理查·科朗特Richard Courant

理查·科朗特的父亲是Siegmund Courant，母亲是Martha Freund。这是一个犹太家庭，但家庭内部存在紧张关系，尤其是Siegmund和他的哥哥Jakob之间。科朗特是Siegmund和Martha Courant孩子中的长子，在他们的第二个儿子出生后不久，Siegmund卖掉了他在Lublinitz家族企业中的股份，他们在Glatz买下了一家企业。他们搬到Glatz的那一年，第三个儿子出生了，当时科朗特三岁。

当科朗特九岁时，他的家庭再次搬迁，这次搬到了布雷斯劳。他的父亲Siegmund当时陷入了困境，因为他已同意购买另一家企业，之后却被他的哥哥Jakob说服毁约并搬到布雷斯劳。Siegmund在布雷斯劳的一家保险公司工作，科朗特在那里上学，进入了约翰·萨穆埃尔·柯尼希-Wilhelm 文理中学（Gymnasium）。由于此前几乎没有受过教育，科朗特起初在学校学习吃力，甚至在算术上“不尽如人意”。

当科朗特十四岁时，他开始做家教以挣足够的钱养活自己。此后不久，家庭遭遇悲剧，Jakob因严重的生意困难而自杀。其他家庭成员责怪科朗特的父母Siegmund和Martha。不久之后，Siegmund被宣布破产，接下来的两年对科朗特来说必定是极其艰难的，他一边上学，一边仍然靠做家教养活自己。1904年，科朗特的父母离开布雷斯劳，搬到柏林。科朗特挣的钱足以养活自己，即使此时他不得不在布雷斯劳租住住所。

尽管他尚未通过进入大学所必需的考试，科朗特于1905年离开学校，在布雷斯劳大学听数学和物理课程。1906年，他通过了大学入学考试并继续学习，此时正式成为一名学生。虽然他最初的意图是学习物理，但科朗特发现物理教学不如数学教学令人满意。Adolf Kneser、Georg 格奥尔格·兰茨贝格和Jakob Rosanes是他的数学老师，但科朗特仍然觉得，对他来说，他们的课程缺乏激情。

科朗特曾在布雷斯劳与两位同学Otto 奥托·特普利茨和Ernst 恩斯特·黑林格一起学习。这两人比科朗特年长几岁，学业也更进一步，此时已在哥廷根学习，并写信给科朗特，告诉他那里多么令人兴奋，尤其是因为大卫·希尔伯特。1907年春天，科朗特离开布雷斯劳，在苏黎世度过了一个学期，然后于1907年11月1日开始在哥廷根学习。

科朗特起初参加大卫·希尔伯特和赫尔曼·闵可夫斯基的课程，他还被允许参加这两位数学家的数学物理联合讨论班。他还参加了物理学和哲学的讲座。阿尔弗雷德·哈尔当时是大卫·希尔伯特的助手，但他在1908年完成了他的博士工作，那一年科朗特成为大卫·希尔伯特的助手。Reid写道（见[3]或[4]）：-

在科朗特担任大卫·希尔伯特助手的四个学期里，大卫·希尔伯特几乎完全致力于分析学科……科朗特对分析如鱼得水，仿佛那是他的自然元素。他未来所有的数学工作都将在大卫·希尔伯特在他学生时代介绍给他的学科中进行。

科朗特于1910年在哥廷根大学获得博士学位，导师是大卫·希尔伯特。他的学位论文题为Über die Anwendung des Dirichletschen Prinzipes auf die Probleme der konformen Abbildung Ⓣ（论约翰·彼得·古斯塔夫·勒热纳·狄利克雷原理在共形映射问题上的应用）。1910年末，他开始了为期一年的义务兵役。库尔特·亨泽尔为他提供了马尔堡的一个职位，让他从事教授资格论文（Habilitation）的工作，他本会接受，但就在他准备回复库尔特·亨泽尔时，他收到了大卫·希尔伯特的邀请，去哥廷根大学做特许任教资格。他接受了大卫·希尔伯特的邀请，但离开兵役后，他遇到了一些经济困难，因为他定期给柏林的父母寄生活费。科朗特又开始做家教以缓解经济压力。

为了他的特许任教资格论文，科朗特再次研究约翰·彼得·古斯塔夫·勒热纳·狄利克雷原理。论文被接受后，他于1912年2月23日作了就职演讲On existence proofs in mathematics。随后他成为哥廷根的数学讲师，直到第一次世界大战开始，但这对他的数学研究来说并不是一个特别多产的时期。1912年夏天，他与Nelly Neumann结婚，她是他布雷斯劳时期的朋友，也是一位数学家。

战争爆发时，科朗特被征召入伍。在他参战之前，他患了严重的伤寒。他回到部队，参与了战斗，战斗中他的一半战友阵亡。他提出了一个设计电报系统的建议，该系统使用大地作为导体，他被允许返回哥廷根讨论这个想法。在哥廷根，他的想法付诸实践，并生产了一个用于传输信号的盒子。科朗特带着他的通信盒回到了部队。

1915年9月27日，科朗特受伤并获准休假。不久之后，他与Nelly Neumann离婚。尽管科朗特重返前线，但说他的那件通信设备救了他的命大概并不夸张，因为科朗特花时间训练士兵使用它，从而避开了最惨烈的战斗。科朗特还抽出时间继续他的数学研究。当Springer于1918年1月创办新期刊Mathematische Zeitschrift时，科朗特在军中写成的一篇论文发表在第二期上。

战后，1918年12月，科朗特回到哥廷根。1919年1月22日，他与Carle 卡尔·龙格的女儿Nerina 卡尔·龙格结婚，几个月后开始在哥廷根担任privatdozent。对科朗特来说，这是一段研究活动密集的时期。1920年春，威廉·基灵退休后，他接受了明斯特的数学讲席。然而几个月后，大卫·希尔伯特和菲利克斯·克莱因安排他回到哥廷根，接替已去汉堡的埃里希·赫克。

1922年，科朗特创立了该大学的数学研究所，但在这个阶段，它只是一个概念，没有专门的建筑——直到1927年，建筑才得以建造。1922年，科朗特出版了一本关于函数论的书。这是与阿道夫·赫维兹的合著，尽管阿道夫·赫维兹已于1919年去世。基于阿道夫·赫维兹的讲义，科朗特加入了自己的材料。有些人，如Kellogg，不喜欢这本书。然而，当时还是学生的卡特·佛莱德里克斯写道：-

……科朗特那一节，第三章——当我拿到那一章时，我一个早晨开始读，从早读到晚，没有停歇。这是我读过的最令人惊叹的数学书。

科朗特在这一时期发表的其他重要数学工作是关于eigenvalue的，特别是存在性证明。1924年，他与大卫·希尔伯特合作出版了一部重要著作Methoden der mathematischen Physik Ⓣ（数学物理方法）。同样，科朗特是唯一作者，而大卫·希尔伯特的贡献是以讲义的形式。此时，大卫·希尔伯特的兴趣已从数学物理转移，他对科朗特正在撰写这部著作只有一时的兴趣。1925年，在卡特·佛莱德里克斯作为他的助手的情况下，科朗特开始撰写科朗特-大卫·希尔伯特的第二卷。

到1928年，前一年动工的新数学研究所接近完工。它于1929年12月2日正式落成。1932年，科朗特应邀赴美国讲学，访问了那里的主要大学。

1933年纳粹上台时，科朗特被逐出哥廷根。1933年1月30日希特勒上台，3月，科朗特离开哥廷根，前往瑞士阿罗萨度春假。他不仅希望度假，还希望在远离数学研究所职务期间完成科朗特-大卫·希尔伯特的第二卷。卡特·佛莱德里克斯与科朗特在一起帮助撰写该书。然而，政治事件毁掉了他的计划，他根据研究所成员的建议于4月初回到哥廷根。1933年4月7日，《公务员法》提供了将犹太教师从大学中清除的手段，当然也借此将犹太血统者从其他职位上清除。所有非雅利安血统的公务员（祖父母中有一人信奉犹太教即被视为非雅利安人）都应被退休。然而，有一项豁免条款，豁免那些在第一次世界大战中为德国作战的非雅利安人。科朗特当然符合豁免条款，他期望自己不受影响。

5日，May Courant收到一封正式信函，通知他已被强制休假。赫尔曼·外尔被任命为数学研究所所长，他竭尽全力让科朗特复职。与此同时，人们试图为科朗特在其他地方提供职位。有人向他提供了伊斯坦布尔的一个职位，他认为值得为此跑一趟，但最终拒绝了。他应邀去英国剑桥访问一年，于是申请休假（他本已被强制休假，却还要申请，这略显奇怪）。他的强制休假被改为普通休假，科朗特前往英国，次年去了纽约大学。

在纽约的最初几个月很艰难。他薪水很低，教职员工中没有有水平数学家，而且他发现他教的学生基础非常差。然而，他尽可能多地邀请数学家来此讲学。到1935年6月，他获得了一个永久职位，并有人建议他可以尝试建立一个强大的研究生院。1936年，他获得了纽约大学的教授职位，并受命建立一个研究生中心。他再次与他的学生们进行了大体成功的合作。为了使这个项目成功，他也必须与教育和金融机构的管理人员相处融洽，尽管他能迷住这些人，但他也可能冒犯他们，尽管他并不总是意识到自己已经这样做了。

科朗特在纽约以哥廷根模式建立了一个应用数学研究中心，做出了许多新任命，例如卡特·佛莱德里克斯。许多在第二次世界大战开始前几年被迫离开德国的数学家，在科朗特的帮助下在美国获得了职位。

1940-41年，他与来自哈佛大学的年轻拓扑学家赫伯特·罗宾斯合作撰写了一本新书。这本书是What is mathematics?，它记录了科朗特的数学观点。正如他在序言中所写，他的目标是让读者：-

……从最基本的元素出发，沿着一条笔直的道路，到达能够俯瞰现代数学的实质和驱动力的制高点。

这本书在销量和评论两方面都极为成功。

也许科朗特这一时期最著名的数学成果之一是他的“有限元方法”。事实上，这种方法首次出现在1922年阿道夫·赫维兹-科朗特书中波恩哈德·黎曼映射定理一个版本的存在性证明中。这个想法再次作为脚注出现在1924年科朗特-希尔伯特的出版物Methoden der mathematischen Physik Ⓣ（数学物理方法）中。然而，作为数值方法的首次应用是由科朗特在1943年解决一个扭转问题时给出的。“有限元方法”这个名称并非源于科朗特，而是直到20世纪60年代才出现。

从1947年直到去世，科朗特几乎每年夏天都访问德国。然而，他似乎从未考虑过回到那里，因为那时他似乎已在美国牢牢扎根。从1953年到1958年，他是纽约大学新成立的数学科学研究所的所长，该研究所于1964年以他的名字命名为科朗特研究所。可以说，这对科朗特来说是一项远比哥廷根数学研究所更大的成就。在哥廷根，他来到一个充满杰出数学人才的地方。在纽约，他白手起家，此前他经历了哥廷根研究所因纳粹的种族政策而几乎被摧毁。他能够从无到有创建科朗特研究所，是一项相当非凡的成就。1971年11月19日，他中风，被送往新罗谢尔的医院，两个月后在那里去世。

Richard Courant's father was Siegmund Courant and his mother was Martha Freund. It was a Jewish family but there were tensions in it, particularly between Siegmund and his elder brother Jakob. Richard was the eldest of Siegmund and Martha Courant's children and soon after the birth of their second son Siegmund sold his share in the family business in Lublinitz and they bought a business in Glatz. A third son was born in the year they moved to Glatz, Richard being three at the time.

When Richard was nine his family moved again, this time to Breslau. His father Siegmund was now in problems since he had agreed to buy another business before being persuaded by his brother Jakob to break the contract and move to Breslau. Siegmund worked for an insurance company in Breslau and Richard attended school there, entering the König-Wilhelm Gymnasium. With little previous education Richard struggled at school at first, even being "less than satisfactory" at arithmetic.

When Richard was fourteen years old he began to tutor to make enough money to support himself. Soon after this tragedy struck the family when Jakob, in severe business difficulties, committed suicide. Other members of the family blamed Richard's parents Siegmund and Martha. Shortly after Siegmund was declared bankrupt and the following two years must have been ones of extreme difficulty for Richard, attending school and still supporting himself tutoring. In 1904 Richard's parents left Breslau and moved to Berlin. Richard was earning enough to support himself, even now that he had to rent accommodation in Breslau.

Although he had not yet passed the examinations necessary to enter university, Richard left school in 1905 and attended classes in mathematics and physics at the University of Breslau. In 1906 he passed the university entrance examinations and continued to study, now officially a student. Although his original intention was to study physics, Courant found the teaching less satisfactory than that in mathematics. Adolf Kneser, Georg Landsberg and Jakob Rosanes were among his mathematics teachers but Courant still found that, for him, their courses lacked excitement.

Courant had studied at Breslau with two fellow students Otto Toeplitz and Ernst Hellinger. These two, several years older than Courant and further on with their education, were by this stage studying at Göttingen and wrote to Courant telling him how exciting it was there, particularly because of Hilbert. In the spring of 1907 Courant left Breslau, spent a semester at Zürich, then began his studies at Göttingen on 1 November 1907.

At Göttingen Courant began by attending courses by Hilbert and Minkowski and he was also allowed to attend the joint seminar of the two mathematicians on mathematical physics. He also attended lectures on physics and philosophy. Haar was Hilbert's assistant at this time but he completed his doctoral work in 1908 and in that year Courant became Hilbert's assistant. Reid writes (see [3] or [4]):-

During the four semesters that Courant served as Hilbert's assistant, Hilbert was devoting himself almost exclusively to subjects in analysis ... Courant took to analysis as if it were his natural element. All his future mathematical work was to be done in subjects to which he was introduced during his student days by Hilbert.

Courant obtained his doctorate from Göttingen in 1910 under Hilbert's supervision. His thesis was entitled Über die Anwendung des Dirichletschen Prinzipes auf die Probleme der konformen Abbildung Ⓣ. Late in 1910 he began his year of compulsory military service. Hensel offered him a place at Marburg to work for his habilitation which he would have accepted had he not received an offer from Hilbert to study at Göttingen for the habilitation just as he was about to reply to Hensel. He accepted Hilbert's offer but once he left military service he had some financial problems since he was sending a regular allowance to his parents in Berlin. Courant began to tutor again to help out his finances.

For his habilitation thesis Courant again worked on the Dirichlet principle. The thesis accepted, he gave his inaugural lecture On existence proofs in mathematics on 23 February 1912. He then became a mathematics lecturer at Göttingen until the start of World War I but this was not a particularly productive period for him mathematically. He had married Nelly Neumann in the summer of 1912, a friend from his days in Breslau who was also a mathematician.

When war broke out Courant was drafted into the army. Before he saw action he became seriously ill with typhoid fever. He returned to his unit and was involved in fighting which saw half his fellow soldiers killed. He made a suggestion about designing a telegraph system which used the earth as a conductor and he was allowed to return to Göttingen to discuss the idea. At Göttingen his idea was put into practice and a box to transmit signals produced. Courant returned to his unit with his communications box.

On the 27 September 1915 Courant was wounded and received leave. Soon after he was divorced from Nelly Neumann. Although Courant returned to the front it is probably no exaggeration to say that his piece of communications equipment saved his life, for Courant spent time training men to use it and avoided the worst of the fighting. Courant found time to carry on with his mathematics research too. When Springer started the new journal Mathematische Zeitschrift in January 1918, one of Courant's papers, written while he was in the army, appeared in the second issue.

After the war, in December 1918, Courant returned to Göttingen. He married Nerina Runge, Carle Runge's daughter, on 22 January 1919 and a couple of months later began teaching as a privatdozent at Göttingen. This was a period of intense research activity for Courant. In the spring of 1920 he accepted the chair of mathematics at Münster when Killing retired. However, after a few months Hilbert and Klein arranged for him to return to Göttingen to replace Hecke who had gone to Hamburg.

In 1922 Courant founded the university's Mathematics Institute but at this stage it was only a concept with no special building - it was 1927 before the building was constructed. In 1922 Courant published a book on function theory. It was a joint publication with Hurwitz, although Hurwitz had died in 1919. Based on Hurwitz's lectures, Courant added material of his own. Some people such as Kellogg disliked the book. However, Friedrichs who was a student at the time wrote:-

... the Courant section, the third chapter - when I got hold of that chapter, I started reading one morning, I read morning and night without stopping. It was the most breathtaking book I have ever read in mathematics.

Other important mathematics which Courant published around this time was work on eigenvalue, in particular proofs of existence. In 1924 he published, jointly with Hilbert, an important text Methoden der mathematischen Physik Ⓣ. Again Courant was the sole author and the contribution from Hilbert was in the form of lecture notes. Hilbert's interests had moved away from mathematical physics by this time and he did not take any more than a passing interest that Courant was writing the text. In 1925, with Friedrichs as his assistant, Courant began work on a second volume of Courant-Hilbert.

By 1928 the new Mathematics Institute, begun the previous year, neared completion. It was formally dedicated on 2 December 1929. Invited to lecture in the United States in 1932 Courant visited the major universities there.

Courant was expelled from Göttingen when the Nazis came to power in 1933. On 30 January 1933 Hitler came to power and in March Courant left Göttingen for his spring holiday in Arosa in Switzerland. He had been hoping not only to have a holiday, but to complete the second volume of Courant-Hilbert when away from his duties in the Mathematics Institute. Friedrichs was with Courant to help with the book. Political events destroyed his plans, however, and he returned to Göttingen at the beginning of April on advice from members of the Institute. On 7 April 1933 the Civil Service Law provided the means of removing Jewish teachers from the universities, and of course also to remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired. However, there was an exemption clause which exempted non-Aryans who had fought for Germany in World War I. Certainly Courant came under the exemption clause and he expected to be unaffected.

On 5 May Courant received an official letter telling him he was on forced leave. Weyl was made director of the Mathematics Institute and he made every effort to have Courant reinstated. Meanwhile attempts were made to offer Courant posts elsewhere. He was offered a position in Istanbul, he considered it enough to make a trip there, but eventually turned it down. Invited to Cambridge in England for a one year visit, he applied for leave (slightly strange that he had to do so since he was already on forced leave). His forced leave was changed to ordinary leave and Courant left for England, going to New York University the following year.

The first few months in New York were difficult. He was poorly paid, there were no mathematicians of quality on the staff and the students he taught he found very badly prepared. However, he invited as many mathematicians as possible to lecture there. By June 1935 he had been offered a permanent post and it was suggested that he might try to build a strong graduate school. In 1936 he was offered a professorship at New York University and given the task of building a graduate centre. Again he had a mostly successful collaboration with his students. He had to get on well too with administrators in educational and financial institutions for the project to succeed and although he could charm such people he could also offend them, though he did not always realise that he had done so.

Courant built up an applied mathematics research centre in New York based on the Göttingen model, making many new appointments such as Friedrichs. Numerous mathematicians who were forced to leave Germany in the years before the start of World War II, were given help by Courant to obtain positions in the United States.

In 1940-41 he worked on a new book with Herbert Robbins, a young topologist from Harvard. This book was What is mathematics? and it records Courant's views of mathematics. His aim, as he writes in the Preface, is to set the reader:-

... on a straight road from the very elements to vantage points from which the substance and driving force of modern mathematics can be surveyed.

The book was highly successful both in terms of sales and reviews.

Perhaps one of Courant's most famous pieces of mathematics from around this time was his "finite element method". In fact this method first appeared in an existence proof of a version of the Riemann mapping theorem in the Hurwitz-Courant book of 1922. The idea appeared again as a footnote in the Courant-Hilbert publication Methoden der mathematischen Physik Ⓣ in 1924. The first application as a numerical method, however, was given by Courant in 1943 in his solution of a torsion problem. The name "finite element method" was not due to Courant, however, but appears only in the 1960s.

From 1947 until his death Courant visited Germany almost every summer. He never seems to have considered returning there, however, for he seemed by then firmly established in the United States. From 1953 to 1958 he was director of his new Institute of Mathematical Sciences at New York University, which in 1964 was named the Courant Institute after him. It is fair to say that this was a far greater achievement for Courant than was the Mathematics Institute at Göttingen. At Göttingen he arrived in a place filled with mathematicians of outstanding talent. In New York he began with nothing, after experiencing almost the destruction of his Göttingen Institute through the racial policies of the Nazis. That he was able to create the Courant Institute starting from nothing is a quite phenomenal achievement. He suffered a stroke on 19 November 1971, was taken to hospital in New Rochelle where he died two months later.