路易·普安索Louis Poinsot

路易·普安索就读于巴黎的普安索-le-Grand学校。他于1794年10月参加了巴黎综合理工学院的入学考试，但在代数评估中表现不佳，未能通过。尽管在入学考试的一部分中表现不佳，普安索仍被巴黎综合理工学院录取。

从1794年到1797年，普安索是巴黎综合理工学院的学生，但后来他离开了，转到桥梁公路学校学习，打算成为一名工程师。普安索在职业生涯的这一阶段，对于自己未来想要什么，似乎有些缺乏远见。一旦进入成为工程师的课程，他的反应却是不去学习实践科目，而是完全沉浸在抽象数学之中。由于把自己的教育搞得相当糟糕，普安索决定放弃成为工程师的念头，离开桥梁公路学校，去当一名数学教师。

从1804年到1809年，普安索是巴黎波拿巴中学的数学教师。随后他被任命为帝国大学的督学。另一位著名数学家当时也在该大学任职，因为让·巴蒂斯特·约瑟夫·德朗布尔已于1808年被任命为帝国大学的司库，并一直担任该职位到1815年。1809年11月1日，普安索接受了巴黎综合理工学院分析与力学助理教授的职位，从而在帝国大学的职务之外又承担了另一项任命。

我们应该稍微谈谈像普安索这样在教育上并未真正取得巨大成功的人，是如何以他那样的方式从学校教学转入高等教育的。原因是，普安索甚至在理应攻读工程资格期间就已经在数学方面非常活跃。他从1803年的Eléments de statique Ⓣ（《静力学原理》）开始，发表了许多关于几何学、力学和静力学的著作，随后又发表了[1]：-

……这些论文涉及矩的合成与面积的合成（1806年）、系统中平衡与运动的一般理论（1806年），以及多边形和多面体（1809年）。

普安索在担任学校数学教师的那些年里非常忙碌，到1809年时他已经为自己赢得了良好的声誉。1812年，普安索安排Reynaud代替他在巴黎综合理工学院授课，从那时起，他就不再在那里教学，并在Reynaud之后请奥古斯丁·路易·柯西代替他。1816年9月，巴黎综合理工学院进行了重组，普安索失去了他此前四年仅名义上担任的职位。

到1816年，普安索已经当选为Académie des Sciences，因为1813年5月31日，他在Académie的数学部门中接替了约瑟夫·拉格朗日。1816年巴黎综合理工学院重组后，普安索成为入学考试审查员，并担任该职位十年。从1839年直到去世，他一直在经度局工作。

在数学研究及其发表方面，普安索有着很高的原则[1]：-

普安索决心只发表完全成熟的结果，并以清晰优雅的方式呈现它们。因此，他留下的著作相当有限……

他在几何学、静力学和动力学方面的研究很重要。他是几何力学的发明者，研究了作用在刚体上的力系如何分解为一个力和一个力偶。他在1809年写了一部关于多面体的重要著作（上面已经提到），发现了四种新的正多面体，其中两种出现在约翰内斯·开普勒1619年的著作中，但普安索并不知道这一点。1810年，奥古斯丁·路易·柯西证明了，按照这种正多面体的定义，正多面体的枚举是完备的。1990年，当内部不一致性变得明显时，人们在普安索（因而也是奥古斯丁·路易·柯西）的定义中发现了一个错误。

此外，普安索还研究数论，在这个主题上，他研究了丢番图方程、如何将数表示为两个平方数之差以及原根。然而，他最著名的还是对几何学的奉献，并且与加斯帕尔·蒙日一起，为几何学在18世纪法国数学研究中重新占据主导地位做出了贡献。除了几何学研究之外，普安索还于1846年在索邦大学创设了高等几何讲席，从而为几何学日益增长的重要性做出了贡献。普安索打算把这个讲席给米歇尔·沙勒，而后者确实被任命到这个新讲席上，并一直担任到1880年去世。

普安索确实像当时法国的许多学者一样，卷入了政治。他既参与了高等教育的政治，也参与了法国的政治。在前一种身份中，他在1830年之后多次担任巴黎综合理工学院完善委员会的成员。1840年，他被任命为负责高等教育的皇家公共教育委员会成员。他是[1]：——

在政治观点上温和自由派[并且]他抗议复辟时期的教权主义，但后来接受了巴黎议院（1846年）和参议院（1852年）的提名。

Louis Poinsot attended the school of Louis-le-Grand in Paris. He sat the entrance examination of the École Polytechnique in October 1794 but he performed poorly in the algebra assessment, which he failed. Despite this poor performance in one part of the entrance examinations, Poinsot was accepted for admission to the École Polytechnique.

From 1794 until 1797 Poinsot was a student at the École Polytechnique but then he left and went to study at the École des Ponts et Chaussée with the intention of becoming an engineer. Poinsot seems to have somewhat lacked vision at this stage in his career as to what he wanted for the future. Once on the course to become an engineer, he reacted by failing to study the practical subjects and became fully engrossed in abstract mathematics. Having made rather a mess of his education, Poinsot decided to give up the idea of becoming an engineer and left the École des Ponts et Chaussée to become a mathematics teacher.

From 1804 until 1809 Poinsot was a mathematics teacher at the Lycée Bonaparte in Paris. Then he was appointed as inspector general of the Imperial University. Another famous mathematician held a post with this university at this time for Delambre had been appointed treasurer to the Imperial University in 1808, holding the position until 1815. Poinsot took on another appointment, in addition to the one with the Imperial University, when he accepted the position of assistant professor of analysis and mechanics at the École Polytechnique on 1 November 1809.

We should say a little about how someone like Poinsot, who had not really made a great success of his education, had moved from school teaching into higher education in the way that he did. The reason is that Poinsot had been very active in mathematics even while he was supposed to be studying for an engineering qualification. He had published a number of works on geometry, mechanics and statics beginning with Eléments de statique Ⓣ in 1803 and following this with [1]:-

... memoirs that dealt with the composition of moments and the composition of areas (1806), the general theory of equilibrium and of movements in systems (1806), and polygons and polyhedra (1809).

Certainly Poinsot had been very busy during his years as a school teacher of mathematics and by 1809 he had made for himself a fine reputation. In 1812 Poinsot arranged for Reynaud to substitute for him in lecturing at the École Polytechnique and, from this time on, he did no further teaching there asking Cauchy to substitute for him after Reynaud. In September 1816 the École Polytechnique was reorganised and Poinsot lost the post which he had held in name only for the previous four years.

By 1816 Poinsot had been elected to the Académie des Sciences for, on 31 May 1813, he had replaced Lagrange in the mathematics section of the Académie. The 1816 reorganisation of the École Polytechnique saw Poinsot become admissions examiner and he held this post for ten years. From 1839 until his death he worked at the Bureau des Longitudes.

Poinsot had high principles when it came to mathematics research and the publication of it [1]:-

Poinsot was determined to publish only fully developed results and to present them with clarity and elegance. Consequently he left a rather limited body of work ...

His research in geometry, statics and dynamics is important. He was the inventor of geometrical mechanics, investigating how a system of forces acting on a rigid body could be resolved into a single force and a couple. He wrote an important work on polyhedra in 1809 (already mentioned above), discovering four new regular polyhedra, two of which appear in Kepler's work of 1619 but Poinsot was unaware of this. In 1810 Cauchy proved that, with this definition of regular, the enumeration of regular polyhedra is complete. A mistake was discovered in Poinsot's (and hence Cauchy's) definition in 1990 when an internal inconsistency became apparent.

In addition Poinsot worked on number theory and on this topic he studied Diophantine equations, how to express numbers as the difference of two squares and primitive roots. However he is best known for his dedication to geometry and, together with Monge, he contributed to the topic regaining its leading role in mathematical research in France in the eighteenth century. As well as his research in geometry, Poinsot contributed to its increasing importance by creating a chair of advanced geometry at the Sorbonne in 1846. Poinsot intended the chair for Chasles and indeed he was appointed to the new chair which he occupied until his death in 1880.

Poinsot did, as many academics at this time in France, become involved in politics. He was involved both in the politics of higher education and also with the politics of France. In the former capacity he served on the Conseil de Perfectionnement of the École Polytechnique on a number of occasions after 1830. In 1840 he was appointed to the Conseil Royal de l'Instruction Publique which dealt with higher education. He was [1]:-

Moderately liberal in his political opinions [and] he protested against the clericalism of the Restoration but later accepted nomination to the Chambre de Paris (1846) and the Senate (1852).