米歇尔·沙勒Michel Chasles

米歇尔·沙勒的父亲Charles-Henri 沙勒是一位木材商人，后来成为沙特尔商会的会长。沙勒出生的小镇埃佩尔农位于沙特尔地区，大约在从沙特尔城到巴黎的三分之一路程处。沙勒出生在一个相当富裕的天主教家庭。事实上，沙勒的父母按照共和历的月份给他取名为Floréal 沙勒。这个历法后来被废弃，在他十六岁生日后几天，通过法院命令将他的名字从Floréal改为沙勒。

沙勒在帝国中学接受中学教育。然后，在1812年，他进入巴黎的综合理工学院。这正是拿破仑竭力为他的军队征召新兵的时候，他试图补充在战斗中损失的部队。1813年1月，在俄国战役的灾难之后，拿破仑征召了更多的人来填补他军队中日益减少的人数。沙勒在1814年初被征召参加巴黎的保卫战。巴黎陷落后不久，拿破仑于1814年4月6日退位，战争结束。沙勒得以回到综合理工学院继续他的学业。

在获得工程兵部队的一个职位后，沙勒决定不接受它，而是把他的位置让给一位经济困难的 fellow student。此时沙勒回到家中居住，但他的父亲坚持要他加入巴黎的一家股票经纪公司。这不是沙勒的职业，但他遵从父亲的意愿，去巴黎加入那家公司学习股票经纪业务。然而，沙勒对历史和数学感兴趣，他在这家公司的见习并不成功。他再次回到家中，在那里他可以追求他的历史和数学兴趣。

1837年，沙勒 出版了他的第一部重要著作 Aperçu historique sur l'origine et le développement des méthodes en géométrie Ⓣ（几何学中方法的起源与发展的历史概述），这部著作迅速为他赢得了数学家和数学史家的声誉。Aperçu historique Ⓣ（历史概述）至今仍是一部重要的历史参考文献。这部著作的写作源于 布鲁塞尔皇家科学院 在1829年提出的一个问题。该问题要求[1]：-

……对现代几何学中不同方法进行哲学考察，特别是配极互反方法。

在 Aperçu historique Ⓣ（历史概述）中，沙勒 将配极互反方法作为 射影几何 中对偶原理的一个应用来研究；同样地，单应原理导出了 quadric surfaces 的大量性质。Académie des Sciences 希望出版 沙勒 提交给他们的这部著作，但他请求能够扩充历史导言，并在正文中增加更多的历史注释，以及加入一些新的材料和注释。这部著作在许多方面对 沙勒 未来的研究至关重要，因为他在余下职业生涯中产生的几乎所有众多著作，都是对他为 Aperçu historique Ⓣ（历史概述）所添加的这些注释中讨论的要点进行阐发。扩充版就是 科学院 于1830年出版的那个版本。Koppelman 在[1]中指出，这部著作有一个弱点。那就是 沙勒 不懂德语，因此他对以德语发表的最新成果不太熟悉。

凭借他出色的工作，沙勒于1841年成为巴黎综合理工学院的教授，时年近48岁。他教授的科目是大地测量学、力学和天文学。1846年，他被任命为索邦大学高等几何讲席，这个讲席是专为他设立的。在索邦大学任职后，他继续在综合理工学院任教，但于1851年辞去了综合理工学院的职务，保留索邦大学的讲席直到去世。

他还写了一部极其重要的几何学著作，展示了综合几何学的力量。在他的著作Traité de géométrie Ⓣ（几何学论）中，1852年沙勒讨论了交比、束和对合，所有这些都是他引入的概念。事实上，奥古斯特·费迪南德·莫比乌斯独立引入了交比。第二部著作Traité des sections coniques Ⓣ（圆锥曲线论）（1865年）将这些技术应用于conic sections。对偶原理贯穿他的全部著作，并由雅各布·施泰纳进一步推进。

沙勒 最为人所知的成果之一是他对圆锥曲线的计数。这类问题可以追溯到 阿波罗尼奥斯，但这类问题是在 沙勒 研究几何学时出现的，特别是 雅各布·施泰纳 的“五圆锥曲线问题”于 1848 年被提出。这个问题，即确定与五条给定圆锥曲线相切的圆锥曲线的数目，被 雅各布·施泰纳 错误地解决，他给出了答案 7776。沙勒 在 1864 年正确地解决了这个问题，给出了答案 3264。沙勒 发展了一套特征理论来解决这个问题，而 沙勒 的特征公式在 [5] 中讨论。

Koppelman 在[1]中写道：-

沙勒直到晚年都发表了极具独创性的工作。他从未结婚，除了研究、教学和科学院之外，他仅有的几项兴趣似乎是在慈善组织，他在其中担任过许多委员会的职务。

沙勒因其极具独创性的工作而获得许多荣誉。他于1839年当选为Académie des Sciences的通讯院士，1851年成为正式院士。他于1854年当选为伦敦皇家学会的会士，并于1865年获得其科普利奖章。London Mathematical Society成立于1865年，并于1867年选举沙勒为其第一位外籍院士。他还是布鲁塞尔、哥本哈根、那不勒斯、斯德哥尔摩、圣彼得堡和美国等地科学院的院士。

沙勒 一生中有一个方面似乎与他作为一位杰出人物的性格如此不符，以至于给他带来了极大的痛苦。他是一起著名欺诈案的受害者，支付了相当于 20,000 英镑的金额，购买了著名科学家和其他人的各种信件，而这些信件后来被证明是伪造的。沙勒 收集签名和手稿，但似乎表现出一种几乎令人难以置信的天真。沙勒 在 1861 年至 1869 年间从 Denis Vrain-爱德华·卢卡斯 那里购买了数千份手稿。Vrain-卢卡斯 出售了 沙勒 文件，这些文件声称是 艾萨克·牛顿、布莱兹·帕斯卡 和 罗伯特·波义耳 之间通信的一部分。沙勒 于 1867 年将这些信件呈交给 Académie des Sciences，因为它们“证明”了 布莱兹·帕斯卡 是第一个提出万有引力定律的人，而不是 艾萨克·牛顿。

正如人们可能预料的那样，这引起了极大的争议。沙勒 强烈主张这些信件是真实的。然而 Vrain-卢卡斯 于 1869-70 年因伪造文件而受审，沙勒 不得不出庭。这对 沙勒 来说是一次极其不舒服的经历，因为他不得不在法庭上承认，他购买了据称由 伽利略、Cleopatra 和 Lazarus 写的文件，而像 沙勒 这样智力超群且对历史有浓厚兴趣的人竟然会相信所有这些人都用法语写作，这简直令人难以置信！Vrain-卢卡斯 被判有罪，而 沙勒，尽管此时已经 77 岁，一定显得极其愚蠢。

Michel Chasles's father, Charles-Henri Chasles, was a wood merchant who became president of the chamber of commerce in Chartres. Epernon, the town where Chasles was born, is in the region of Chartres lying about one third of the way from the town of Chartres to Paris. Chasles was born into a fairly well off Catholic family. In fact Chasles was christened Floréal Chasles by his parents after the month of the Republican calendar. This calendar fell out of use and a court order was obtained to change his name from Floréal to Michel a few days after his sixteenth birthday.

Chasles attended the Lycée Impérial for his secondary education. Then, in 1812, he entered the École Polytechnique in Paris. This was the period when Napoleon was desperately trying to call up conscripts for his armies as he attempted to replenish the troops lost in the fighting. In January 1813, after the disaster of the Russian campaign, Napoleon called up more men to fill the dwindling numbers in his armies. Chasles was called up to take part in the defence of Paris in early 1814. Shortly after Paris fell, Napoleon abdicated on 6 April 1814 and the war was over. Chasles was able to return to his studies at the École Polytechnique.

Having obtained a place in the engineering corps, Chasles decided not to accept it but to give his place to one of his fellow students who was in financial difficulties. At this point Chasles returned to living at home but his father insisted that he join a firm of stockbrokers in Paris. This was not the occupation for Chasles but he obeyed his father's wishes and went to join the firm in Paris to learn the trade of a stockbroker. However, Chasles was interested in history and in mathematics and he was not successful as a trainee in the firm. He returned again to his home where he could pursue his historical and mathematical interests.

In 1837 Chasles published his first major work Aperçu historique sur l'origine et le développement des méthodes en géométrie Ⓣ which quickly made his reputation as both a mathematician and as an historian of mathematics. Aperçu historique Ⓣ is still an important historical reference. It was written because of a question asked in 1829 by the Royal Academy in Brussels. The question asked for [1]:-

... a philosophical examination of the different methods in modern geometry, in particular the method of reciprocal polars.

In Aperçu historique Ⓣ Chasles studied the method of reciprocal polars as an application of the principle of duality in projective geometry; in the same way the principle of homography leads to a great number of properties of quadric surfaces. The Académie des Sciences wanted to publish the work which Chasles submitted to them but he asked to be able to add to the historical introduction as well as to add further historical notes to the text and include some new material and notes. This work in many ways is the crucial one for Chasles's future research since almost all of the many works he produced throughout the rest of his career elaborate on points discussed in these notes he added to the Aperçu historique Ⓣ. The extended version is the one which the Academy published in 1830. Koppelman notes in [1] that the work had one weakness. This was that Chasles could not read German so he was not so familiar with the recent results published in that language.

On the strength of his fine work Chasles became professor at the École Polytechnique in Paris in 1841, at the age of nearly 48. Topics he taught were geodesy, mechanics, and astronomy. In 1846 he was appointed to a chair of higher geometry at the Sorbonne which had been specially created for him. He continued to teach at the École Polytechnique after this appointment at the Sorbonne but he resigned his post at the École Polytechnique in 1851, retaining his chair at the Sorbonne until his death.

He also wrote an extremely important text on geometry showing the power of synthetic geometry. In his text Traité de géométrie Ⓣ in 1852 Chasles discusses cross ratio, pencils and involutions, all notions which he introduced. In fact Möbius independently introduced the cross ratio. A second text, Traité des sections coniques Ⓣ (1865), applied these techniques to conic sections. The principle of duality occurs throughout his work which was carried further by Steiner.

One of the results for which Chasles is well known is his enumeration of conics. Questions of this type go back to Apollonius, but such questions had arisen while Chasles was working on geometry, in particular the Steiner "problem of five conics" was posed in 1848. This problem, namely to determine the number of conics tangent to five given conics, was solved incorrectly by Steiner who gave the answer 7776. Chasles solved this problem correctly in 1864 when he gave the answer of 3264. Chasles' developed a theory of characteristics to solve this problem and Chasles's characteristic formula is discussed in [5].

Koppelman writes in [1]:-

Chasles published highly original work until his very last years. He never married, and his few interests outside his research, teaching, and the Academy, which he served on many commissions, seem to have been in charitable organisations.

Chasles received many honours for this highly original work. He was elected a corresponding member of the Académie des Sciences in 1839 and a full member in 1851. He was elected a Fellow of the Royal Society of London in 1854 and won its Copley Medal in 1865. The London Mathematical Society was founded in 1865 and it elected Chasles in 1867 as its first foreign member. He was also a member of academies in Brussels, Copenhagen, Naples, Stockholm, St Petersburg, and the United States.

There is one aspect of Chasles's life which seems so out of character with the brilliant man that he was that it caused him great distress. He was the victim of a celebrated fraud paying the equivalent of 20,000 pounds for various letters from famous men of science and others which turned out to be forged. Chasles collected autographs and manuscripts but appears to have displayed a naiveté which is almost unbelievable. Chasles bought thousands of manuscripts from Denis Vrain-Lucas between 1861 and 1869. Vrain-Lucas sold Chasles documents which purported to be part of correspondence between Newton, Pascal, and Boyle. Chasles presented the letters to the Académie des Sciences in 1867 for they "proved" that Pascal was the first to propose the universal law of gravitation, and not Newton.

As one might expect this created a great controversy. Chasles argued strongly that the letters were genuine. However Vrain-Lucas was tried in 1869-70 for forging the documents and Chasles had to appear at the trial. It was an extremely uncomfortable experience for Chasles since he had to admit in court that he had purchased documents supposedly written by Galileo, Cleopatra and Lazarus and how someone of Chasles's intelligence and a deep interest in history would have believed that these all these wrote in French is beyond belief! Vrain-Lucas was found guilty and Chasles, although 77 by this time, must have looked extremely silly.