皮埃尔·杜埃姆Pierre Duhem

皮埃尔·杜埃姆的父亲是Pierre-Joseph Duhem，一位商业旅行者，他的母亲是Alexandrine Fabre。这是一个佛兰芒家庭。杜埃姆是他父母四个孩子中的长子，在父母搬到巴黎后出生在巴黎的Rue des Jeûneurs。他十一岁时进入斯坦尼斯拉斯学院，在那里他证明是一个才华横溢的学生。

离开斯坦尼斯拉斯学院时，他在拉丁语、希腊语、科学、数学和其他科目上取得了杰出成就，他不得不在巴黎综合理工学院（原则上培养工程师）和巴黎高等师范学院（两者中更学术的）之间选择。杜埃姆的父亲希望他在巴黎综合理工学院学习科学，因为他希望儿子从事技术职业。另一方面，杜埃姆的母亲希望他在巴黎高等师范学院学习拉丁语和希腊语，主要是因为她担心学习科学会让他背离她灌输给孩子们的罗马天主教信仰。杜埃姆在两所机构的入学考试中均排名第一，但他选择在巴黎高等师范学院学习纯科学，以不取悦父母任何一方。他于1882年8月2日开始学习。

当雅克·阿达马来到高等师范学校时，杜埃姆正在那里读第三年。然而两人很快成了挚友。雅克·阿达马在17中写道：-

在这些漫长而珍贵的交谈中，从我进入高等师范学校那一刻起，我们的友谊便日渐深厚，我如何感受到他被夏尔·埃尔米特的天才所激动，或是被儒勒·昂利·庞加莱的天才所激动，后者他比我们大多数人（我指的是数学上最专门化的人）都更了解其著作！但总的来说，所有伟大的数学思想，所有真正富有成果的思想，他都熟悉。从那时起，我得益于他给我的启示、洞见（多么宽广，多么不屑于细节，而着眼于真正本质的东西！），这些对我来说，毫不费力地、仿佛不知不觉地，取代了数月的学习。

1884年，还在高等师范学校时，杜埃姆发表了他的第一篇论文，是关于电化学电池的。甚至在获得数学学位之前，杜埃姆就于1884年提交了他的博士论文。突然，他辉煌的职业生涯戛然而止。这篇论文是关于物理和化学中的热力学势，在其中他以自由能定义了化学反应的判据。在此他取代了马塞兰·贝特洛二十年前提出的错误判据。杜埃姆非常正确地批评了贝特洛的理论，提出了正确的替代方案。遗憾的是，正确并不总是足够，像贝特洛这样有影响力的科学家能够设法让杜埃姆的论文被拒绝。

杜埃姆知道自己是对的，并于1886年大胆地发表了被拒绝的论文。可以想象，这当然无助于他与Berthelot的关系，而对杜埃姆来说坏消息是Berthelot于1886年成为法国教育部长。与此同时，杜埃姆在撰写第二篇论文，这次明智地选择了一个数学主题，不太可能受到他第一篇论文命运的影响。他关于磁性的数学工作于1888年被接受，但他一生都因Berthelot而受苦。

在第二篇论文提交之前，杜埃姆已经在里尔教书。他从1887年10月13日接受任命起在那里工作，直到1893年。在里尔，他讲授流体动力学、弹性和声学，并于1891年出版了这些讲义。在里尔期间，他于1890年10月与Adèle Chayet结婚。她两年后在他们第二个女儿出生时去世，女儿也夭折了。这一个人悲剧可能使他更难与里尔的上司相处，尽管他有许多良好的个人友谊，但他总是觉得这很难。

正是在与院长德马特尔先生发生争执之后，杜埃姆请求从里尔调离，并于1893年10月被任命为雷恩的讲师。到达雷恩后，他发现那里对他的工作条件不佳，便立即请求另一个职位。他于1894年10月13日成为波尔多大学的理论物理学教授，但调往巴黎——一位像他这样杰出能力的科学家自然会期望的——却被阻挠了。亚基在4中写道：-

尽管贝特洛已经意识到杜埃姆在科学上胜过自己，他却无法承认到让他获得巴黎讲席的程度。利害攸关的是贝特洛对其庞大而极有价值的实验研究所作的理论解释的声誉。贝特洛保护那种解释免受杜埃姆毁灭性批评，这实在太人之常情了，而那种批评如果从巴黎的讲席上发出，就会迫使贝特洛公开表态。这就是杜埃姆三十年来——从他第一篇博士论文直到他去世，也就是他的整个学术生涯——所遭受轻视的线索。不仔细审视这一点，对杜埃姆生平的呈现就不会显出它实际上那样的凄美戏剧。

杜埃姆接任波尔多的讲席时，雅克·阿达马已在波尔多待了一年。他在17中写道：-

就我而言，我们在波尔多理学院的重逢，使我有幸通过宝贵而持续的观点交流来补充我的阅读。我后来的大部分著作都归功于这种阅读和这些观点交流，这些著作几乎全都涉及变分法、杜埃姆理论、双曲型偏微分方程、克里斯蒂安·惠更斯原理。杜埃姆本人在其浩大工作的后续部分中几乎重新讨论了所有这些问题，而他曾如此成功、如此清晰地阐述的大多数理论，有时使他提出一些细节上的观察，有时则促使他作出一些具有根本重要性的补充。

还必须补充的是，杜埃姆的学位论文并不是他未能在巴黎获得任命的唯一原因。除了科学上的争论之外，杜埃姆在宗教问题上也与Berthelot不和。此外，正如Miller在[1]中所写，他：-

……性情好斗而尖刻，具有在科学事务上树敌的才能。

在1900年7月30日成为Académie des Sciences通讯院士之后，次年他再次请求从波尔多调离，但再次遭到拒绝。

很少有科学家像杜埃姆那样，在科学哲学、科学史学和科学本身方面做出了具有头等重要意义的贡献。然而，必须看到他的许多著作深受其极端天主教观点的影响，这使他无法以开放的心态接近这些主题。他的母亲曾不希望他学习科学，唯恐科学会削弱他的宗教信仰。也许实际情况恰恰相反，他的宗教信仰在形成他的科学信念方面起了过大的作用。然而，这些评论不应被视为以任何方式贬低杜埃姆在其所有三个兴趣领域所提出的观点的重要性。

他对科学本身的兴趣主要在数学物理领域，尤其是热力学、流体动力学、弹性、数学化学和力学。他把力学视为更一般的空间理论的一个特例，并认为广义的热力学将提供一种解释全部物理学和化学的理论。论文[27]考察了杜埃姆的：-

……理论物理学的统一：热力学势、拉格朗日分析形式体系以及杜埃姆关于理论物理学的哲学构想。这种统一的数学方面以及杜埃姆在热力学公理化中的优先权得到了强调。

在许多方面，杜埃姆的研究方法可以被视为非常现代。他会首先建立他所研究的物理系统所满足的公理。然后，他深入研究初始公理的推论，仅从公理发展出的数学定理中推导出物理系统的性质。然而，他反对研究并非源自物理情境的数学问题。

他对热力学的贡献具有重大重要性，他还在约西亚·威拉德·吉布斯和赫尔曼·冯·亥姆霍兹的工作之后研究了磁性。他在这些主题上的一些最重要的论文是Étude sur les travaux thermodynamiques de J Willard Gibbs Ⓣ（爱德华·斯图迪论J Willard 约西亚·威拉德·吉布斯的热力学功）（1887）和Commentaire aux principes de la theormodynamique Ⓣ（热力学原理评注）（1892）。三部主要论著是Thermodynamique et chimie Ⓣ（热力学与化学）（1902）、两卷本著作Recherches sur l'hydrodynamique Ⓣ（流体动力学研究）（1903-4）和Recherches sur l'élasticité Ⓣ（弹性研究）（1906）。

除了对科学的主要贡献外，他还撰写了关于科学哲学的重要文章。他的方法与他进行科学研究的方式非常一致，正如我们上面所概述的。他写道：-

一个物理理论……是一个数学命题系统，从少量原理中推导出来，其目标是以尽可能简单、完整和精确的方式表示一组实验定律。

可以想象，杜埃姆在科学哲学的许多方面与儒勒·昂利·庞加莱意见不合，两人进行了激烈的辩论。他在科学哲学方面最重要的著作之一是La Théorie physique, son objet et sa structure Ⓣ（物理理论、目的和结构）（1906年）。

如果说科学工作本身将杜埃姆引向了科学哲学，那么科学哲学又将他引向了科学史。他1902年的论文L'évolution de la mécanique Ⓣ（力学的演进）实际上是一篇关于科学哲学的文章，但它大量基于历史事例的使用。较早的科学史重要著作是1895年出版的Les théories de la chaleur Ⓣ（热理论）。然而，他在科学史方面最重要的著作是表明从1200年起并非一个科学被忽视的时期的研究。当然，他非常热衷于证明这一点，因为天主教会曾被许多人指责在这一时期阻碍了科学工作。

1903年深秋，杜埃姆在研究Les origines de la statique Ⓣ（静力学的起源）时，遇到了在列奥纳多·达·芬奇之前工作的科学家Jordanus Nemorarius。在此之前，杜埃姆接受了中世纪没有科学工作的普遍观点。正是这一意外发现促使杜埃姆去寻找其他在文艺复兴力学发展之前工作的科学家。他在这一领域最著名的著作包括Études sur Léonard de Vinci Ⓣ（列奥纳多·达·芬奇研究）（1906-13）。1913年，他开始出版Le Système du monde, Histoire des doctrines cosmologiques, de Platon à Copernic Ⓣ（世界体系：从柏拉图到尼古拉·哥白尼的宇宙学学说史）（1913-17），但在他去世前只完成了计划10卷中的5卷。

杜埃姆认为不同的民族特征导致不同的科学方法。他不喜欢英国科学，特别是詹姆斯·克拉克·麦克斯韦的工作，他将其描述为广博而浅薄，而他说法国科学是狭窄而深刻的。他声称德国科学高度几何化，这对杜埃姆来说是一种批评，因为他认为使用分析风格的数学方法远优于几何方法。雅克·阿达马写道（例如见[7]）：-

在第一次世界大战开始时，我们最伟大的科学家和科学史家之一，物理学家杜埃姆，被[民族主义激情]所误导。……在一篇相当详细的文章中，他将德国科学家，特别是数学家，描绘为缺乏直觉，甚至故意将其搁置……

在职业生涯后期，杜埃姆被提供了一份巴黎的教授职位，是作为科学史家而非数学物理学家。杜埃姆拒绝了去巴黎工作的机会，尽管他一直渴望去那里，他说自己是数学物理学家，不想通过后门去巴黎。

他在卡布雷皮讷徒步度假时去世。有些报道说是心脏病发作，另一些说是胸部感染。

Pierre Duhem's father was Pierre-Joseph Duhem, a commercial traveller, and his mother was Alexandrine Fabre. It was a Flemish family. Pierre, the eldest of his parents four children, was born in the Rue des Jeûneurs in Paris after his parents moved there. When he was eleven years old he entered the Collège Stanislas where he proved a brilliant student.

Leaving the Collège Stanislas with outstanding achievements in Latin, Greek, science, mathematics and other subjects, he had to choose between studying at the École Polytechnique which, in principle, prepared one to be an engineer, and the École Normale, the more academic of the two. Duhem's father wanted him to study science at the École Polytechnique since he wanted his son to follow a technical career. Duhem's mother, on the other hand, wanted him to study Latin and Greek at the École Normale, principally because she feared that a study of science would turn him away from the Roman Catholic beliefs that she had instilled in her children. Duhem was ranked first in the entrance examinations of both institutions but he chose to please neither of his parents by studying pure scientific at the École Normale. He began his studies on 2 August 1882.

When Hadamard arrived at the École Normale Duhem was beginning his third year of study there. However the two quickly became firm friends. Hadamard wrote in [17]:-

In these long and precious conversations during which, from the moment of my entry to the École, our friendship grew, how I felt him being thrilled by the genius of Hermite, or that of Poincaré, whose works he followed better than most of us could (I mean the most specialised in mathematics)! But in a general way, all the great mathematical ideas, all the one which were truly fruitful, were familiar to him. From this time I owe him revelations, insights (how broad, how disdainful of details to the profit of that which was really essential!) which for me, effortlessly and as if unconsciously, replaced long months of study.

In 1884, while still at the École Normale, Duhem published his first paper which was on electrochemical cells. Even before receiving his licence in mathematics, Duhem submitted his doctoral thesis in 1884. Suddenly his brilliant career shuddered to a halt. The thesis was on thermodynamic potential in physics and chemistry and in it he defined the criterion for chemical reactions in terms of free energy. In this he was replacing the incorrect criterion which Marcellin Berthelot had put forward twenty years earlier. Quite correctly Duhem criticised Berthelot's theory putting forward a correct alternative. Sadly being right is not always good enough and a scientist as influential as Berthelot was able to arrange for Duhem's thesis to be rejected.

Duhem knew he was right and boldly published the rejected thesis in 1886. This certainly did not help his relations with Berthelot, as one might imagine, and the bad news for Duhem was that Berthelot became French Minister of Education in 1886. Duhem meanwhile worked on a second thesis, this time wisely choosing a mathematical topic which was less likely to be affected by the fate of his first thesis. His mathematical work on magnetism was accepted in 1888 but he suffered all his life because of Berthelot.

Before his second thesis was submitted Duhem was already teaching at Lille. He worked there from the time he took up the appointment on 13 October 1887 until 1893. In Lille he lectured on hydrodynamics, elasticity, and accoustics, publishing these lectures in 1891. While in Lille he married Adèle Chayet in October 1890. She died two years later during the birth of their second daughter, who also died. This personal tragedy may have made it harder for him to get on with his superiors in Lille, something he always found hard despite having many good personal friendships.

It was after a dispute with the Dean, M. Demartres, that Duhem requested a move from Lille and was appointed maître de conférence at Rennes in October 1893. Arriving in Rennes he found that it was not well equipped for his work and he at once requested another post. He became professor of theoretical physics at the University of Bordeaux on 13 October 1894 but a move to Paris, which a scientist of his outstanding ability would naturally expect, was blocked. Jaki writes in [4]:-

In spite of having grown aware of Duhem's scientific triumph over him, Berthelot could not bring himself to acknowledge this to the extent of letting him obtain a chair in Paris. At stake was the renown of the theoretical interpretation which Berthelot gave to his vast and most valuable experimental researches. It was all too human of Berthelot to protect that interpretation from Duhem's devastating criticism which, if delivered from a chair in Paris, would have forced Berthelot into the open. Herein lies the clue to the slighting which affected Duhem for thirty years, from his first doctoral dissertation to his very death, that is his whole academic career. Without a careful look at it a presentation of Duhem's life would not appear that poignant drama which it actually was.

Hadamard had been in Bordeaux for a year when Duhem took up the chair there. He writes in [17]:-

For my part, our meeting again at the Faculté des Sciences of Bordeaux gave me the good fortune of supplementing my reading with invaluable and constant exchanges of views. It is to this reading, to these exchanges of views, that I owe the greater part of my later works, almost all of which deal with the calculus of variations, the theory of Hugoniot, hyperbolic partial differential equations, Huygens' principle. Duhem himself returned to almost all these questions in the continuation of his immense work, and most of the theories which he had so happily and so clearly explained, suggested to him sometimes some observations on details, sometimes some additions of fundamental importance.

One would have to add that Duhem's thesis was not the only reason that he did not achieve the appointment in Paris. As well as the scientific dispute, Duhem was at odds with Berthelot on religious issues too. In addition as Miller writes in [1] he:-

... was of a contentious and acrimonious disposition, with a talent for making personal enemies over scientific matters.

After becoming a corresponding member of the Académie des Sciences on 30 July 1900, in the following year he again requested a move from Bordeaux but again it was refused.

Few scientists have contributed in works of leading importance, as Duhem did, to the philosophy of science, the historiography of science, and science itself. One has to see much of his writings, however, strongly influenced by his ultra-Catholic views which prevented him approaching subjects with an open mind. His mother had not wanted him to study science in case science would diminish his religious beliefs. Perhaps in the event the opposite happened and his religious beliefs played too large a part in formulating his scientific beliefs. These comments, however, should not be taken as in any way lessening the importance of the views that Duhem put forward in all three areas of his interests.

His interests in science itself were mainly in the area of mathematical physics, and in particular thermodynamics, hydrodynamics, elasticity, mathematical chemistry, and mechanics. He viewed mechanics as a special case of a more general theory of space and he considered that a generalised version of thermodynamics would provide a theory to explain all of physics and chemistry. The paper [27] considers Duhem's:-

... unification of theoretical physics: the thermodynamical potentials, the Lagrangian analytical formalism and Duhem's philosophical conception of theoretical physics. The mathematical aspects of this unification and Duhem's priority in the axiomatization of thermodynamics are emphasized.

In many ways Duhem can be seen as very modern in his approach. He would begin by setting up axioms which the physical system that he was studying satisfied. He then studied in depth the consequences of the initial axioms deducing properties of the physical system from mathematical theorems developed from the axioms alone. He was opposed, however, to studying mathematical problems which did not arise from physical situations.

His contributions to thermodynamics are of major importance and he also studied magnetism following the work of Gibbs and Helmholtz. Some of his most important papers on these topics are Étude sur les travaux thermodynamiques de J Willard Gibbs Ⓣ (1887) and Commentaire aux principes de la theormodynamique Ⓣ (1892). Three major treatises are Thermodynamique et chimie Ⓣ (1902), the two volume work Recherches sur l'hydrodynamique Ⓣ (1903-4), and Recherches sur l'élasticité Ⓣ (1906).

As well as his major contributions to science he was led to write articles of major importance on the philosophy of science. His approach was very much in line with the way that he went about his scientific studies as we have outlined above. He wrote:-

A physical theory ... is a system of mathematical propositions, deduced from a small number of principles, which has the object of representing a set of experimental laws as simply, as completely, and as exactly as possible.

As one might imagine, Duhem disagreed with Poincaré on many aspects of the philosophy of science and the two engaged in a vigorous debate. One of his most important works on philosophy of science was La Théorie physique, son objet et sa structure Ⓣ (1906).

If scientific work itself led Duhem towards the philosophy of science, then in turn the philosophy of science led him towards the history of science. His paper L'évolution de la mécanique Ⓣ in 1902 is really an article on the philosophy of science but it is based heavily on using historical examples. Earlier important work on the history of science was Les théories de la chaleur Ⓣ published in 1895. His most important work on the history of science was, however, research which showed that the period from 1200 onwards was not a period when science had been ignored. Of course he was very keen to show that this was the case since the Catholic Church had been blamed by many for preventing scientific work during this period.

While working on Les origines de la statique Ⓣ in the late autumn of 1903, Duhem came across the scientist Jordanus Nemorarius who worked before Leonardo da Vinci. Until that time Duhem had accepted the commonly held view that there had been no scientific work in the Middle Ages. It was this surprise which led Duhem to look for other scientists who worked before the development of Renaissance mechanics. His most famous works in this area include Études sur Léonard de Vinci Ⓣ (1906-13). In 1913 he began publication of Le Système du monde, Histoire des doctrines cosmologiques, de Platon à Copernic Ⓣ (1913-17) but only 5 of the intended 10 volumes were written before his death.

Duhem saw different national characteristics lead to different approaches to science. He disliked British science, in particular the work of Maxwell, and he described it as broad and shallow while he said that French science was narrow and deep. German sciences he claimed were highly geometrical, which for Duhem was a criticism for he considered an approach using an analytical style of mathematics to be far superior to a geometrical one. Hadamard writes (see for example [7]):-

At the beginning of the first World War one of our greatest scientists and historians of sciences, the physicist Duhem, was misled by [nationalistic passions]. ... In a rather detailed article, he depicts German scientists, especially mathematicians, as lacking intuition or even deliberately setting it aside ...

Late in his career Duhem was offered a professorship in Paris as a historian of science and not as a mathematical physicist. Duhem refused the chance to work in Paris that he had always longed for saying that he was a mathematical physicist and did not want to get to Paris through the back door.

He died while on a walking holiday in Cabrespine. Some reports say it was a heart attack, others that he died of a chest infection.