Hilda Geiringer

Hilda Geiringer的父亲Ludwig Geiringer出生于匈牙利。她的母亲玛莎·韦特海默来自维也纳，路德维希和玛莎结婚时，他正在维也纳做纺织品制造商。这是一个犹太家庭，后来对希尔达的生活产生了重大影响。在文理中学，希尔达展现出极高的数学才能，她的父母在经济上支持她，使她能够在维也纳大学学习数学。

获得第一个学位后，Geiringer在维也纳继续数学研究，在威廉·维廷格指导下攻读博士学位。1917年，她以一篇关于二元Fourier series的学位论文获得博士学位。随后两年，她担任利昂·利希滕斯坦的助手，编辑数学评论期刊Jahrbuchs über die Fortschritte der MathematikⓉ（数学进展年鉴）。

1921年，Geiringer迁往柏林，在应用数学研究所担任理查德·冯·米泽斯的助手。同年，她嫁给了Félix Pollaczek，后者与Geiringer一样，出生于维也纳的一个犹太家庭，但在柏林求学。他于1922年在伊赛·舒尔指导下获得博士学位，随后在柏林的帝国邮政工作，将数学方法应用于电话连接。希尔达和Félix于1922年育有一子，玛格达·波拉切克，但他们的婚姻破裂了。离婚后，Geiringer继续为理查德·冯·米泽斯工作，同时独自抚养孩子。

尽管Geiringer接受的是纯数学训练，但她转向了应用数学，以适应应用数学研究所正在开展的工作。她此时的工作涉及统计学，特别是概率论，以及塑性数学理论。她向柏林大学提交了教授资格论文（Habilitation）学位论文，但没有立即被接受。Siegmund-Schultze在[3]中写道：-

围绕Hilda Geiringer在柏林大学申请任教资格（1925-1927）的争议，为“应用数学”争取认知与制度独立性的斗争提供了一些启示。这场争议以及Geiringer未发表的回忆录揭示了理查德·冯·米泽斯……对她的事业以及柏林大学应用数学的发展方向所产生的决定性影响。……关于Geiringer任教资格论文的辩论，开启了数学统计学史的一章，即把取无穷多个值的离散分布展开为西莫恩·德尼·泊松分布关于参数的逐次导数的级数。

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，当然也把有犹太血统的人从其他职位上清除。所有非雅利安血统的公务员（只要有一位祖父母信奉犹太教，此人即被视为非雅利安人）都应被令退休。根据这项法律，Geiringer于1933年12月失去了在大学授课的权利。事实上，她曾在1933年被提名为编外教授职位的候选人，但在当年4月《公务员法》生效后，这一提名便被搁置了。

Geiringer在被柏林大学解职后离开了德国，带着孩子前往布鲁塞尔。在那里，她被任命到力学研究所，从事振动理论的研究。理查德·冯·米泽斯虽然从犹太教改宗天主教，却在1933年底离开德国，前往伊斯坦布尔就任新设立的数学讲席，1934年，Geiringer跟随他去了伊斯坦布尔。在那里，她被任命为数学教授，2中写道：-

In Turkey, Geiringer是寻求躲避希特勒政权的一个较大的德国群体的一部分。尽管这种流亡带来了明显的困难——例如，她必须学习土耳其语才能讲课——Geiringer仍继续追求她的数学兴趣，尤其是在塑性方面。

1938年凯末尔·阿塔图尔克去世，那些从纳粹手中逃到土耳其的人担心他们的避难所会变得不安全。1939年，理查德·冯·米泽斯离开土耳其前往美国。Geiringer担心自己可能不那么容易获得进入美国的许可，她从伊斯坦布尔写信给理查德·冯·米泽斯：-

难道没有办法以代理方式结婚吗？这里有一位持有居留许可的移民与他的“新娘”结了婚，随后她就被允许直接从维也纳来到他身边。

然而，她对拿不到入学许可的担心是多余的，她带着女儿去了布林莫尔学院，在那里被聘为讲师。当然，Geiringer为了教书又得学一门语言。她还必须适应她所谓的“美国式教学”，在这方面安娜·约翰逊·佩尔·惠勒给了她很大帮助。

除了在布林莫尔学院的授课职责外，Geiringer还为国家研究委员会承担了作为战争努力一部分的机密工作。1942年期间，她在布朗大学讲授了一门高等力学课程，目的是将美国的教育标准提高到德国已达到的水平。她整理了她关于力学几何基础的杰出系列讲座，尽管这些讲座从未正式出版，但多年来在美国被广泛使用。

人们必须理解当时美国面临的问题，因为它正试图——总体而言非常成功地——将许多逃离纳粹的顶尖科学家纳入其体系。耶日·奈曼本人已移居美国，1940年4月，在Geiringer从土耳其抵达后不久，他写了一份关于她的报告。这份报告非常公正地说明了Geiringer在数学教授群体中处于什么位置：

她是否应被视为能力出众，取决于比较的标准。在当今数学家中，名字能留在数学史上的人寥寥无几……至于来到这个国家的新人，我毫不怀疑理查德·冯·米泽斯就是这种水准的人之一。……全世界也许会有十来个，也许二十个这样的人。……而Geiringer夫人不属于这一类。但采用另一个标准也许是合理的，即概率论与统计学大学教授的标准，或许是如今众多统计方法著作作者的标准。与这些人中的许多人相比，Geiringer夫人是杰出人物，我认为让她留在某所大学里符合美国科学与教育的利益。

Geiringer于1943年与理查德·冯·米泽斯结婚，次年她离开布林莫尔学院的讲师职位，以便离他更近。她接受了马萨诸塞州诺顿市惠顿学院的教授兼系主任职位。工作日她在学院教书，每个周末前往剑桥，与当时在哈佛工作的理查德·冯·米泽斯相聚。

由于多种原因，这并非一个好的安排。惠顿学院数学系只有两名成员，Geiringer渴望置身于从事研究的数学家之中。她申请了许多其他职位，但都因对女性相当公开的歧视而失败。正如2在[2]中所写，她收到的一个回复相当典型：

我相信我们校长不会同意聘用女性。我们员工中有些女性，所以这不仅仅是对女性的偏见，但部分原因确实如此，因为如果能聘到男性，我们就不想再增加女性。

For Geiringer在德国因犹太背景而备受歧视，如今又因身为女性而遭受歧视，这一定是一个沉重的打击。然而，她非常平静地接受了这一切，相信如果她能为未来的女性世代做些事情，那么她就取得了积极的成就。在惠顿学院期间，她也从未放弃自己的研究；1953年她写道：-

除了学院的工作，我还必须进行科学研究。这对我来说是一种必需；自学生时代起我从未停止过，这是我生命中最深层的需要。

1953年理查德·冯·米泽斯去世，次年Geiringer虽然保留了惠顿学院的职位，但开始到哈佛大学编辑理查德·冯·米泽斯的著作。1956年，柏林大学选举她为全额薪水的荣休教授。1959年，她正式从惠顿学院退休，次年该学院授予她荣誉理学博士学位以表彰她。

Hilda Geiringer's father Ludwig Geiringer was born in Hungary. Her mother, Martha Wertheimer was from Vienna and Ludwig and Martha had married while he was working in Vienna as a textile manufacturer. It was a Jewish family which would later have a significant effect on Hilda's life. At Gymnasium Hilda showed great mathematical ability and her parents supported her financially so that she could study mathematics at the University of Vienna.

After receiving her first degree, Geiringer continued her study of mathematics at Vienna, working under Wirtinger for her doctorate. This was awarded in 1917 for a thesis on Fourier series in two variables. She spent the following two years as Leon Lichtenstein's assistant editing the mathematics review journal Jahrbuchs über die Fortschritte der Mathematik Ⓣ.

In 1921 Geiringer moved to Berlin where she was employed as an assistant to von Mises in the Institute of Applied Mathematics. In this same year she married Félix Pollaczek who, like Geiringer, had been born in Vienna into a Jewish family but had studied in Berlin. He obtained his doctorate in 1922 working under Schur and went on to work for the Reichspost in Berlin applying mathematical methods to telephone connections. Hilda and Félix had a child, Magda Pollaczek, in 1922 but their marriage broke up. After the divorce Geiringer continued working for von Mises and at the same time brought up her child on her own.

Although trained as a pure mathematician, Geiringer moved towards applied mathematics to fit in with the work being undertaken at the Institute of Applied Mathematics. Her work at this time was on statistics, in particular probability theory, and also on the mathematical theory of plasticity. She submitted a thesis for her habilitation to the University of Berlin but it was not immediately accepted. Siegmund-Schultze writes in [3]:-

The controversy surrounding Hilda Geiringer's application for Habilitation at the University of Berlin (1925 - 1927) sheds some light on the struggle of 'applied mathematics' for cognitive and institutional independence. The controversy and Geiringer's unpublished reminiscences reveal the decisive influence of Richard von Mises ... on both her career and the course of applied mathematics at the University of Berlin. ... The debate over Geiringer's theses for Habilitation opens up a chapter of the history of mathematical statistics, namely, expansions of a discrete distribution with an infinite number of values in a series in successive derivatives of the Poisson distribution with respect to the parameter.

On 30 January 1933 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 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. Under this law, Geiringer lost the right to teach at the university in December 1933. In fact she had been proposed for appointment to the position of extraordinary professor in 1933 but the proposal had been put on hold after the Civil Service Law came into effect in April of that year.

Geiringer left Germany after she was dismissed from the University of Berlin and, together with her child, she went to Brussels. There she was appointed to the Institute of Mechanics and worked on the theory of vibrations. Von Mises, though a convert to Catholicism from Judaism, left Germany at the very end of 1933 to take up a newly founded chair of mathematics in Istanbul and, in 1934, Geiringer followed him to Istanbul. There she was appointed as professor of mathematics and Richards writes in [2]:-

In Turkey, Geiringer was part of a larger German community that was seeking refuge from Hitler's regime. Despite the obvious difficulties associated with this exile - for example, she had to learn Turkish in order to give her lectures - Geiringer continued to pursue her mathematical interests, particularly in plasticity.

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. Geiringer feared that she might not find it so easy to obtain an entrance permit to the United States and she wrote to von Mises from Istanbul:-

Is there no way to marry pro cura? Here an emigrant who has a resident's permit has married his 'bride' and she was then allowed to come to him straight from Vienna.

Her fears of not getting an entrance permit were unfounded, however, and together with her daughter she went to Bryn Mawr College where she was appointed as a lecturer. Again of course, Geiringer had to learn another language in order to teach. She also had to adjust to what she referred to as "the American form of teaching" and in this she was greatly assisted by Anna Wheeler.

In addition to her lecturing duties at Bryn Mawr College, Geiringer undertook classified work for the National Research Council as part of the war effort. During 1942 she gave an advanced course in mechanics at Brown University, with the aim of raising the American standards of education to the level that had been attained in Germany. She wrote up her outstanding series of lectures on the geometrical foundations of mechanics and, although they were never properly published, these were widely used in the United States for many years.

One has to understand the problems that there were in the United States at this time as they tried, in general very successfully, to integrate many leading scientists fleeing from the Nazis into their system. Neyman, who himself had emigrated to the United States, wrote a report on Geiringer in April 1940, shortly after she arrived from Turkey. This is very fair in explaining where Geiringer fitted into the spectrum of professors of mathematics:-

Whether she is to be considered outstanding in ability or not depends on the standards of comparison. Among the present day mathematicians there are few whose names will remain in the history of mathematics ... As for the newcomers to this country, I have not the slightest doubt that von Mises is one of the men of such calibre. ... There will perhaps be a dozen or perhaps a score of such persons all over the world. ... and Mrs Geiringer does not belong in this category. But it may be reasonable to take another standard, that of a university professor of probability and statistics, perhaps an author of the now numerous books on statistical methods. In comparison with many of these people Mrs Geiringer is an outstanding person and I think it would be in the interests of American science and instruction to keep her in some university.

Geiringer married von Mises in 1943 and the following year she left her lecturing post at Bryn Mawr College to be nearer to him. She accepted a post as professor and chairman of Wheaton College in Norton, Massachusetts. During the week she taught at the College, travelling to Cambridge every weekend to be with von Mises who worked at Harvard at this time.

For many reasons this was not a good arrangement. There were only two members of the mathematics faculty at Wheaton College and Geiringer longed for a situation where she was among mathematicians who were carrying out research. She made many applications for other posts but these failed due to fairly open discrimination against women. As Richards writes in [2] one response she received was quite typical:-

I am sure that our President would not approve of a woman. We have some women on our staff, so it is not merely prejudice against women, yet it is partly that, for we do not want to bring in more if we can get men.

For Geiringer who had been so discriminated against in Germany because of her Jewish background, to now be discriminated against because she was a woman must have been a difficult blow. However, she took it all remarkably calmly, believing that if she could do something for future generations of women then she would have achieved something positive. She also never gave up her research while at Wheaton College; in 1953 she wrote:-

I have to work scientifically, besides my college work. This is a necessity for me; I never stopped it since my student days, it is the deepest need of my life.

In 1953 von Mises died and the following year Geiringer, although retaining her job at Wheaton College, began to work at Harvard on editing von Mises' works. The year 1956 saw the University of Berlin elect her professor emeritus on full salary. In 1959 she formally retired from Wheaton College and the following year the College honoured her with the award of an honorary Doctorate of Science.