sort of position that most young men of the time could only dream about, it did not suit Maupertuis. By 1722 he had given up his career as a cavalry officer and was living in Paris enjoying the intellectual life of the cafés. He became friendly with the dramatist, novelist and journalist Marivaux, the playwright La Motte, and mathematicians Joseph Saurin, Nicole, and Terrasson. His early interest in mathematics now blossomed and, with instruction in the higher reaches of the subject from these men, he soon acquired a deep understanding.

Maupertuis became an adjoint in the Académie des Sciences in 1723 and in the following year he produced his first paper Sur la forme des instruments de musique which studied the effect of the shape of an instrument on the characteristics of the note it produced. Further papers followed: on maxima and minima in 1726, on the cycloid in 1727, and further papers on curves in 1727, 1728 and 1729. During this period, however, Maupertuis was also interested in biology. He acted as secretary to the naturalist Bignon and wrote an important paper on the salamander which shows his talents as an excellent observer of the natural world. In 1728 Maupertuis visited London and during this short visit he was elected a Fellow of the Royal Society.

In order to extend the range of his mathematical and scientific knowledge Maupertuis went to Basle to study under Johann Bernoulli. He matriculated in Basle on 30 September 1729 and spent the session living in Johann Bernoulli's home. At the University of Basle he received an outstanding education and training. He learnt of Descartes' vortex theory model of the solar system and of Leibniz's views on mechanics from his teacher Johann Bernoulli who was perhaps the strongest supporter of these theories. At the same time, however, Maupertuis learnt of Newton's physics from Johann Bernoulli who accepted the results of universal gravitation but looked towards Leibniz's theories to provide an explanation for them which Newton left completely unexplained. How could two bodies effect each other when separated by a vacuum?

Back in Paris by July of 1730, Maupertuis began writing papers on mechanics in which he used the expertise he had already developed on curves. By 1731 he had written his first paper on astronomy and another on differential equations, and was rapidly developing a reputation as an all round mathematician and scientist. In 1732 he published a paper in the Philosophical Transactions of the Royal Society of London which treated rotating bodies, discussing in particular the nature of Saturn's rings (which he believed to be the captured tail of a comet) and the shape that a rotating body assumes. It is an interesting paper but it contains some errors and shows that Maupertuis has not fully understood Newton's inverse square law and the resulting gravitational force within a solid body. In November 1732 he declared himself a supporter of Newton's theory of gravitation in France with his publication of a major treatise Figures des astres Ⓣ. It announced Maupertuis's position on one of the biggest problems of the day, namely the shape of the Earth.

In May 1735 the Paris Academy sent an expedition to Peru to make measurements of the Earth. It was headed by La Condamine and had Bouguer and Godin as members. A second expedition was sent to Lapland headed by Maupertuis, also to measure the length of a degree along the meridian. It left Dunkirk on 2 May 1736 with the scientists Clairaut and Camus under Maupertuis. They set up base in Tornio in northern Finland and managed to make their measurements despite the problems of being attacked by insects in summer and suffering unbearably cold weather during the winter. They were shipwrecked in the Baltic on their return journey but managed to keep the records of their observations undamaged. Rather strangely Maupertuis brought back with him two native girls from Finland. Back in Paris he attended the meeting of the Academy on 20 August 1737, reporting that his results confirmed that the Earth was oblate. He made a full report to the Academy on 13 November.

Maupertuis gained fame from this expedition but he forced home his advantage by publishing some vicious attacks on his opponents, in particular on Jacques Cassini. Even his friends were shocked at the personal venom he displayed. His relations with Clairaut and Johann Bernoulli had broken down a little while before. In 1739 he became friendly with du Châtelet and Voltaire spending some time living at their home at Cirey. He tried to patch up relations with Johann Bernoulli, visiting Basle, and became increasing friendly with Johann(II) Bernoulli. By the end of 1739 he had been awarded a good salary to work on problems of navigation.

He was invited to Germany by King Frederick the Great in 1740 as part of Frederick's aim of bringing top philosophers and scientists to Berlin. Frederick informed Maupertuis that he was going to set up the Berlin Academy and invited him to be its president. After staying a while in Berlin while Frederick occupied himself with military matters, he joined the King with the Prussian army at the battle of Mollwitz in April 1741. Frederick left the field early, fearing defeat, and Maupertuis was taken prisoner by the Austrians. He was treated kindly, taken to Vienna, but soon released and returned to Berlin. By June he was back in Paris, somewhat shaken by his experiences.

Back in Paris, Maupertuis was appointed assistant director of the Académie des Sciences and in the following year be became its director. On 27 June 1743 he was admitted to the Académie Française. In the autumn of 1744 he went to Basle, and from there he went to the French camp at the siege of Freiburg im Breisgau. He then went back to Prussia taking with him news of the French victory which he delivered to Frederick. The Berlin Academy was now taking shape and Frederick again pressed Maupertuis to become its first president. He decided to accept the position and returned to Paris in the spring of 1745 to tidy up his affairs before taking up his new role. While in Berlin he had arranged a marriage to Eleonor Borck and, after his brief visit to Paris, he married her in Berlin on 25 August 1745.

Maupertuis had now committed himself to Berlin, and the Paris Academy cancelled his membership in September 1745 after a campaign against him led by Jacques Cassini. On 12 May 1746 Maupertuis was officially appointed as president of the Berlin Academy, a post which he was to hold for eight years. His presidency did not get off to a good start, however, for in June his father died and he returned to Paris, remaining there until September. Although he tried very hard to make a success of his role as president of the Berlin Academy, things were rather against him. On the one hand he did not speak German, and although the official business of the Academy was conducted in French or Latin, Maupertuis was rather cut off from the day to day administration which was conducted in German. His other problem was that Frederick wanted his Academy to be world class, but he was not prepared to put up the necessary funds to attract the top people. Maupertuis tried to overcome this by making appointments of foreigner scientists as associate members who did not work at the Academy. Of course the Academy did contain one person of the very highest calibre, namely Euler.

Maupertuis published on many topics including mathematics, geography, moral philosophy, biology, astronomy and cosmology. We have mentioned some of his contributions above, but let us now mention some others. One important publication on natural history was Vénus physique Ⓣ in 1745 in which he discussed the biological theory of the formation of the embryo. This work, and other work by Maupertuis on heredity, proposed a series of conjectures which some see as an early version of the theory of evolution. Indeed if he had taken his conjectures forward and developed them into a more fully formed theory he might now be recognised as putting forward the foundations of the theory of evolution. As it was, although he put forward the mechanism for one species developing into another, he failed to postulate the driving mechanism, namely natural selection.

We have left until late in this article a discussion of the topic for which Maupertuis is best known, namely the Principle of Least Action. One reason is that indeed it was late in his career that he proposed the principle. It was in 1746, soon after becoming director of the Berlin Academy, that he first enunciated the Principle of Least Action and it was four years later that he published it in Essai de cosmologie Ⓣ. Maupertuis hoped that the principle might unify the laws of the universe and combined it with an attempted proof of the existence of God. He wrote (see for example [1]):-

The laws of movement thus deduced [from the Principle of Least Action], being found to be precisely the same as those observed in nature, we can admire the application of it to all phenomena, in the movement of animals, in the vegetation of plants, in the revolution of the heavenly bodies: and the spectacle of the universe becomes so much the grander, so much the more beautiful, so much more worthy of its Author ...

These laws, so beautiful and so simple, are perhaps the only ones which the Creator and Organizer of things has established in matter in order to effect all the phenomena of the visible world ...

Another reason for leaving a discussion of the Principle of Least Action to now is that it played a large role in the sad events near the end of his life.

Samuel König was a mathematician whom Maupertuis had known for a long time. Both had been students of Johann Bernoulli, both had taught du Châtelet, both had studied the shape of the Earth, and Maupertuis had proposed Samuel König for election to the Berlin Academy. The strange affair began in 1751 when König visited Berlin and gave a paper to Maupertuis to be considered for publication. Clearly Maupertuis never read it, but simply returned it the following day recommending publication. It was indeed published in March 1751 and only then did Maupertuis read it and discover that on the one hand it argued that the Principle of Least Action was false, on the other hand it argued that Leibniz was the first to propose the theory. The evidence which was put forward to support the claim was a letter of 1707 from Leibniz to Jacob Hermann.

It is fair to say that by this time Maupertuis had serious health problems. Also he never reacted well to criticism, becoming ever more sensitive as his health declined, and we have already described the vicious personal attacks he made on his opponents in the argument about the shape of the Earth many years before. However, perhaps most relevant of all, he felt that the Principle of Least Action was his greatest achievement, the one for which he would go down in history. Maupertuis was strongly defended by Euler but he used his position as director of the Academy to have it declare publicly that König had forged the quotation. This left König no option but to resign from the Academy. Voltaire had at one time been a close friend of Maupertuis, but the two had fallen out years before this sad affair. Voltaire now used his great literary skill to rubbish Maupertuis's ideas, his voyage to Lapland, and he [1]:-

... lampooned Maupertuis's amorous adventures in the North.

Frederick tried to support the president of his Academy, but Maupertuis's failing health collapsed under the strain and he left Berlin for Paris in 1753. He remained there for over a year, being pressed by Frederick to return to Berlin who claimed that the Academy was out of control now its director was absent. This Maupertuis did in 1754 but then he was apparently blackmailed by a girl who claimed that he was the father of her child.

In 1756 Jacques Cassini died. Shortly after this Maupertuis's membership of the Académie des Sciences was renewed and he was awarded a pension from the Paris Academy. He returned to Paris in July 1756, but by September he was in his home town of Saint Malo. Advised to travel to Italy for health reasons, he set out in June 1757. By now the French were at war with the Prussians and his position became even more difficult. He spent seven months in Bordeaux but eventually reached Basle in October 1758 where he was a guest in the home of Johann Bernoulli. By the following summer he realised that his life was nearly over and his wife set out to travel to Basle to be with him. He died before she reached Basle, and was buried at Dornach.

Beeson writes [4]:-

The brilliance of much of what he did was undermined by his tendency to leave work unfinished, his failure to realise his own potential: it was the insight of genius that led him to least-action principle, but a lack of intellectual energy or rigour that prevented his giving it the mathematical foundation that Lagrange would provide. ... he reveals remarkable powers of perception in heredity, in understanding the mechanism by which species developed, even in immunology, but no fully elaborated theory. His philosophical work is his most enthralling: bold, exciting, well argued.