米哈伊尔·奥斯特罗格拉德斯基Mikhail Ostrogradsky

奥斯特罗格拉德斯基 Vasilevich 米哈伊尔·奥斯特罗格拉德斯基的父亲Vasili Ivanovich Ostrogradski是一位地主，但尽管家族有显贵市民作为亲戚，他们却很穷。奥斯特罗格拉德斯基的母亲是Irina Andreevna Sakhno-Ustimovich。奥斯特罗格拉德斯基家族和Sakhno-Ustimovich家族都是有着长期服兵役传统的哥萨克人。我们在此记录一个事实：奥斯特罗格拉德斯基的名字常以三种形式之一给出：奥斯特罗格拉德斯基、Ostrogradskii或奥斯特罗格拉德斯基。Vasili Ivanovich和Irina Andreevna有五个孩子；奥斯特罗格拉德斯基有两个兄弟Osip和Andrei，以及两个姐妹Elena和Maria。他出生在他父亲土地上的一座茅草屋里。像大多数孩子一样，他对周围的世界表现出极大的好奇心，但与大多数孩子不同的是，他从测量物体中获得极大的乐趣。他不仅测量玩具的尺寸，还测量水井的深度和田地的长度。他总是在口袋里装一块石头，上面系着一根长绳子，这样他就可以测量遇到的任何水井的深度。他还对磨坊着迷，长时间坐着观看风帆旋转、水轮转动以及磨石旋转以磨碎谷物。

他于1809年开始在波尔塔瓦 文理中学 中学接受教育。他寄宿在一所提供“贫困贵族子弟教育”住宿的房子里。他的导师是 Ivan Petrovych Kotlyarevsky（1769-1838），他作为作家、诗人和社会活动家而闻名。奥斯特罗格拉德斯基 在中学的学业科目上并不出色。当他即将离开时，奥斯特罗格拉德斯基 表达了从军的愿望。几乎可以肯定 Kotlyarevsky 影响了这一决定，因为他曾在俄罗斯帝国军队服役，参加过俄土战争。然而 奥斯特罗格拉德斯基 的家庭并不富裕，尽管他们有军事传统，但人们觉得士兵的薪水不够好。最终决定他应该从事文职工作，而为了获得高级职位，大学教育是必要的。然而，他没有开始大学学习所需的背景，因此他听课并自学以获得必要的专业知识。

奥斯特罗格拉德斯基 于1816年进入哈尔科夫大学，经过一年的预科学习后，于1817年开始学习物理和数学。起初，他并不特别热衷于在大学学习，并以相当不情愿的态度对待学业。然而，Andrei Fedorovich Pavlovsky（1789-1875）是他的老师之一，他注意到了这个年轻人的非凡才能，并能够唤醒他对科学的兴趣。当时另一位影响 奥斯特罗格拉德斯基 的人是 季莫菲·奥西波夫斯基，他既是数学教授，又是哈尔科夫大学的校长。1820年，奥斯特罗格拉德斯基 参加并通过了获得学位所需的考试，但宗教事务和国民教育部长拒绝确认这一决定，并要求他重新参加考试。问题似乎出在他的数学教授 季莫菲·奥西波夫斯基 于1820年因宗教原因被停职。做出这一决定的官员也让 季莫菲·奥西波夫斯基 的学生遭受了痛苦。让我们给出这一事件的更多细节。1816年，Aleksandr Nikolaevich Golitsyn 公爵（1773-1844）被任命为教育部长和宗教事务部长。他发动了一场针对“不敬神和革命倾向”的宗教讨伐，要求科学必须从基督教原则出发进行教授。哈尔科夫与其他大学一样，收到了如何从基督教观点出发进行教学的指示，以展示上帝的无所不知。1820年，在 Golitsyn 的领导下，季莫菲·奥西波夫斯基 被哈尔科夫大学督学 Zakharii Iakovlevich Karneev（1747-1828）解职，原因是在对一名研究生进行口试时，被指控在说“上帝存在”时缺乏热情。这对 奥斯特罗格拉德斯基 产生了相当严重的后果，他曾在1820年由 季莫菲·奥西波夫斯基 考核，因为在 季莫菲·奥西波夫斯基 被解职后，教育部拒绝确认 奥斯特罗格拉德斯基 的博士学位授予。他们要求他重新参加考试（官方理由是他没有参加哲学和神学讲座），但他知道真正的原因是他由 季莫菲·奥西波夫斯基 考核，因此拒绝重新参加考试，并且从未获得该学位。

当时世界领先的数学中心是巴黎，奥斯特罗格拉德斯基做出了大胆的决定去那里学习，于1822年5月到达。这是一个艰难的决定，因为他的家人不赞成，而且他有经济困难。更糟糕的是，他在旅途中被抢劫了。1822年至1827年间，他在巴黎综合理工学院、索邦大学和法兰西学院听课，涉及数学、物理学、力学和天文学。这些课程由路易·普安索、皮埃尔·西蒙·拉普拉斯、约瑟夫·傅里叶、阿德里安-马里·勒让德、西莫恩·德尼·泊松、雅可·比内和奥古斯丁·路易·柯西讲授。他与这些领先的数学家变得友好，进步迅速，并很快开始在巴黎科学院上发表论文。其中第一篇是Memoir on wave propagation in a cylindrical vessel（1826年）。他此时的论文显示了巴黎数学家的影响，他写了关于物理学和积分学的文章。例如，他于1826年2月13日向巴黎科学院提交了他的论文Démonstration d'un théorème du calcul intégral Ⓣ（一个微积分定理的证明）。在这篇论文中，奥斯特罗格拉德斯基陈述并证明了一般散度定理。卡尔·弗里德里希·高斯不知道奥斯特罗格拉德斯基的论文，在1833年和1839年证明了散度定理的特殊情况，该定理现在通常以卡尔·弗里德里希·高斯命名。Victor Katz写道[19]：-

奥斯特罗格拉德斯基于1827年8月6日在巴黎的一篇论文中再次提出了这个定理，最后于1828年11月5日在圣彼得堡提出。后一次演讲是奥斯特罗格拉德斯基唯一发表的，出现在1831年的《Note sur la Théorie de la Chaleur Ⓣ（关于热的理论的注记）（1831年）》中。前两次演讲仅以手稿形式保存下来，尽管它们已以俄语翻译出版。

事实上，奥斯特罗格拉德斯基在巴黎写的许多论文后来被纳入他于1832年在巴黎出版的一部关于流体动力学的主要著作中。他此时在留数理论方面获得的其它结果出现在奥古斯丁·路易·柯西的著作中。然而，他在巴黎的时光确实有它的困难。奥斯特罗格拉德斯基的父亲不满儿子在国外待得太久，停止给他寄钱。奥斯特罗格拉德斯基无法支付住宿费用，最终负债累累。他因未付款而被告上法庭，但奥古斯丁·路易·柯西听说奥斯特罗格拉德斯基的困难后，还清了他所有的债务。奥古斯丁·路易·柯西然后设法为奥斯特罗格拉德斯基在亨利四世学院（今天称为亨利四世中学）获得了一个教职，这样他就可以继续住在巴黎。肯尼思·梅在评论[30]时解释说，这篇论文：-

……描述了四份可追溯到奥斯特罗格拉德斯基在巴黎居住期间（1822-1827年）的手稿，由A.П. 尤什克维奇于1963年在法国科学院档案中发现。其中前两份手稿（1824年）是关于定积分的，记录了奥斯特罗格拉德斯基在奥古斯丁·路易·柯西留数方法发展中的作用。……第三和第四份手稿（1826年和1827年）[已被]翻译……它们包括乔治·格林定理的一个特殊情况、分离变量法的一般发展（据A.П. 尤什克维奇说，这是第一次这样的发展），以及三角棱柱中热扩散问题的第一个解。

奥斯特罗格拉德斯基离开法国前往圣彼得堡，于1828年春天到达。尽管他满怀热情来到圣彼得堡，希望创造一个像他在巴黎所经历的那样的研究环境，但他还是受到当地警察的怀疑和不信任，他们将他置于监视之下。然而，他受到圣彼得堡数学家的热情欢迎。他于1828年被任命为海军学院（当时实际上称为海军军团）的讲师。后来他获得了额外的教学职位，从1830年开始在交通学院，两年后，他开始在普通师范学院任教。他于1830年5月第二次访问巴黎，当时城市中发生了街头骚乱并筑起了街垒。这是1830年的七月革命，奥斯特罗格拉德斯基在访问快结束时严重损伤了他的一只眼睛。看来这不是任何骚乱的结果，而是他对一根磷火柴不小心。他的右眼失明了。他于1831年与Maria结婚；他们有三个孩子，两个女儿和一个儿子。奥斯特罗格拉德斯基喜欢和孩子们玩耍，像孩子一样和他们一起跳跑。

在圣彼得堡，他向Imperial (St Petersburg) Academy of Sciences提交了三篇关于热理论、二重积分和potential theory的重要论文。主要凭借这些论文，他当选为科学院应用数学部的院士。他于1828年12月当选为初级院士，1830年晋升为通讯院士，最终于1832年成为正式院士。奥斯特罗格拉德斯基在研究上目标高远，他的目标是提供一个流体动力学、弹性、热和电的综合理论。他于1830年向帝国科学院提交了一份报告，其中包含以下极其雄心勃勃的目标（见[17]）：-

艾萨克·牛顿的追随者详细发展出了万有引力定律，并将数学分析应用于普通物理学和无重量物质物理学的众多重要问题。他们关于宇宙体系的著作汇集成了不朽的对开本《天体力学》，天文学家将在很长一段时间内从中获取编制星表的要素。然而，物理理论和数学理论仍未统一；它们分散在众多学术论文集里，用不同的方法研究，这些方法往往很可疑、不完善；此外，还有一些理论已经发展出来却从未发表。我把综合这些理论、用统一的方法表述它们并指出其最重要的应用作为目标。我已经收集了关于弹性体运动和平衡、不可压缩液体表面波的传播、以及热在固体内部特别是地球内部传播的必要材料。然而，这些理论将只构成整部著作的必要部分，整部著作还将涵盖电和磁在能够通过电动力学影响而带电或磁化的物体中的分布、电流体的运动、液体的运动和平衡、毛细作用、热在液体中的分布，以及概率论；在最后这部分，我将讨论几个问题，其中《天体力学》的著名作者显然是错的。

当然，这远远超出任何一个人所能达到的范围，但通过瞄准一个宏大的方案，他在广泛的领域取得了重大进展。他于1834年1月24日向圣彼得堡科学院提交了Mémoire sur le Calcul des Variations des Integrales Multiples Ⓣ（关于多重积分的变分计算回忆录）。这是偏微分方程理论中的一部重要著作，并于1836年重印于奥古斯都·利奥波德·克雷勒的Journal中，艾萨克·托德夯特作了英译并于1861年出版。1840年他写了关于弹道学的文章，将这一主题引入俄国。他关于ordinary differential equations的重要著作考虑了非线性方程的解法，其中涉及关于参数alpha的幂级数展开。约瑟夫·刘维尔曾得出过类似结果。此外，他关于热的一些结果与加布里尔·拉梅和让-马里·迪阿梅尔得出的结果相似。他必须被视为俄国理论力学学派的创始人。除了对偏微分方程的重要贡献外，他在弹性理论和代数方面也取得了重大进展，发表了80多篇报告并授课。他关于代数的工作是对尼尔斯·阿贝尔关于代数函数及其积分工作的扩展。

从1847年起，他担任军事学校数学科学教学的总督学。他写了许多优秀的教科书，并创造了使巴夫尼提·列波维奇·切比雪夫学派得以在圣彼得堡繁荣的条件。然而，这一巨大贡献占去了他大量时间，否则他本可以用这些时间在数学物理方面取得进一步的重大进展。巴夫尼提·列波维奇·切比雪夫关于奥斯特罗格拉德斯基写了以下内容（见[17]）：-

毫无疑问，他是一个才华横溢的人，如果不是被烦人的长期教学工作“拖累”，他本可以完成的事情连一半都没有完成。

Victor Katz在[18]中写道：-

不幸的是，[奥斯特罗格拉德斯基]的一些最重要的发现似乎被完全忽视了，至少在西欧是如此。他不仅首次将变量替换定理推广到$n$个变量，还首次证明并后来推广了散度定理，写了$n$-形式在$n$维“超曲面”上的积分，并且……利用无穷小概念首次证明了二重积分的变量替换定理。所有这些结果最终都被其他数学家重复，却没有归功于奥斯特罗格拉德斯基。

奥斯特罗格拉德斯基身材高大，声音洪亮。他的外貌相当令人敬畏，尤其是失去右眼之后，但他性格开朗，头脑异常敏锐。他深爱着自己的故土、人民和文化。他喜爱古典法国和俄罗斯文学，尽管在家时他偏爱的语言始终是乌克兰语。他喜欢朗诵莫里哀和高乃依的独白，但他最喜爱的作家是乌克兰诗人兼作家塔拉斯·赫里霍罗维奇·舍甫琴科。奥斯特罗格拉德斯基能背诵舍甫琴科的许多作品，并经常朗诵它们。奥斯特罗格拉德斯基于1858年结识舍甫琴科，当时这位诗人前来与他同住。事实上，舍甫琴科在日记中记载（见[23]）：-

……我们和谢苗一起去了M V 奥斯特罗格拉德斯基家。这位伟大的数学家像对待同胞，而且显然像对待一位失散已久的亲戚一样张开双臂欢迎我。愿上帝保佑他。奥斯特罗格拉德斯基夏天携家人前往小俄罗斯[乌克兰]。他说他想邀请谢苗同行，但担心整个波尔塔瓦省都没有足够的培根满足他的需求。

引文中提到的谢苗是谢苗·胡拉克-阿尔捷莫夫斯基（1813-1873），一位著名的乌克兰作曲家和歌剧演唱家。

最后，让我们提及奥斯特罗格拉德斯基晚年所做的关于保险的杰出工作。其背景颇为有趣，由阿列克谢·克雷洛夫描述（见[12]）：-

1856年，根据巴黎条约，俄国被剥夺了在黑海拥有舰队的权利。大量办公人员不得不被解雇，为改善他们的境况，决定在海军部设立退休基金，并从1859年开始支付养老金。当时人寿保险尚属新奇事物，而与退休基金工作相关的计算，或根据工资中相应扣款确定养老金数额的计算，则更为鲜为人知。因此，身为圣彼得堡科学院成员的两名数学家，奥斯特罗格拉德斯基和维克托·布尼亚科夫斯基，都被纳入负责起草基金章程的委员会。他们确实完成了所有必要的计算，并提供了理论依据。委员会的交易记录随即出版；其中包含奥斯特罗格拉德斯基的一篇杰出札记……

我们注意到，1856年的巴黎条约结束了俄国对抗由英国和法国支持的土耳其的克里米亚战争。这是一场以双方无能而闻名的战争。看到俄国和法国站在对立面，必定让奥斯特罗格拉德斯基深感痛苦。

奥斯特罗格拉德斯基内心始终是乌克兰人，他在遗嘱中指定自己应被安葬在家乡村庄帕申纳亚。1861年夏天，当他洗澡时，人们注意到他背上有一个脓肿。他接受了手术，脓肿被切除，但他的健康状况迅速恶化，并于次年一月去世。我们注意到，有些资料将他的去世日期记为1861年，而非1862年，因为按旧历日期是1861年12月20日。他的遗愿得以实现，他被安葬在帕申纳亚的家族墓穴中。

Mikhail Vasilevich Ostrogradski's father Vasili Ivanovich Ostrogradski, was a landowner but, although the family had leading citizens as relations, they were poor. Mikhail's mother was Irina Andreevna Sakhno-Ustimovich. Both the Ostrogradski and the Sakhno-Ustimovich family were Cossacks with a long tradition of serving in the military. Let us record at this point the fact that Ostrogradski's name is often given in one of the three forms: Ostrogradski, Ostrogradskii, or Ostrogradsky. Vasili Ivanovich and Irina Andreevna had five children; Mikhail had two brothers Osip and Andrei, and two sisters Elena and Maria. He was born in a thatched hut on his father's land. As most children do, he showed great curiosity in the world around him but, unlike most, he derived great pleasure from measuring objects. Not only did he measure the dimensions of his toys but he also measured the depth of wells and lengths of fields. He always carried a stone in his pocket which had a long piece of string tied round it so that he could measure the depth of any well he came across. He was also fascinated by mills, sitting for long periods watching the sails rotate, the water wheel turning, and the mill stone rotating to grind the grain.

He attended the Poltava Gymnasium secondary school, beginning his education there in 1809. He boarded in a house which offered accommodation for the "education of children of impoverished nobles". His tutor was Ivan Petrovych Kotlyarevsky (1769-1838), who made a name for himself as a writer, poet and social activist. Ostrogradski did not shine in his academic subjects at the Gymnasium. When the time came for him to leave, Ostrogradski expressed a wish to have a military career. Almost certainly Kotlyarevsky influenced him in this decision since he had served in the Imperial Russian Army, fighting in the Russo-Turkish war. However Ostrogradski's family was not wealthy and, despite their military traditions, it was felt that a soldier's pay was not good enough. Eventually it was decided that he should take up a career in the civil service and in order to obtain a high ranking position a university education was necessary. However, he did not have the necessary background to begin university studies so he attended lectures and studied on his own to gain the necessary expertise.

Ostrogradski entered the University of Kharkov in 1816 and, after a preparatory year, began to study physics and mathematics in 1817. Initially, he had not been particularly keen on studying at university and approached his studies with considerable reluctance. However, Andrei Fedorovich Pavlovsky (1789-1875) was one of his teachers and he noticed the extraordinary ability of the young man and was able to awaken in him an interest in science. Another who influenced Ostrogradski at this time was Timofei Fedorovic Osipovsky who was both a professor of mathematics and the rector of the University of Kharkov. In 1820 Ostrogradski took and passed the exams necessary for his degree but the minister of religious affairs and national education refused to confirm the decision and required him to retake the examinations. The problem appears to have been his mathematics professor Osipovsky, in the year 1820, was suspended from his post on religious grounds. The officials who made this decision made Osipovsky's pupil suffer too. Let us give some further details of this episode. In 1816 Prince Aleksandr Nikolaevich Golitsyn (1773-1844) was appointed Minister of Education and Minister of Religious Affairs. He carried out a religious crusade against "ungodly and revolutionary tendencies", requiring that science be taught from Christian principles. Kharkov, like other universities, received instructions on how to teach from a Christian viewpoint, demonstrating God's omniscience. In 1820, following Golitsyn's lead, Osipovsky was dismissed by the Curator of Kharkov University, Zakharii Iakovlevich Karneev (1747-1828), because of an alleged lack of fervour when saying "God lives" during an oral examination of a graduate student. This had a rather serious consequence for Ostrogradski who had been examined by Osipovsky in 1820, for, following Osipovsky's dismissal, the Ministry of Education refused to confirm the award of Ostrogradski's doctorate. They required him to retake the examinations (officially on the grounds that he had not attended lectures on philosophy and theology), but, knowing that the real reason was that he had been examined by Osipovsky, he refused to retake the examinations and never received the degree.

The leading mathematical centre in the world at this time was Paris and Ostrogradski made the bold decision to study there, arriving in May 1822. It had been a hard decision since his family did not approve and he had financial difficulties. To make matters even worse, he was robbed on the journey. Between 1822 and 1827, he attended lectures at the École Polytechnique, the Sorbonne, and the Collège de France, on mathematics, physics, mechanics, and astronomy. These were delivered by Louis Poinsot, Pierre-Simon Laplace, Joseph Fourier, Adrien-Marie Legendre, Siméon-Denis Poisson, Jacques Binet and Augustin-Louis Cauchy. Becoming friendly with these leading mathematicians, he made rapid progress and soon began to publish papers in the Paris Academy of Sciences. The first of these is Memoir on wave propagation in a cylindrical vessel (1826). His papers at this time show the influence of the mathematicians in Paris and he wrote on physics and the integral calculus. For example, he submitted his paper Démonstration d'un théorème du calcul intégral Ⓣ to the Paris Academy of Sciences on 13 February 1826. In this paper Ostrogradski states and proves the general divergence theorem. Gauss, nor knowing about Ostrogradski's paper, proved special cases of the divergence theorem in 1833 and 1839 and the theorem is now often named after Gauss. Victor Katz writes [19]:-

Ostrogradski presented this theorem again in a paper in Paris on 6 August 1827, and finally in St Petersburg on 5 November 1828. The latter presentation was the only one published by Ostrogradski, appearing in 1831 in 'Note sur la Théorie de la Chaleur Ⓣ (1831).' The two earlier presentations have survived only in manuscript form, though they have been published in Russian translation.

In fact many of Ostrogradski's papers which he wrote in Paris were later incorporated in a major work on hydrodynamics with he published in Paris in 1832. Other results which he obtained at this time on residue theory appeared in Cauchy's works. His time in Paris, however, did have its problems. Ostrogradski's father, unhappy that his son was spending so long abroad, stopped sending him money. Ostrogradski, unable to pay the bills for his accommodation, ended up badly in debt. He was taken to court for non-payment, but Cauchy, hearing of Ostrogradski's difficulties, paid off all his debts. Cauchy then managed to get Ostrogradski a position teaching at the Collège Henri IV (today called Lycée Henri-IV) so he could continue living in Paris. Kenneth May, reviewing [30], explains that the paper:-

... describes four manuscripts dating from Ostrogradski's Paris residence (1822-1827) and discovered by Yushkevich in the French Academy archives in 1963. The first two of those manuscripts (1824) are on definite integrals and document Ostrogradski's role in the development of Cauchy's method of residues. ... the third and fourth manuscripts (1826 and 1827) [have been] translated .... They include a special case of Green's theorem, a general development (the first such, according to Yushkevich) of the method of separation of variables, and the first solution of the problem of heat diffusion in a triangular prism.

Ostrogradski left France and went to St Petersburg, arriving in the spring of 1828. Although he came to St Petersburg full of enthusiasm looking to create a research environment like he had experienced in Paris, nevertheless he was looked at with suspicion and distrust by the local police who put him under surveillance. However, he was greeted with enthusiasm by the St Petersburg mathematicians. He was appointed as a lecturer at the Naval Academy (actually called the Naval Corps at this time) in 1828. Later he gained additional teaching positions, at the Institute of Means of Communication beginning in 1830 and, two years later, he began teaching at the General Pedagogical Institute. He had a second visit to Paris in May 1830 being in the city at the time when there were street disorders and barricades were erected. This was the July revolution of 1830 and Ostrogradski seriously damaged one of his eyes towards the end of his visit. It appears that this was not as a result of any disturbances but rather that he was careless with a phosphorous match. He became blind in his right eye. He married Maria in 1831; they had three children, two daughters and a son. Ostrogradski loved to play with his children, jumping and running with them in a childlike way.

In St Petersburg, he presented three important papers on the theory of heat, double integrals and potential theory to the Imperial (St Petersburg) Academy of Sciences. Largely on the strength of these papers he was elected an academician in the applied mathematics section of the Academy. He was elected a junior academician in December 1828, promoted to associate academician in 1830, and finally became a full academician in 1832. Ostrogradski aimed high in his research and his objective was to provide a combined theory of hydrodynamics, elasticity, heat and electricity. He submitted a report to the Imperial Academy of Sciences in 1830 which contains the following remarkably ambitious aim (see [17]):-

The followers of Newton developed the great law of universal gravitation in detail and applied mathematical analysis to numerous important problems in general physics and physics of weightless substances. The collection of their works about the system of the universe forms the immortal folios of 'Celestial mechanics,' from which astronomers will take the elements for their tables for a long time. However, physical and mathematical theories are still not unified; they are distributed over numerous collections of academic memoirs and are investigated by different methods, often very doubtful and imperfect; moreover, there are theories developed but never presented. I set it as my aim to combine these theories, present them by using a uniform method, and indicate their most important applications. I already collected the necessary materials on the motion and equilibrium of elastic bodies, propagation of waves on the surface of incompressible liquids, and propagation of heat inside solid bodies and, in particular, inside the globe. However, these theories will constitute only a necessary part of the entire work, which will also embrace the distribution of electricity and magnetism in bodies capable of being electrified or magnetized through electrodynamic influence, motion of electric fluids, motion and equilibrium of liquids, capillarity action, distribution of heat in liquids, and probability theory; in this last part, I will dwell upon several issues in which the famous author of 'Celestial Mechanics' was apparently wrong.

Of course this was far beyond what could be achieved by any one man but, by aiming at a grand scheme, he made major developments in a wide range of areas. He submitted Mémoire sur le Calcul des Variations des Integrales Multiples Ⓣ to the St Petersburg Academy of Sciences on 24 January 1834. This is an important work in the theory of partial differential equations and was reprinted in Crelle's Journal in 1836 and an English translation was made by Todhunter and published in 1861. In 1840 he wrote on ballistics introducing the topic to Russia. His important work on ordinary differential equations considered methods of solution of non-linear equations which involved power series expansions in a parameter alpha. Liouville had produced similar results. Also some of his results on heat were similar to results produced by Lamé and by Duhamel. He must be considered as the founder of the Russian school of theoretical mechanics. In addition to his important contributions to partial differential equations, he made significant advances to the theory of elasticity and to algebra publishing over 80 reports and giving lectures. His work on algebra was an extension of Abel's work on algebraic functions and their integrals.

From 1847 he was chief inspector for the teaching of mathematical sciences in military schools. He wrote many fine textbooks and established the conditions which allowed Chebyshev's school to flourish in St Petersburg. However, this huge contribution took up much of his time which he might otherwise have been able to devote to making further major progress in mathematical physics. Chebyshev wrote the following about Ostrogradski (see [17]):-

A man, without doubt, of brilliant mind, he did not accomplish even half of what he could have done if he were not "bogged down" with tiresome permanent pedagogic work.

Victor Katz write in [18]:-

Unfortunately, some of [Ostrogradski's] most important discoveries appear to have been totally ignored, at least in Western Europe. Not only did he give the first generalization of the change-of-variable theorem to $n$ variables, but he also first proved and later generalized the divergence theorem, wrote integrals of $n$-forms over $n$-dimensional "hypersurfaces," and ... gave the first proof of the change-of-variable theorem for double integrals using infinitesimal concepts. All of these results were eventually repeated by other mathematicians with no credit to Ostrogradski.

Ostrogradski was a big tall man with a loud voice. He appearance was quite formidable, especially with the loss of his right eye, but had a cheerful character and an exceptionally sharp mind. He passionately loved his native land, its people, and its culture. He loved classical French and Russian literature although his language of choice when at home was always Ukrainian. He loved to recite the monologues of Molière and Corneille but his favourite writer was Taras Hryhorovych Shevchenko, the Ukrainian poet and writer. Ostrogradski knew many of Shevchenko's works by heart and often recited them. Ostrogradski met Shevchenko in 1858 when the poet came to stay with him. In fact Shevchenko records in his diary (see [23]):-

... we went together with Semen to M V Ostrogradski's. A great mathematician, he greeted me with open arms as a countryman and, apparently, a long-lost relative. Bless him. Ostrogradski with his family goes to Malorossia [Ukraine] in summer. He says he would invite Semen to come with him, but fears that in the whole of the Poltava Guberniia there would not be enough bacon for his needs.

Semen, who is mentioned in this quote, is Semen Hulak-Artemovski 1813-1873), a famous Ukrainian composer and opera singer.

Finally let us mention the remarkable work that Ostrogradski did on insurance towards the end of his life. The circumstances are interesting and were described by Aleksei Nikolaevich Krylov (see [12]):-

In 1856, in accord with the Paris treatise, Russia was deprived of the right to have a fleet on the Black Sea. A large number of office workers had to be fired, and, to improve their circumstances, it was decided to establish a retirement fund at the Naval Department, and to begin paying pensions in 1859. Life insurance was then a novelty, and calculations connected with the work of the retirement funds, or with determining the amount of pensions in accord with the pertinent deductions from wages were known still less. For this reason, both mathematicians who were members of the St Petersburg Academy of Sciences, Ostrogradski and Bunyakovsky, were included in the committee charged with drawing up a charter of the fund. They have indeed made all the necessary calculations and provided their theoretical justification. The transactions of the committee were published without delay; they contain a remarkable note by Ostrogradski ...

We note that the Treaty of Paris of 1856 ended the Crimean war which Russia fought against Turkey supported by Britain and France. It was a war renowned for the incompetence of both sides. It must have pained Ostrogradski greatly to see Russia and France on opposing sides.

Always a Ukrainian at heart, Ostrogradski specified in his will that he should be buried in his home village of Pashennaya. In the summer of 1861, when he was bathing, it was noticed that he had an abscess on his back. He was operated on and the abscess was removed but his health rapidly deteriorated and he died in the January of the following year. We note that some sources give his date of death as 1861, rather than 1862, since the old style calendar date was 20 December 1861. His wishes were carried out and he was buried in the family vault at Pashennaya.