埃米尔·皮卡Charles Émile Picard

埃米尔·皮卡的父亲是一家丝绸工厂的经理，于1870年巴黎围城期间去世。围城是1870年7月19日开始的普法战争的结果。战争对法国不利，1870年9月19日德国人开始围攻巴黎。对城中居民来说这是一个绝望的时期，他们杀死马、猫和狗作为食物。正是在这次围城期间，皮卡的父亲去世了。巴黎于1871年1月28日投降，1871年5月10日签署的《法兰克福条约》对法国是一种屈辱。

皮卡的母亲是一位医生的女儿，在丈夫去世后陷入了极其艰难的境地。除了皮卡之外，她还有一个年幼的次子，为了供养他们完成学业，她不得不寻找工作。正是她决心让儿子们有一个良好的开端，尽管遭遇了这场悲剧，才使皮卡得以接受教育，从而有机会在数学上取得最高的国际地位。皮卡的中学教育是在拿破仑中学，后来改称亨利四世中学。奇怪的是，他几乎在所有科目上都是出色的学生，尤其是在翻译希腊和拉丁诗歌方面，但他不喜欢数学。他自己写道，他讨厌几何，但他：-

……为了免于受罚而把它背了下来。

直到完成中学学业后的假期，皮卡才读到一本代数书，突然对数学产生了浓厚的兴趣。他参加了巴黎综合理工学院和巴黎高等师范学院的入学考试；在两次考试中分别名列第二和第一。雅克·阿达马在[8]中写道：-

正如我们时代任何一位有科学天赋的法国年轻人一样，他不得不在原则上培养人成为工程师的巴黎综合理工学院和具有纯粹科学方向的高等师范学院之间做出选择。他排名第一，选择了后者。据说他是在一次令人兴奋的拜访巴斯德之后做出这个决定的，其间这位细菌学之父以如此崇高的措辞谈论纯粹科学，使这位年轻人完全被说服了。

皮卡于1877年获得他的教师资格会考（Agrégation），名列第一。他在巴黎高等师范学院留了一年，担任助理。他于1878年被任命为巴黎大学讲师，然后于1879年被任命为图卢兹教授。1881年，他回到巴黎，被任命为高等师范学院的力学和天文学主讲。

1881年，皮卡被提名为Académie des Sciences数学部门的成员。他在如此年轻时就获得提名，这充分说明了他所展现出的非凡才能。他已经证明了两个重要的定理，这两个定理今天都以皮卡的名字命名，但获得这所著名科学院的录取仍然为时稍早，他还得再等几年。在他第一次获得提名的这一年，他娶了夏尔·埃尔米特的女儿。皮卡和妻子有三个孩子，一个女儿和两个儿子，他们都在第一次世界大战中阵亡。他的孙子们在第二次世界大战中受伤并被俘。

1885年，克劳德让-克劳迪·波桂去世后，索邦大学的微分学讲席空缺，皮卡被任命担任此职。然而，一项大学规定禁止三十岁以下的人担任讲席。通过让皮卡担任自己的代课教师直到他年满三十岁（即次年）来规避了这些规定。1897年，他请求将自己的讲席换成分析与高等代数讲席，以便能够培养研究生。

皮卡在分析、函数论、微分方程和解析几何领域做出了最重要的贡献。他使用逐次逼近法来证明常微分方程解的存在性，解决了这些微分方程的奥古斯丁·路易·柯西问题。从1890年开始，他将皮埃尔·西蒙·拉普拉斯方程的性质推广到更一般的椭圆方程。皮卡的解以收敛级数的形式表示。

1879年，他证明了一个非常数的整函数会无穷多次取到每一个值，可能有一个例外。皮卡在证明这一重要结果时使用了夏尔·埃尔米特的模函数理论。

在尼尔斯·阿贝尔和波恩哈德·黎曼工作的基础上，皮卡对附着于代数曲面的积分以及相关的topological问题的研究发展成为代数几何的一个重要部分。关于这一主题，他与Georges Simart合作出版了Théorie des fonctions algébriques de deux variables indépendantes Ⓣ（两个独立变量的代数函数论），这是一部两卷本著作，第一卷于1897年出版，第二卷于1906年出版。皮卡还发现了一个群，现在称为皮卡群，它作为一个线性微分方程上的变换群起作用。

他的三卷本杰作Traité d'analyseⓉ（分析教程）于1891年至1896年间出版。该论著[1]：-

……立即成为经典，并在随后的每一版中加以修订。这部著作因其涵盖的学科范围、清晰的阐述和明晰的风格而为许多学生所接受。皮卡在讨论其一般理论之前考察了几个具体情形。

皮卡还将分析应用于弹性、热和电的研究。他研究了电脉冲沿导线的传输，找到了该问题的一个优美解。可以看出，他的贡献既广泛又重要。

授予皮卡的荣誉中包括他于1889年当选Académie des Sciences，而八年前他首次被提名时未能成功。后来他于1917年起担任该科学院终身秘书，直至1941年去世。在这一职位上[1]：——

……他每年撰写一篇关于某位科学家或某个当前关注主题的公告。他还为许多数学书籍撰写序言，并参与了夏尔·埃尔米特和G H Halphen著作的出版工作。

皮卡于1886年获得让-维克托·彭赛列奖，1888年获得数学科学大奖。除了五所大学的荣誉博士学位和三十七个学术团体的荣誉会员资格外，他还于1932年获得荣誉军团大十字勋章，1937年获得约斯塔·米塔格-莱弗勒金质奖章。他于1924年成为法兰西学院院士。授予他的另一项荣誉是让他担任1920年9月在斯特拉斯堡举行的国际数学家大会主席。

雅克·阿达马在1937年向皮卡致辞时，这样评价作为教师的他：——

你能够使[力学]几乎变得有趣；我一直想知道你是怎么做到的，因为轮到我时我从来做不到这一点。但你也逃脱了，你不仅向我们介绍了流体动力学和湍流，还介绍了许多其他数学物理甚至无穷小几何的理论；所有这一切都在讲座中，在我看来是我听过的最精湛的讲座，其中没有一个多余的字，也没有一个缺少的字，问题的本质和用来克服它的手段都显得一清二楚，所有次要细节都得到彻底处理，同时又各得其所。

雅克·阿达马在[8]中写道：-

皮卡科学个性的一个显著特点是他教学的完美，这是我所知道的最奇妙的之一，如果不是最奇妙的话。

一个引人注目的事实是，在1894年至1937年间，他培养了超过10000名在中央工艺与制造学院学习的工程师。

Émile Picard's father was the manager of a silk factory who died during the siege of Paris in 1870. The siege was a consequence of the Franco-Prussian War which began on 19 July 1870. It went badly for France and on 19 September 1870 the Germans began a siege of Paris. This was a desperate time for the inhabitants of the town who killed their horses, cats and dogs for food. It was during this siege that Émile's father died. Paris surrendered on 28 January 1871 and The Treaty of Frankfurt, signed on 10 May 1871, was a humiliation for France.

Picard's mother, the daughter of a medical doctor, was put in an extremely difficult position when her husband died. As well as Émile, she had a second young son, and in order to support them through their education she had to find employment. Only her determination to give her sons a good start, despite the tragedy, allowed Émile to receive the education which gave him the chance to achieve the highest international stading in mathematics. Picard's secondary education was at the Lycée Napoléon, later called the Lycée Henri IV. Strangely he was a brilliant pupil at almost all his subjects, particularly in translating Greek and Latin poetry, but he disliked mathematics. He himself wrote that he hated geometry but he:-

... learned it by heart in order to avoid being punished.

It was only during the vacation after completing his secondary studies that Picard read an algebra book and suddenly he became fascinated in mathematics. He took the entrance examinations for École Polytechnique and École Normale Supérieure; he was placed second and first respectively in the two examinations. Hadamard wrote in [8]:-

As any young Frenchman of our time who was gifted in science, he was obliged to choose between the École Polytechnique which, in principle, prepared one to be an engineer, and the École Normale, with its pure scientific orientation. He was ranked first and chose the latter. It is said that he made this decision after an exciting visit to Pasteur, during which the father of bacteriology spoke about pure science in such lofty terms that the young man was completely persuaded.

Picard received his agrégation in 1877, being placed first. He remained at the École Normale Supérieure for a year where he was employed as an assistant. He was appointed lecturer at the University of Paris in 1878 and then professor at Toulouse in 1879. In 1881 he returned to Paris when appointed maître de conférence in mechanics and astronomy at the École Normale.

In 1881 Picard was nominated for membership of the mathematics section of the Académie des Sciences. It says much of the extraordinary ability that he was showing at such a young age that he was nominated. He had already proved two important theorems which are both today known under Picard's name, yet it was still a little soon to gain admission to the prestigious academy and he would have to wait a few more years. In this year of his first nomination he married Hermite's daughter. Picard and his wife had three children, a daughter and two sons, who were all killed in World War I. His grandsons were wounded and captured in World War II.

In 1885 Picard was appointed to the chair of differential calculus at the Sorbonne in Paris when the chair fell vacant on the death of Claude Bouquet. However a university regulation prevented anyone below the age of thirty holding a chair. The regulations were circumvented by making Picard his own suppléant until he reached the age of thirty which was in the following year. He requested exchanging his chair for that of analysis and higher algebra in 1897 so that he was able to train research students.

Picard made his most important contributions in the fields of analysis, function theory, differential equations, and analytic geometry. He used methods of successive approximation to show the existence of solutions of ordinary differential equations solving the Cauchy problem for these differential equations. Starting in 1890, he extended properties of the Laplace equation to more general elliptic equations. Picard's solution was represented in the form of a convergent series.

In 1879 he proved that an entire function which is not constant takes every value an infinite number of times, with one possible exception. Picard used the theory of Hermite's modular functions in the proof of this important result.

Building on work by Abel and Riemann, Picard's study of the integrals attached to algebraic surfaces and related topological questions developed into an important part of algebraic geometry. On this topic he published, with Georges Simart, Théorie des fonctions algébriques de deux variables indépendantes Ⓣ which was a two volume work, the first volume appearing in 1897 and the second in 1906. Picard also discovered a group, now called the Picard group, which acts as a group of transformations on a linear differential equation.

His three volume masterpiece Traité d'analyse Ⓣ was published between 1891 and 1896. The treatise [1]:-

... immediately became a classic and was revised with each subsequent edition. The work was accessible to many students through its range of subjects, clear exposition, and lucid style. Picard examined several specific cases before discussion his general theory.

Picard also applied analysis to the study of elasticity, heat and electricity. He studied the transmission of electrical pulses along wires finding a beautiful solution to the problem. As can be seen his contributions were both wide ranging and important.

Among the honours given to Picard was his election to the Académie des Sciences in 1889, eight years after he was first unsuccessfully nominated. He later served the Academy as its permanent secretary from 1917 until his death in 1941. In this role [1]:-

... he wrote an annual notice on either a scientist or a subject of current interest. He also wrote many prefaces to mathematical books and participated in the publication of works of C Hermite and G H Halphen.

Picard was awarded the Poncelet Prize in 1886 and the Grand Prix des Sciences Mathématiques in 1888. In addition to honorary doctorates from five universities and honorary membership of thirty-seven learned societies he received the Grande Croix de la Légion d'Honneur in 1932 and the Mittag-Leffler Gold Medal in 1937. He became a member of the Académie Française in 1924. Another honour was given to him was making him President of the International Congress of Mathematicians at Strasbourg in September 1920.

Hadamard had this to say of Picard as a teacher when he addressed him in 1937:-

You were able to make [mechanics] almost interesting; I have always wondered how you went about this, because I was never able to do it when it was my turn. But you also escaped, you introduced us not only to hydrodynamics and turbulence, but to many other theories of mathematical physics and even of infinitesimal geometry; all this in lectures, the most masterly I have heard in my opinion, where there was not one word too many nor one word too little, and where the essence of the problem and the means used to overcome it appeared crystal clear, with all secondary details treated thoroughly and at the same time consigned to their right place.

Hadamard wrote in [8]:-

A striking feature of Picard's scientific personality was the perfection of his teaching, one of the most marvellous, if not the most marvellous, that I have ever known.

It is a remarkable fact that between 1894 and 1937 he trained over 10000 engineers who were studying at the École Centrale des Arts et Manufactures.