理查德·冯·米泽斯Richard von Mises

理查德·冯·米泽斯出生于利沃夫，当时该地处于奥地利统治之下，称为伦贝格。他的父亲Arthur Edler 冯·米泽斯是奥地利国家铁路的技术专家，母亲是Adele von Landau。冯·米泽斯是家中次子，长子是Ludwig 冯·米泽斯，后来与冯·米泽斯一样出名。Ludwig比冯·米泽斯大约十八个月，后来成为经济学家，对经济理论中的自由主义有所贡献，并将他对消费者权力的信念作为该理论的重要组成部分。冯·米泽斯还有一个弟弟，幼年夭折。

冯·米泽斯走上的是技术道路，在维也纳技术高等学校学习数学、物理和工程。毕业后，他被任命为乔治·哈梅尔在布吕恩的助手。布吕恩市今天称为布尔诺，位于捷克共和国东南部。直到第二次世界大战前，居民主要是德国人，尽管今天他们主要是捷克人。Von 冯·米泽斯于1907年在维也纳获得博士学位，次年从布吕恩获得他的教授资格论文（Habilitation），取得讲授工程和机械制造的资格。

从1909年到1918年，他是斯特拉斯堡（当时称为Strassburg）的应用数学教授，尽管这段时期被第一次世界大战打断。甚至在战争爆发前，冯·米泽斯就已取得飞行员资格，并于1913年开设了第一门关于动力飞行的大学课程。战争爆发时，冯·米泽斯加入奥匈军队并驾驶飞机。战前他曾讲授飞机设计，现在他将此付诸实践，带领一个团队于1915年为奥地利军队制造了一架600马力的飞机。

战争结束后，冯·米泽斯 被任命为德累斯顿技术学院新设立的流体力学和空气动力学讲席教授。他于1919年被任命后不久再次调动，这次是到柏林大学，成为那里新成立的应用数学研究所所长。艾尔哈德·施密特 曾在1918年主张设立该研究所：-

数学方法对实际生活的渗透，是战前技术发展的结果，尤其是战争期间对……数学家的意外需求，使得在最大的普鲁士大学设立应用数学成为不可否认的必要……然而，在大学学生中，经常可以发现一种观点，认为应用数学是一门次要的学科，不需要全力以赴。要创造新的传统，就需要一位公认的重要人物。这样的人物只能通过正教授职位来吸引。

艾尔哈德·施密特 的这些话显示出极大的智慧，当局确实设立了正教授职位，并为第一任持有者 冯·米泽斯 做出了富有灵感的选任。亚历山大·奥斯特洛夫斯基 在1965年的一次讲座中写道（例如见[16]）：-

只有随着 冯·米泽斯 被任命到柏林大学，第一个具有广泛影响力的严肃德国应用数学学派才得以诞生。Von 冯·米泽斯 是一个极具活力的人，同时像 卡尔·龙格 一样多才多艺。他尤其精通技术领域。

应用数学研究所在他的掌控下蓬勃发展。1921年，他创办了期刊Zeitschrift für Angewandte Mathematik und Mechanik，并成为该期刊的主编。在第一期中，他撰写了一篇引言，强调应用数学的广泛范围，并指出纯粹数学与应用数学之间的界限并非固定不变，而是随着“纯粹数学”的不同领域在实际情境中找到应用而随时间变化。

他在大学为应用数学设立了一套新的课程，涵盖六个学期，包括数学在天文学、大地测量学和技术中的应用。这并非一门“轻松的选择”，冯·米泽斯特意强调应用数学与纯粹数学同样严谨，需要[13]：-

……一个尽可能广泛通用的数学模型，其论证可以清晰、优雅且严谨地进行。

他的研究所迅速成为probability、统计学、微分方程的数值解、弹性力学和空气动力学等领域的研究中心。冯·米泽斯也是一位出色的讲师。他的学生之一洛萨·考拉兹写道：-

我于1930年在柏林入学。……冯·米泽斯教授博士[讲授]了关于应用分析的出色、非常清晰且富有启发性的讲座……

由考拉兹撰写的论文[8]讨论了冯·米泽斯在数值数学方面的工作，讨论了他创办期刊Zeitschrift für Angewandte Mathematik und Mechanik，并审视了冯·米泽斯在20世纪20年代和30年代初提升应用数学地位时所面临的困难。

然而，1933年1月30日，希特勒上台，1933年4月7日的《公务员法》提供了将犹太教师从大学中清除的手段，当然也提供了将犹太裔从其他职位上清除的手段。所有非雅利安裔的公务员（只要有一位祖父母信奉犹太教，此人即被视为非雅利安裔）都应被解职。冯·米泽斯从某种意义上说并非犹太人，因为他在宗教上是罗马天主教徒。他仍然属于该法案的非雅利安定义范围，但有一项豁免条款，豁免了那些在第一次世界大战中战斗过的非雅利安人。冯·米泽斯当然符合这一条款，这本来可以使他在1933年保住他在柏林的讲席。他相当正确地认识到，豁免条款不会长久地保护他。1933年6月10日，他就一位正在寻找职位的年轻德国人Walter Tollmien写信给von 西奥多·冯·卡门：-

我必须告知您，任何形式的就业或奖学金之类的不可撤销的前提条件是，他须以名誉担保声明他的四位祖父母都是雅利安人，特别是非犹太裔。……我相信，在有利的情况下，前景并不那么糟糕，因为根据现行法律，之前所有候选人中的很大一部分确实可以被排除。

Von 西奥多·冯·卡门将信转寄给了Tollmien，并在背面写道“确实是我们时代的一份文献”！

冯·米泽斯把土耳其的一个讲席职位视为摆脱他在德国困境的一条出路，但他试图确保自己的养老金权利得到保留。1933年10月12日，他写信给该部解释说，如果他接受土耳其的职位，将对德国有利，并且他应该被允许为其24年的服务保留养老金权利。他收到的答复是，他将不得不放弃所有薪水、养老金或对其受抚养人的支持的权利。他在给该部的另一封信中抗议说，他在法律上有权享有他不准备放弃的权利。纳粹分子Theodor Vahlen尽管学术素质不佳，却想接任研究所所长。他向冯·米泽斯承诺，如果他支持他继任研究所所长，那么他将确保冯·米泽斯不会失去养老金权利。

1933年10月，冯·米泽斯写信支持Vahlen作为他的继任者。冯·米泽斯的学生考拉兹写道：-

我在1933年11月参加了国家考试（Staatsexamen）考试，冯·米泽斯教授在他离开的前一天对我进行了考试。同一天，他与我谈了大约一个小时，为我的进一步研究提供建议……

Vahlen于1933年12月被任命为研究所所长。在伊斯坦布尔就任新讲席后，冯·米泽斯于1934年1月收到一封信，完全剥夺了他的所有权利。这是冯·米泽斯一直感到极其愤愤不平的事情，他在1953年去世前不久写信给部里，仍然试图恢复他的权利。

数学家Hilda Geiringer于1934年跟随他去了伊斯坦布尔。在那里她被任命为数学教授。

1938年，凯末尔·阿塔图尔克去世，土耳其那些从纳粹手中逃出的人担心他们的避风港会变得不安全。1939年，冯·米泽斯离开土耳其前往美国。他成为哈佛大学教授，并于1944年被任命为那里的Gordon-McKay空气动力学与应用数学教授。Geiringer跟随他去了美国，他们于1943年结婚。

冯·米泽斯从事流体力学、空气动力学、航空学、统计学和概率论的研究。他在去世前不久将自己的工作分为八个领域：实用分析、积分和微分方程、力学、流体力学和空气动力学、构造几何、概率演算、统计学和哲学。他引入了一种应力张量，用于材料强度的研究。他对飞机机翼理论的研究使他开始探究湍流。他的许多工作涉及数值方法，这促使他在数值分析中开发新技术。他最著名、同时也最具争议的工作是在概率论方面。

他在由约翰·维恩开创的频率分析领域取得了相当大的进展。他把约翰·维恩极限的思想与随机事件序列结合起来。我们在上面引用过的亚历山大·奥斯特洛夫斯基在同一讲演中写道（例如见[16]）：-

由于他充满活力的个性，他偶尔犯下的重大错误在某种程度上得到了容忍。人们甚至原谅了他的概率论。

然而，亚历山大·奥斯特洛夫斯基的这一评价相当严厉，许多人认为冯·米泽斯的理论在该学科的发展中很重要。在安德雷·柯尔莫哥洛夫的测度论方法几乎被所有统计学家所青睐、胜过冯·米泽斯的极限频率理论方法之后，又出现了向冯·米泽斯思想的回归，并有人试图把它们纳入安德雷·柯尔莫哥洛夫的测度论方法中，后者本人于1963年写道：-

……概率的数学理论结果适用于真实“随机现象”的基础，必须依赖于某种形式的概率频率概念，其不可避免的性质已由冯·米泽斯以有力的方式确立。

在论文[18]中讨论了：-

……冯·米泽斯在其概率论方法背景下的随机序列概念。[作者声称]接受安德雷·柯尔莫哥洛夫的竞争性公理化是由于一种关于概率的不同直觉占了上风，正如鞅的概念所说明的那样。

Phillip 菲利普·弗兰克在[4]中写道：-

...在审视冯·米泽斯的工作时...我们不能不认识到一个完整的研究谱系，从科学的哲学意义延伸到数值计算的实用方法。...冯·米泽斯一直是一个真正胸怀宽广的人...尽管他的主题范围广泛，他的工作显示出极大的内在统一性：从一个确定的中心出发，它分支为对各种各样问题的系统研究。...冯·米泽斯根据一个非常确定的观点选择主题，这个观点由他对每一项彻底科学研究本质和方法的想法所决定。

冯·米泽斯的书Positivism: A Study in Human Understanding（1951年）中，他表达了对科学和生活的看法。他在书中赞同一种实证主义学说，说道：-

实证主义并不声称所有问题都能理性地回答，正如医学并非基于所有疾病都可治愈的前提，或者物理学并非从所有现象都可解释的假设出发。但仅仅因为某些问题可能没有答案，并不足以成为不去寻找答案或不使用那些可获得的答案的理由。

这种对哲学的兴趣只是冯·米泽斯在数学领域之外的兴趣之一。另一个是他曾是奥地利诗人Rainer Maria Rilke（1875-1926）的国际权威。

1950年，冯·米泽斯被授予东德科学院的荣誉会员资格。这对冯·米泽斯来说很困难，特别是在麦卡锡时代的美国，任何与共产主义的联系都会被视为严重罪行。他在1950年9月15日写的一封信中遗憾地拒绝了：-

我非常乐意接受这一提名，以纪念我在柏林的教学活动，从而重新建立长期将我同德国科学生活联系在一起的纽带。遗憾的是，德国目前的状况以及这个国家的状况使得接受这样一种荣誉可能被解释为我的一种政治表态。……我只是在外部环境的压力下放弃接受这一提名，而我在各方面都将其视为极大的荣誉。

Richard von Mises was born in Lviv when it was under Austrian control and known as Lemberg. His father, Arthur Edler von Mises, worked for the Austrian State Railways as a technical expert and his mother was Adele von Landau. Richard was the second son of the family, the elder son being Ludwig von Mises who went on to become as famous as Richard. Ludwig, who was about eighteen months older than Richard, went on to become an economist who contributed to liberalism in economic theory and made his belief in consumer power an important part of that theory. Richard also had a younger brother, who died as an infant.

It was on the technical course that von Mises embarked, studying mathematics, physics and engineering at the Technische Hochschule in Vienna. After graduating he was appointed as Georg Hamel's assistant in Brünn. The city of Brünn is today called Brno in the south-eastern Czech Republic. Up to World War II the inhabitants were predominantly German, although today they are now mainly Czech. Von Mises was awarded a doctorate from Vienna in 1907 and the following year he was awarded his habilitation from Brünn, becoming qualified to lecture on engineering and machine construction.

He was professor of applied mathematics at Strasbourg (then called Strassburg) from 1909 until 1918, although this was a period which was interrupted by World War I. Even before the outbreak of the war von Mises had qualified as a pilot and he gave the first university course on powered flight in 1913. When war broke out von Mises joined the Austro-Hungarian army and piloted aircraft. He had lectured on the design of aircraft before the war and he now put this into practice leading a team which constructed a 600-horsepower plane for the Austrian army in 1915.

After the end of the war von Mises was appointed to a new chair of hydrodynamics and aerodynamics at the Technische Hochschule in Dresden. Appointed in 1919 he soon moved again, this time to the University of Berlin to become the director of the new Institute of Applied Mathematics which had been set up there. Schmidt had argued for the setting up of the Institute in 1918:-

The pervasion of practical life by mathematical methods, as a result of the development of technology before the war and, above all, the unexpected need for ... mathematicians during the war make it an undeniable necessity to install applied mathematics at the largest Prussian university... Among university students, however, one frequently finds the opinion that applied mathematics is a subject of inferior importance, which does not require one's full attention. to create a new tradition, it needs an important personality of approved name. Such a personality can only be attracted by a full professorship.

These words by Schmidt show great wisdom, and the authorities did indeed create the full professorship and made an inspired choice for the first holder in von Mises. Ostrowski wrote in a 1965 lecture (see for example [16]):-

Only with the appointment of Richard von Mises to the University of Berlin did the first serious German school of applied mathematics with a broad sphere of influence come into existence. Von Mises was an incredibly dynamic person and at the same time amazingly versatile like Runge. He was especially well versed in the realm of technology.

The Institute of Applied Mathematics flourished under his control. In 1921 he founded the journal Zeitschrift für Angewandte Mathematik und Mechanik and he became the editor of the journal. In the first edition he wrote an introduction stressing the wide range of applied mathematics and also the fact that the line between pure and applied mathematics is not a fixed one, but one which changes over time as different areas of "pure mathematics" find applications in practical situations.

He set up a new curriculum for applied mathematics at the university which spread over six semesters and included applications of mathematics to astronomy, geodesy and technology. It was not a "soft option" and von Mises went out of his way to stress that applied mathematics was every bit as rigorous as pure mathematics requiring [13]:-

... a mathematical model of the widest possible generality, where the argument could be made with clarity, elegance, and rigour.

His Institute rapidly became a centre for research into areas such as probability, statistics, numerical solutions of differential equations, elasticity and aerodynamics. Von Mises was also an excellent lecturer. Collatz, one of his students, wrote:-

I was enrolled in Berlin in 1930. ... Professor Dr Richard von Mises [gave] excellent, very clear and stimulating lectures on applied analysis ....

The paper [8], written by Collatz, discusses von Mises' work on numerical mathematics, discusses his founding of the journal Zeitschrift für Angewandte Mathematik und Mechanik and looks at the difficulties faced by von Mises in bringing up the status of applied mathematics during the 1920s and early 1930s.

On 30 January 1933, however, Hitler came to power and 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. Von Mises in one sense was not Jewish for he was a Roman Catholic by religion. He still fell under the non-Aryan definition of the act but there was an exemption clause which exempted non-Aryans who had fought in World War I. Von Mises certainly qualified under this clause and it would have allowed him to keep his chair in Berlin in 1933. He realised, quite correctly, that the exemption clause would not save him for long. On the 10 June 1933 he wrote to von Kármán about a young German, Walter Tollmien, who was looking for a position:-

I have to advise you that the irrevocable prerequisite for any kind of employment or scholarship or suchlike is to make a statement on his word of honour that his four grandparents are Aryan and in particular are of non-Jewish descent. ... I believe that in a favourable case the prospects are not quite so bad as indeed a large part of all the previous candidates can be omitted under the present law.

Von Kármán forwarded the letter to Tollmien, writing "Indeed a document of our time" on the back!

Von Mises saw an offer of a chair in Turkey as a way out of his predicament in Germany but he tried to ensure that his pension rights were preserved. On 12 October 1933 he wrote to the ministry explaining that it would benefit Germany if he accepted a post in Turkey and that he should be allowed to retain his pension rights for his 24 years of service. He received the reply that he would have to relinquish all rights of a salary, a pension or support for his dependants. He protested in a further letter to the Ministry that he was legally entitled to rights that he was not prepared to relinquish. The Nazi Theodor Vahlen wanted to take over as director of the Institute despite poor academic qualities. He promised von Mises that if he would support him to succeed as Director of the Institute then he would ensure that von Mises would not lose his pension rights.

In October 1933 von Mises wrote his letter to support Vahlen as his successor. Collatz, von Mises' student, wrote:-

I took my Staatsexamen in November 1933, and Professor von Mises examined me on the day before his departure. The same day, he talked to me for about one hour, giving advice for my further research ...

Vahlen was appointed Director of the Institute in December 1933. Having taken up the new chair in Istanbul, von Mises received a letter in January 1934 denying him any rights at all. It was something that von Mises continued to feel extremely aggrieved about, writing to the Ministry in 1953, shortly before his death, still trying to restore his rights.

The mathematician Hilda Geiringer followed him to Istanbul in 1934. There she was appointed as professor of mathematics.

In 1938 Kemal Atatürk died and those in Turkey who had fled from the Nazis feared that their safe haven would become unsafe. In 1939 von Mises left Turkey for the United States. He became professor at Harvard University and in 1944 he was appointed Gordon-McKay Professor of Aerodynamics and Applied Mathematics there. Geiringer followed him to the USA and they were married in 1943.

Von Mises worked on fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He classified his own work, not long before his death, into eight areas: practical analysis, integral and differential equations, mechanics, hydrodynamics and aerodynamics, constructive geometry, probability calculus, statistics and philosophy. He introduced a stress tensor which was used in the study of the strength of materials. His studies of wing theory for aircraft led him to investigate turbulence. Much of his work involved numerical methods and this led him to develop new techniques in numerical analysis. His most famous, and at the same time most controversial, work was in probability theory.

He made considerable progress in the area of frequency analysis which was started by Venn. He combined the idea of a Venn limit and a random sequence of events. Ostrowski in the same lecture which we quoted from above wrote (see for example [16]):-

Because of his dynamic personality his occasional major blunders were somehow tolerated. One has even forgiven him his theory of probability.

This judgement by Ostrowski is rather harsh, however, and many consider von Mises' theories to be important in the development of the subject. After the measure theory approach by Kolmogorov had become favoured by almost all statisticians over von Mises' limiting frequency theory approach, there was a return to von Mises ideas and there was an attempt to incorporate them into the measure theoretic approach of Kolmogorov who wrote himself in 1963:-

... that the basis for the applicability of the results of the mathematical theory of probability to real 'random phenomena' must depend on some form of the frequency concept of probability, the unavoidable nature of which has been established by von Mises in a spirited manner.

In paper [18] discusses:-

... von Mises' notion of a random sequence in the context of his approach to probability theory. [The author claims] that the acceptance of Kolmogorov's rival axiomatisation was due to a different intuition about probability getting the upper hand, as illustrated by the notion of a martingale.

Phillip Frank, writing in [4] says:-

... in looking over the work of von Mises ... we cannot fail to recognise a whole spectrum of research, extending from the philosophical meaning of science to practical methods of numerical computation. ... von Mises has always been a truly broad-minded man ... notwithstanding the wide range of his topics, his work shows a great intrinsic unity: starting from a definite center, it branches out in systematic investigations of a great diversity of problems. ... von Mises chose the topics according to a very definite view-point, determined by his ideas about the essence and method of every thoroughly scientific research.

In von Mises' book Positivism: A Study in Human Understanding (1951) he expressed his views on science and life. He subscribes to a doctrine of positivism in the book saying:-

Positivism does not claim that all questions can be answered rationally, just as medicine is not based on the premise that all diseases are curable, or physics does not start out with the postulate that all phenomena are explicable. But the mere possibility that there may be no answers to some questions is no sufficient reason for not looking for answers, or for not using those which are attainable.

This interest in philosophy was only one of von Mises' interests outside the realm of mathematics. Another was the fact that he was an international authority on the Austrian poet Rainer Maria Rilke (1875-1926).

In 1950 von Mises was offered honorary membership of the East German Academy of Science. This was difficult for von Mises, particularly in McCarthy era America where any link with communism would have been viewed as a serious offence. He sadly declined in a letter written on 15 September 1950:-

I would very gladly accept the nomination in remembrance of my teaching activities in Berlin and thus re-establish the bond which connected me for a long time to the German scientific life. Unfortunately the present circumstances in Germany as well as those in this country are such that the acceptance of such a distinction could be interpreted as a political demonstration on my part. ... I only relinquish acceptance of this nomination under the pressure of outward circumstances, a nomination which I regard as a great honour in every respect.