马丁·威廉·库塔Martin Wilhelm Kutta

马丁·威廉·库塔的父亲是库塔，母亲是Anna Koschinsky。他有一个比他大三岁的兄弟Karl，也很有才华，后来获得了博士学位。不幸的是，库塔的父母在他还年幼时就去世了，他和兄弟Karl一起前往布雷斯劳，由一位叔叔抚养。正是在布雷斯劳，他进入了文理中学。

中学毕业后，库塔于1885年至1890年在布雷斯劳大学学习。之后他前往慕尼黑，于1891年至1894年在该地的大学学习。在整个学习期间，数学始终是他的主修科目，但他兴趣广泛，还修习了语言、音乐和艺术课程。他终生保持着这些兴趣。他没有参加那些能使他获得在巴伐利亚中学任教资格的考试，而是更愿意协助大学教学。

库塔于1894年起在慕尼黑工业高等学校担任数学和物理助教。他后来成为瓦尔特·冯·戴克在慕尼黑工业高等学校的助手，为瓦尔特·冯·戴克的高等数学课程主持习题课。在此期间，他于1898至1899年在英国剑桥大学度过了一年。1900年，他凭借学位论文Beiträge zur näherungsweisen Integration totaler Differentialgleichungen Ⓣ（《全微分方程近似积分论》）获得慕尼黑大学博士学位，其学位论文导师为费迪南德·冯·林德曼和Gustav Bauer。该学位论文于次年出版。其中包含了如今著名的用于求解常微分方程的卡尔·龙格-库塔方法。

Sebastian Finsterwalder也在库塔工作的慕尼黑研究所任教，他对航空感兴趣。他把早期飞机的照片带到研究所，库塔由此对航空背后的数学，即空气动力学，产生了浓厚兴趣。他对这一课题的研究使他发现了关于机翼升力与其环量关系的重要公式。1902年，他向慕尼黑工业高等学校提交了关于空气动力学的教授资格论文（Habilitation）学位论文。1907年，他被提升为应用数学编外教授。两年后，即1909年，他转到耶拿大学，随后于次年受聘为亚琛工业高等学校正教授。1911年，他成为斯图加特工业高等学校正教授，并一直在那里任职，直至1935年退休。在斯图加特，库塔将教学重点放在工程师身上，他们从他富有启发的讲授中受益匪浅。

他最著名的是其博士论文和取得任教资格论文中所包含的工作。前者包含用于求解常微分方程的卡尔·龙格-库塔方法，而后者包含给出机翼升力的尼古拉·叶戈罗维奇·茹科夫斯基-库塔（或Joukowski-库塔）定理。尼古拉·叶戈罗维奇·茹科夫斯基独立于库塔作出了这些发现，并在库塔之后四年发表了他的版本。然而，库塔后来对空气动力学作出了进一步的重要贡献。我们特别要提到他关于这一课题的两篇重要出版物，由慕尼黑的巴伐利亚皇家科学院于1910年和1911年出版，其中一篇题为Über ebene Zirkulationsströmungen nebst flugtechnischen Anwendungen Ⓣ（《论平面环流，连同航空应用》），其中包含了他来自函数论的著名映射定理。

库塔还从事过另外两个课题：冰川研究和数学史研究。他对冰川的兴趣，如同他对空气动力学的兴趣一样，是由Sebastian Finsterwalder引发的。库塔根据在东阿尔卑斯山拍摄的照片对冰川进行了测量，还与他人合作绘制冰川覆盖区域的地图。关于另一个课题，即数学史，我们首先要说的是，这对库塔来说是一种非常自然的兴趣。毕竟，他对历史，特别是历史文献，有着深切的兴趣，因此当他在慕尼黑工业高等学校时，那里有一个活跃的数学史研讨班，这显然是一个会强烈吸引他的领域。他写了一篇关于约翰·沃利斯1659年关于积分和椭圆弧长的工作的论文。库塔的论文于1901年发表。

库塔除了对数学做出杰出贡献外，还是一个非凡的人。F Pfeiffer写道：-

……我一生中有幸结识了许多杰出的数学家……但我从未遇到过一位像库塔那样对如此多不同领域的心智活动有着如此深厚兴趣和熟悉程度的数学家……

然而，Pfeiffer也写道，尽管库塔兴趣广泛，但他是一个孤独的人。

Wilhelm Kutta's father was Wilhelm Kutta and his mother was Anna Koschinsky. He had a brother Karl, three years older than he was, who was also very talented and went on to obtain a doctorate. Tragically Kutta's parents died when he was still young and, together with his brother Karl, he went to Breslau to be brought up by an uncle. It was in Breslau that he attended the Gymnasium.

After graduating from the Gymnasium, Kutta studied at the University of Breslau from 1885 to 1890. Then he went to Munich where he studied at the university there from 1891 to 1894. Throughout his studies, mathematics was always his main subject, but he had broad interests, also taking courses in languages, music and art. He kept these interests throughout his life. He did not take the examinations which would qualify him to teach in Bavarian secondary schools, preferring to assist with university teaching.

Kutta was appointed to a post at the Technische Hochschule at Munich as an assistant in mathematics and physics from 1894. He later became an assistant to von Dyck at the Technische Hochschule conducting the exercise classes for von Dyck's course on Higher Mathematics. During this period he spent the year 1898-99 in England at the University of Cambridge. He was awarded his doctorate from the University of Munich for his thesis Beiträge zur näherungsweisen Integration totaler Differentialgleichungen Ⓣ in 1900, his thesis advisors being C L Ferdinand Lindemann and Gustav Bauer. The thesis was published in the following year. It contains the now famous Runge-Kutta method for solving ordinary differential equations.

Sebastian Finsterwalder also taught at the Institute in Munich where Kutta worked and he was interested in aviation. He brought photographs of early aircraft to the Institute and Kutta became fascinated by the mathematics behind aviation, namely aerodynamics. His studies of the topic led him discover important formulas relating to the lift on an aerofoil in terms of the circulation round it. He submitted his habilitation thesis on aerodynamics to the Technische Hochschule at Munich in 1902. He was promoted to extraordinary professor in Applied Mathematics in 1907. Two years later, in 1909, he moved to the University of Jena, then in the following year he was appointed as an ordinary professor at the Technische Hochschule at Aachen. He became an ordinary professor at the Technische Hochschule in Stuttgart in 1911 and remained there until he retired in 1935. At Stuttgart Kutta concentrated his teaching on engineers who benefited greatly from his inspiring presentation.

He is best known for the work contained in his doctoral thesis and that contained in his habilitation thesis. The former contains the Runge-Kutta method for solving ordinary differential equations while the latter contains the Zhukovsky-Kutta (or Joukowski-Kutta) theorem giving the lift on an aerofoil. Zhukovsky made the discoveries independently of Kutta, and published his version four years after Kutta. However, Kutta went on to make further important contributions to aerodynamics. Let us mention, in particular, his two important publications on this topic by the Königlich Bayerischen Akademie der Wissenschaften of Munich (Royal Bavarian Academy of Sciences) in 1910 and 1911, one of which was entitled Über ebene Zirkulationsströmungen nebst flugtechnischen Anwendungen Ⓣ and contains his famous mapping theorem from function theory.

Two further topics which Kutta worked on were research on glaciers and also research in the history of mathematics. His interest in glaciers was, like his interest in aerodynamics, brought about by Sebastian Finsterwalder. Kutta made measurements of glaciers working from photographs taken in the East Alps and also worked with others in constructing maps of the area covered by glaciers. On the other topic, namely the history of mathematics, our first comment is that this was a very natural interest for Kutta to have. He was, after all, deeply interested in history, particularly historical literature, so when at the Technische Hochschule at Munich where there was an active seminar on the history of mathematics, it was clearly an area which would strongly attract him. He wrote a paper on Wallis's 1659 work on integration and the length of an ellipse. Kutta's paper was published in 1901.

Kutta was a remarkable person quite apart from his outstanding contributions to mathematics. F Pfeiffer writes:-

... I had the good fortune in my life to become acquainted with a large number of outstanding mathematicians ..., but I never met a mathematician who had such a deep interest and familiarity with so many different areas of mental activity as Kutta ...

However, Pfeiffer also writes that despite Kutta's wide ranging interests, he was a lonely man.