康斯坦丁·卡拉西奥多里Konstantinos Carathéodory

康斯坦丁·卡拉西奥多里的父亲斯特凡诺斯卡拉西奥多里是一位奥斯曼希腊人，曾在柏林学习法律，之后在奥斯曼驻柏林、斯德哥尔摩和维也纳的使馆担任秘书。斯特凡诺斯娶了德斯皮娜·彼得罗科基诺，她来自一个定居马赛的希腊商人家庭。卡拉西奥多里出生时，全家人在柏林，因为斯特凡诺斯两年前已被任命为奥斯曼公使馆一等秘书。

卡拉西奥多里一家于1874至1875年在君士坦丁堡度过，卡拉西奥多里的祖父住在那里，当时斯特凡诺斯正在休假。1875年，他们前往布鲁塞尔，因为斯特凡诺斯被任命为奥斯曼驻那里的大使。在布鲁塞尔，卡拉西奥多里的妹妹卢利娅出生了。1895年对这个家庭来说是悲惨的一年，因为卡拉西奥多里的祖父在那一年去世，但更悲惨的是，卡拉西奥多里的母亲德斯皮娜在戛纳死于肺炎。卡拉西奥多里的外祖母承担起在比利时他父亲家中抚养卡拉西奥多里和卢利娅的任务。他们雇了一位德国女仆，教孩子们说德语。此时卡拉西奥多里已经能说法语和希腊语两种语言。

卡拉西奥多里于1881年在范德斯特克的一所私立学校开始接受正规教育。两年后他离开那里，随后与父亲一起访问了柏林，并在1883-84年和1884-85年的冬天在意大利里维埃拉度过。1885年回到布鲁塞尔后，他上了一年文法学校，在那里第一次对数学产生兴趣。1886年，他进入伊克塞尔皇家中学，并在那里学习直到1891年毕业。在这所学校期间，卡拉西奥多里两次获得比利时最佳数学学生奖。

在这个阶段，卡拉西奥多里开始接受军事工程师的训练。他从1891年10月到1895年5月在比利时军事学院学习，并从1893年到1896年在应用学校学习。1897年，土耳其和希腊之间爆发战争。这让卡拉西奥多里处于困难境地，因为他支持希腊人，而他的父亲为奥斯曼帝国政府服务。由于他是一名训练有素的工程师，他获得了英国殖民服务部门的工作。这份工作把他带到了埃及，在那里他参与建设阿西乌特水坝，直到1900年4月。在洪水导致施工停止的时期，他利用随身携带的一些教科书学习数学，例如卡米耶·若尔当的Cours d'AnalyseⓉ（分析教程）和乔治·萨蒙关于圆锥曲线解析几何的教材。他还参观了胡夫金字塔并进行了测量，他在1901年将这些测量写出来并发表。同年他还出版了一本书Egypt，其中包含大量关于该国历史和地理的信息。

卡拉西奥多里于1900年5月进入柏林大学，当时费迪南德·格奥尔格·弗罗贝尼乌斯和赫尔曼·阿曼杜斯·施瓦茨是那里的教授。他听了费迪南德·格奥尔格·弗罗贝尼乌斯的讲座，但受益最大的是赫尔曼·阿曼杜斯·施瓦茨每月两次主持的讨论班，当时赫尔曼·阿曼杜斯·施瓦茨正在讲授自己的文集。在柏林期间，他还与费耶尔成了密友。在听到哥廷根数学研究的出色报告后，他决定去那里继续学业，并于1902年夏季学期注册入学。卡拉西奥多里确实对哥廷根印象深刻，将其描述为[3]：-

……一个永久处于会议状态的国际数学家大会的所在地。

他研究变分法，深受大卫·希尔伯特和菲利克斯·克莱因的影响。1904年，他凭借学位论文Über die diskontinuierlichen Lösungen in der Variationsrechnung Ⓣ（《论变分法中的不连续解》）从哥廷根大学获得博士学位，该论文提交给雅各布·赫尔曼 赫尔曼·闵可夫斯基。他的口试于7月13日举行，当时菲利克斯·克莱因和卡尔·史瓦西还对他进行了应用数学和天文学副科的考试。他留在哥廷根撰写他的教授资格论文（Habilitation）论文Über die starken Maxima und Minima bei einfachen Integralen Ⓣ（《论简单积分中的强极大值与强极小值》），并于1905年3月5日提交。此后他在哥廷根担任Privatdozent直到1908年。

卡拉西奥多里在1907年夏天与父亲Stephanos在布鲁塞尔度过了一段时间。在健康状况恶化几个月后，Stephanos于1907年末去世。在波恩的爱德华·斯图迪曾提议卡拉西奥多里作为菲利浦·富特文勒的继任者，在认真考虑是否应离开哥廷根后，卡拉西奥多里前往波恩，并于1908年4月1日成为那里的编外讲师。在波恩，他与爱德华·斯图迪合作研究等周问题。1909年2月5日，他在君士坦丁堡与Euphrosyne卡拉西奥多里结婚。通过娶Euphrosyne——她是他的姑姑，比他小十一岁——卡拉西奥多里遵循了与近亲结婚的家族传统。

在波恩一年后，卡拉西奥多里被任命为汉诺威技术大学高等数学教授，从而成为Stäckel的继任者。同样，不久之后他又调动，并于1910年10月1日被任命为布雷斯劳技术大学高等数学讲席教授。这一次他担任该讲席两年半，然后从1913年4月1日起被任命为哥廷根大学教授。第一次世界大战的岁月对卡拉西奥多里及其家人来说是艰难的。他的大多数同事和学生都在军队服役，他在哥廷根感到孤立。1917年的饥荒打击沉重，但卡拉西奥多里继续在大学讲授课程。

在哥廷根五年后，他于1918年被任命到柏林大学，但在那里一年后，应希腊政府的要求，他于1919年12月31日终止了与柏林的合同，并前往希腊开展新的事业。此时，卡拉西奥多里和Euphrosyne已有两个孩子，Stephanos于1909年11月7日在汉诺威出生，Despina于1912年10月13日出生。卡拉西奥多里还接受了两家主要数学期刊编委会的编辑职位，从1909年起担任Rendiconti del Circolo Matematico di Palermo的编辑，从1914年起担任Mathematische Annalen的编辑。

希腊政府曾要求卡拉西奥多里在士麦那的塞翁建立第二所大学。然而，他也需要一个大学职位，因此于1920年6月2日被任命为雅典大学的分析学与高等几何学教授。7月14日，希腊政府公布了一项法案，在士麦那的塞翁建立一所希腊大学，不久其他人也被任命来协助卡拉西奥多里。7月28日，卡拉西奥多里被正式任命为士麦那的塞翁的伊奥尼亚大学的组织者，同时也是这所新大学的数学教授。1921年下半年，他广泛游历欧洲，为新大学购买书籍和设备。1922年9月，土耳其人进攻士麦那的塞翁，因此原定于当年10月大学开学的计划变得不可能。卡拉西奥多里得以挽救他如此努力建立起来的大学图书馆，以及他为理科各系购买的大部分设备，并乘坐一艘希腊战舰逃到雅典。他在雅典的国家大学和国家技术大学任教，直到1924年他搬到慕尼黑，填补费迪南德·冯·林德曼退休后留下的讲席。

1928年，卡拉西奥多里成为美国数学会的第一位访问讲师。一月，他与妻子乘船前往美国，在巡回演讲并在哈佛担任访问教授之后，于九月返回慕尼黑。次年，他收到斯坦福大学的职位邀请，并实际上于1929年9月被任命到那里。然而，他似乎只是利用这个邀请作为从慕尼黑获得更好薪水和条件的手段，而他确实做到了这一点。

1933年1月30日，希特勒领导的纳粹党在德国上台[3]：-

卡拉西奥多里几乎无法想象这会在一个拥有德国文化传统的国家发生。他起初倾向于以某种过于自信的轻蔑看待希特勒政权，而后来，当希特勒获得绝对权力时，他已无力抵抗。事实上，他在纳粹时代的行为与……受过教育的资产阶级如出一辙，后者尽管有人文主义背景，却绝大多数都放弃了对希特勒独裁、尤其是希特勒战争的任何反对，从而戏剧性地未能对德国和整个人类履行其历史责任。

卡拉西奥多里继续在慕尼黑担任他的职位，直到1938年8月退休。然而，他确实承担了许多使他前往其他地方的职责。特别是，他继续致力于重组希腊的大学，尤其是在1930-32年间，目的是将希腊在学术上融入欧洲。1936-37年，他再次访问美国，于1936年8月31日在美国数学会会议上发表演讲，以纪念哈佛大学三百周年，然后在威斯康星大学作为卡尔·舒尔茨纪念教授度过冬季学期。

第二次世界大战对卡拉西奥多里来说是一段艰难的时期。Georgiadou写道[3]：-

……在第二次世界大战期间，他参与了巴伐利亚科学院的程序。他没有参与国家社会主义运动，但他确实与纳粹党成员有联系[特别是哈塞、威海姆·布拉希开和威廉·聚斯]。他从未公开提及大屠杀或纳粹对希腊的罪行。……面对违反任何人类体面观念的罪行保持沉默，接受一个非法国家的权威，做出妥协并屈服于将犹太人驱逐出科学机构……然而，他费尽心思在战后重建数学作为德国的一门学科，从而为这个国家重新融入文明国家共同体做出贡献。

卡拉西奥多里对变分法、点集测度论和实变函数论做出了重要贡献。他为一阶偏微分方程与变分法之间的关系增添了重要结果。他为多变量函数论贡献了重要结果。他研究了单连通区域的conformal representations，并发展了边界对应理论。他还在热力学、狭义相对论、力学和几何光学方面做出了贡献。

卡拉西奥多里写了许多优秀的书，包括Lectures on Real Functions（1918）、Conformal representation（1932）、Calculus of Variations and Partial Differential Equations（1935）、Geometric Optics（1937）、Real functions Vol. 1: Numbers, Point sets, Functions（1939）以及Funktionentheorie，这是一部1950年出版的两卷本著作。

人们可能会想知道为什么这个列表中没有Real functions Vol. 2。事实上，卡拉西奥多里确实写了这部著作的第二卷，但它在1943年莱比锡轰炸期间在出版商Teubner处被毁。

奥斯卡·佩龙在1952年写道，卡拉西奥多里[8]：-

……没有发表他的许多想法；它们出现在其他人的作品中，尤其是在众多学生的作品中，这些学生由他引入科学研究的精髓和方法，其中部分人今天自己占据大学讲席。

他在哥廷根指导了两名博士生（汉斯·拉代马海尔和保罗·芬斯勒），在柏林指导了一名，在慕尼黑指导了17名。

Constantin Carathéodory's father, Stephanos Carathéodory, was an Ottoman Greek who had studied law in Berlin and then served as secretary in the Ottoman embassies in Berlin, Stockholm and Vienna. Stephanos had married Despina Petrocochino, who came from a Greek family of businessmen who had settled in Marseille. At the time of Constantin's birth, the family were in Berlin since Stephanos had been appointed there two years earlier as First Secretary to the Ottoman Legation.

The Carathéodory family spent 1874-75 in Constantinople, where Constantin's paternal grandfather lived, while Stephanos was on leave. Then in 1875 they went to Brussels when Stephanos was appointed there as Ottoman Ambassador. In Brussels, Constantin's younger sister Loulia was born. The year 1895 was a tragic one for the family since Constantin's paternal grandfather died in that year, but much more tragically, Constantin's mother Despina died of pneumonia in Cannes. Constantin's maternal grandmother took on the task of bringing up Constantin and Loulia in his father's home in Belgium. They employed a German maid who taught the children to speak German. Constantin was already bilingual in French and Greek by this time.

Constantin began his formal schooling at a private school in Vanderstock in 1881. He left after two years and then spent time with his father on a visit to Berlin, and also spent the winters of 1883-84 and 1884-85 on the Italian Riviera. Back in Brussels in 1885 he attended a grammar school for a year where he first became interested in mathematics. In 1886 he entered the high school Athénée Royal d'Ixelles and studied there until his graduation in 1891. Twice during his time at this school Constantin won a prize as the best mathematics student in Belgium.

At this stage Carathéodory began training as a military engineer. He attended the École Militaire de Belgique from October 1891 to May 1895 and he also studied at the É d'Application from 1893 to 1896. In 1897 a war broke out between Turkey and Greece. This put Carathéodory in a difficult position since he sided with the Greeks, yet his father served the government of the Ottoman Empire. Since he was a trained engineer he was offered a job in the British colonial service. This job took him to Egypt where he worked on the construction of the Assiut dam until April 1900. During periods when construction work had to stop due to floods, he studied mathematics from some textbooks he had with him, such as Jordan's Cours d'Analyse Ⓣ and Salmon's text on the analytic geometry of conic sections. He also visited the Cheops pyramid and made measurements which he wrote up and published in 1901. He also published a book Egypt in the same year which contained a wealth of information on the history and geography of the country.

Carathéodory entered the University of Berlin in May 1900 where Frobenius and Schwarz were professors. He attended Frobenius's lectures but benefited most from a twice monthly colloquium run by Schwarz who was lecturing on his collected works. He also became close friends with Fejér while at Berlin. After hearing excellent reports of mathematics research at Göttingen, he decided to continue his studies there and enrolled for the summer semester of 1902. Carathéodory was indeed impressed with Göttingen, describing it as the [3]:-

... seat of an international congress of mathematicians permanently in session.

He worked on the calculus of variations and was much influenced by both Hilbert and Klein. He received his doctorate in 1904 from Göttingen University for his thesis Über die diskontinuierlichen Lösungen in der Variationsrechnung Ⓣ which he submitted to Hermann Minkowski. His oral examination was held on 13 July when he was also examined in his subsidiary subjects of applied mathematics and astronomy by Klein and Schwarzschild. He remained at Göttingen to write his habilitation thesis Über die starken Maxima und Minima bei einfachen Integralen Ⓣ which he submitted on 5 March 1905. He then lectured as a Privatdozent at Göttingen until 1908.

Carathéodory had spent time in Brussels with his father Stephanos over the summer of 1907. After a few months of deteriorating health Stephanos died in late 1907. Study, at Bonn, had proposed Carathéodory as Furtwängler's successor and, after serious thought as to whether he should leave Göttingen, Carathéodory went to Bonn where he became a Provatdozent on 1 April 1908. At Bonn he collaborated with Study on isoperimetric problems. On 5 February 1909 he married Euphrosyne Carathéodory in Constantinople. In marrying Euphrosyne, who was his aunt and eleven years his junior, Carathéodory was following a family tradition of marrying close relatives.

After a year at Bonn, Carathéodory was appointed as Professor of higher Mathematics at the Technical University of Hanover, so becoming Stäckel's successor. Again it was not long before he moved on and on 1 October 1910 he was appointed to the Chair of Higher Mathematics at the Technical University of Breslau. This time he held the chair for two and a half years before being appointed professor at Göttingen from 1 April 1913. The years of World War I were difficult ones for Carathéodory and his family. Most of his colleagues and students served in the military and he was isolated in Göttingen. The famine of 1917 hit hard but Carathéodory continued to give lecture courses at the university.

After five years Göttingen he was appointed to the University of Berlin in 1918 but after he had been there for a year, at the request of the Greek government, he ended his contract with Berlin on 31 December 1919 and travelled to Greece to undertake a new venture. By this time Constantin and Euphrosyne had two children, Stephanos born in Hanover on 7 November 1909 and Despina born on 13 October 1912. Carathéodory had also accepted editorial positions on the boards of two major mathematics journals, the Rendiconti del Circolo Matematico di Palermo from 1909 and the Mathematische Annalen from 1914.

The Greek government had asked Carathéodory to establish a second university in Smyrna. However, he also required a university post so he was appointed as Professor of Analytical and Higher Geometry at the University of Athens on 2 June 1920. On 14 July the Greek government published a bill setting up a Greek University in Smyrna and soon others were appointed to assist Carathéodory. On 28 July Carathéodory was officially appointed as organiser of the Ionian University in Smyrna and also Professor of Mathematics at the new university. In the second half of 1921 he travelled widely through Europe purchasing books and equipment for the new university. The Turks attacked Smyrna in September 1922 and so the planned opening of the university in October of that year became impossible. Carathéodory was able to save the university library, which he had worked so hard to establish, and most of the equipment which he had purchased for the science departments, and escaped to Athens on a Greek battleship. He taught at Athens at the National University and the National Technical University until 1924 when he moved to Munich to fill the chair left vacant when Lindemann retired.

In 1928 Carathéodory became the first visiting lecturer of the American Mathematical Society. He sailed to the United States with his wife in January and after a lecture tour and time spent as a visiting professor at Harvard, returned to Munich in September. In the following year he received an offer of a post from Stanford university and was in fact appointed there in September 1929. However, he seems to have only been using this offer as a means of getting better salary and conditions from Munich, which indeed he managed to do.

On 30 January 1933 the National Socialist party led by Hitler came to power in Germany [3]:-

Carathéodory could hardly conceive how this could happen in a country with the cultural traditions of Germany. He initially tended to view the Hitler regime with a somewhat overconfident contempt, whereas later, when Hitler gained absolute power, he was incapable of resistance. His behaviour in the Nazi era was, in fact, identical with that of the ... educated bourgeois who, despite their humanistic background, in their overwhelming majority abstained from any opposition against Hitler's dictatorship, and especially Hitler's war, and thus dramatically failed to exercise their historic responsibility towards both Germany and humanity as a whole.

Carathéodory continued to hold his position in Munich until he retired in August 1938. However he certainly undertook many duties which took him to other places. In particular he continued to work on reorganising the Greek universities, particularly during 1930-32, with the aim of integrating Greece academically into Europe. In 1936-37 he made another visit to the United States, giving a lecture at the American Mathematical Society meeting to commemorate the tercentenary of Harvard University on 31 August 1936, then spending the winter semester at the University of Wisconsin as Carl Schurz Memorial Professor.

The World War II was a difficult time for Carathéodory. Georgiadou writes [3]:-

... during World War II he took part in the procedures of the Bavarian Academy of Sciences. He did not get involved in the movement for national socialism, but he did have connections with Nazi party members [particularly Hasse, Blaschke and Süss]. He never openly mentioned the holocaust or the Nazi crimes against Greece. ... kept silent in the face of crimes that violated any idea of human decency, accepted the authority of an illegal state, made his compromises and submitted to the expulsion of Jews from scientific institutions ... However, he took great pains to re-establish mathematics as an academic discipline in Germany after the war and thus to contribute to the reintegration of this country into the community of civilised nations.

Carathéodory made significant contributions to the calculus of variations, the theory of point set measure, and the theory of functions of a real variable. He added important results to the relationship between first order partial differential equations and the calculus of variations. He contributed important results to the theory of functions of several variables. He examined conformal representations of simply connected regions and he developed a theory of boundary correspondence. He also made contributions in thermodynamics, the special theory of relativity, mechanics, and geometrical optics.

Carathéodory wrote many fine books including Lectures on Real Functions (1918), Conformal representation (1932), Calculus of Variations and Partial Differential Equations (1935), Geometric Optics (1937), Real functions Vol. 1: Numbers, Point sets, Functions (1939), and Funktionentheorie, a 2 volume work published in 1950.

One might wonder why there is no Real functions Vol. 2 in this list. In fact Carathéodory did write the second volume of this work but it was destroyed while at the publisher Teubner during the bombing of Leipzig in 1943.

Perron, writing in 1952, remarks that Carathéodory [8]:-

... had not published many of his ideas; they result in others works, especially in those of the numerous students who were introduced by him to the spirit and ways of scientific research and who partly themselves occupy university chairs today.

He supervised two doctoral students at Göttingen (Hans Rademacher and Paul Finsler), one at Berlin, and 17 at Munich.