塔季扬娜·埃伦费斯特Tatyana Afanasyeva

塔季扬娜·阿列克谢耶夫娜塔季扬娜·埃伦费斯特的父亲是亚历山大·阿法纳西耶夫。亚历山大在俄罗斯帝国的帝国铁路上担任总工程师，塔季扬娜小时候跟随父亲走遍了俄罗斯帝国。然而，在她还很小的时候，父亲去世了，之后她在圣彼得堡由叔叔彼得·阿法纳西耶夫（理工学院教授）和他的妻子索尼娅抚养长大。塔季扬娜在圣彼得堡的师范学校学习，专攻数学和科学。

从师范学校毕业后，埃伦费斯特进入圣彼得堡的女子大学，在奥雷斯特·德·奇沃尔苏的指导下学习数学和物理。1902年，她前往德国，在哥廷根大学跟随菲利克斯·克莱因和大卫·希尔伯特继续学习。在那里，她遇到了保罗·埃伦费斯特。

保罗·埃伦费斯特于1901年搬到哥廷根，像塔季扬娜埃伦费斯特一样，在菲利克斯·克莱因和大卫·希尔伯特的指导下学习。保罗和塔季扬娜都参加了菲利克斯·克莱因和大卫·希尔伯特的课程，正是在这个时候两人相识。保罗·埃伦费斯特想知道为什么塔季扬娜不来参加数学俱乐部的会议，但后来发现原因是女性不被允许参加。保罗·埃伦费斯特挑战这一规定，经过一番斗争，终于改变了规定。这是他们友谊的开始，最终导致他们在1904年结婚。这发生在保罗·埃伦费斯特回到维也纳之后，他于1904年6月23日获得博士学位。此后，塔季扬娜离开哥廷根，前往维也纳与保罗·埃伦费斯特会合，他们在克服了不同宗教的严重问题后结婚（保罗是犹太人，塔季扬娜是俄罗斯东正教徒）。他们两人都必须在婚礼被允许之前放弃自己的宗教——婚礼于1904年12月21日举行。

保罗和塔季扬娜·埃伦费斯特虽然保罗在那里没有职位，但仍留在维也纳。他们的第一个孩子，埃伦费斯特·帕夫洛夫娜·埃伦费斯特，于1905年10月出生在维也纳。1906年9月，全家返回哥廷根，希望可能有适合保罗的职位，但没有。菲利克斯·克莱因请保罗和塔季扬娜·埃伦费斯特撰写一篇关于统计力学的文章。两位埃伦费斯特此时开始撰写这篇文章，但直到1911年才付印。

1907年，艾伦费斯特夫妇去了圣彼得堡。这并不是因为他们中任何人在那里有职位，而是通过这次搬迁，塔蒂亚娜回到了她长大的城市，这次搬迁旨在找到一个这对夫妇能感到像在家一样的地方。当然，鉴于他遇到的反犹太态度，保罗·埃伦费斯特对自己的国家感情复杂。艾伦费斯特夫妇在圣彼得堡度过了五年，在此期间，他们组织了一个非正式的物理学讨论会，该讨论会定期举行：-

……每隔一周，通常在埃伦费斯特家中，报告物理学文献中最近发表的工作。偶尔，其中一位参与者会报告自己当前的一些工作。讨论生动而热烈，常常持续到午夜甚至更晚。

那是一个保罗·埃伦费斯特深深沉浸于研究问题、而塔季扬娜参与改革俄罗斯数学教学项目的时期。塔季扬娜与丈夫还致力于统计力学的综述文章，该文完成的时间比预期要长。他们与菲利克斯·克莱因通信，后者告诉他们，需要的是综述，而不是由埃伦费斯特夫妇自己完全解决该学科的所有问题。

从1907年到1912年，埃伦费斯特夫妇在圣彼得堡生活和工作。他们的第二个孩子安娜（常被称为加利亚或加林卡）于1910年7月出生。由于没有带薪职位，这个家庭非常贫困，现在还要照顾两个孩子。1912年，菲利克斯·克莱因所请求的重要文章Begriffe Grundlagen der statischen Auffassung in der Mechanik Ⓣ（力学中统计概念的基础）在Encyclopädie der mathematische Wissenschaften上发表。一篇题为The conceptual foundations of the statistical approach in mechanics 的英译本于1959年问世（并于1990年重印）。N G van 埃格伯特·范坎彭在一篇评论中写道：-

这是保罗和塔季扬娜·埃伦费斯特于1912年发表的著名百科全书文章的第一个英译本。它包括对（经典）统计力学基础的批判性讨论，特别是“概率”概念的使用、路德维希·玻尔兹曼的H定理、洛施密特和恩斯特·策梅洛的反对意见以及克服这些反对意见的各种尝试，还有路德维希·玻尔兹曼和约西亚·威拉德·吉布斯方法的差异。由于不可逆过程理论已成为统计力学的一个重要分支，这一讨论获得了新的意义。许多英语读者将能够从作者的批判态度以及他们认识和剖析困难的透彻方式中获益，而不是将其隐藏在某种简化形式主义中。

1912年9月29日，保罗·埃伦费斯特收到一封电报，说他被任命为莱顿的教授，于是全家搬到了那里。1915年，他们的第三个孩子保罗出生，然后在1918年8月，第二个儿子瓦西里出生[1]：-

在二十年代的某个时候，埃伦费斯特-埃伦费斯特回到了俄罗斯，在那里教授数学并继续发表论文，尽管这对夫妇仍然偶尔见面。

保罗·埃伦费斯特 一生都饱受自卑之苦，但此时开始患上抑郁症。他最年幼的儿子 Vassily 患有唐氏综合征，在身体和精神上都有严重问题，这也让他极为悲伤。1933年9月25日，保罗·埃伦费斯特 在阿姆斯特丹的沃特林研究所教授候诊室开枪打死了正在那里接受治疗的 Vassily。随后他开枪自杀。荷兰报纸只报道了他的突然死亡，并长篇叙述了他的成就。Ehrenfest-埃伦费斯特 回到莱顿，并在那里度过了余生。她不仅以如此悲惨的方式失去了丈夫和最小的儿子，而且几年后，在1939年，她的长子 Paul 在法国阿尔卑斯山滑雪时被雪崩夺去生命。

塔季扬娜·埃伦费斯特在荷兰的数学教育中发挥了重要作用。1924年与爱德华·扬·戴克斯特豪斯关于几何教学直观方法的讨论，促成了一份数学教学法杂志的问世，以“欧几里得”为名出版。直观方法的特点是思考明显的空间概念和现象。从1936年起，塔季扬娜·埃伦费斯特成为创新与教育协会数学工作组的推动力量。该工作组为荷兰数学教学的发展做出了许多决定性贡献，尤其是在第二次世界大战结束后。她还继续出版著作，如Die Grunglagen der Thermodynamik Ⓣ（热力学基础）（1956年）和1957年在American Journal of Physics上发表的On the use of the notion of 'probability' in physics。

塔季扬娜的长女塔季扬娜·帕夫洛夫娜·埃伦费斯特就读于莱顿大学，学习数学和物理学。像她的母亲一样，她对数学比物理学更感兴趣，并在莱顿大学教授数学。在数学方面，她与尼古拉斯·霍弗特·德布鲁因、塞德里克·史密斯和威廉·托马斯·塔特合作完成了重要工作。她嫁给了外科医生范阿尔登内博士。

Tatiana Alexeyevna Afanassjewa's father was Alexander Afanassjev. Alexander worked as Chief Engineer on the Imperial Railways in the Russian Empire and as a young girl, Tatiana went all over the Russian Empire with her father. However, while she was still quite young, her father died and after that she was brought up in St Petersburg by her uncle Peter Afanassjev, a professor at the Polytechnic Institute, and his wife Sonya. Tatiana studied at the normal school in St Petersburg, specialising in mathematics and science.

After graduating from the normal school, Afanassjewa entered the Women's University in St Petersburg where she studied mathematics and physics under Orest D Chvolsou. In 1902 she went to Germany to continue her studies with Felix Klein and David Hilbert at the University of Göttingen. There she met Paul Ehrenfest.

Paul Ehrenfest had moved to Göttingen in 1901, like Tatiana Afanassjewa to study under Klein and Hilbert. Both Paul and Tatiana attended courses by Klein and Hilbert, and it was at this time that the two met. Ehrenfest wondered why Tatiana did not come to meetings of the mathematics club but he then discovered that the reason was that women were not allowed to attend. Ehrenfest challenged this rule and, after quite a battle, was able to get the rule changed. It was the beginning of their friendship which led eventually to their marriage in 1904. This took place after Ehrenfest had returned to Vienna where he received his doctorate on 23 June 1904. After this Tatiana left Göttingen to join Ehrenfest in Vienna and they married after overcoming the severe problem of having different religions (Paul was Jewish and Tatiana was Russian Orthodox). They both had to renounce their religion before the marriage was allowed - it took place on 21 December 1904.

Paul and Tatiana Ehrenfest remained at Vienna although Paul had no position there. Their first child, Tatyana Pavlovna Ehrenfest was born in October 1905 in Vienna. The family returned to Göttingen in September 1906, hoping there might be a position available for Paul but there was not. Klein asked Paul and Tatiana Ehrenfest to write an article on statistical mechanics. The two Ehrenfests began working on the article at this time but it did would not appear in print until 1911.

In 1907 the Ehrenfests went to St Petersburg. It was not that either of them had a post there but with this move Tatiana was returning to the city in which she was brought up and the move was aimed at finding somewhere where the couple could feel at home. Certainly Ehrenfest had mixed feelings about his own country given the anti-Semitic attitudes he had encountered. The Ehrenfests spent five years in St Petersburg during which time they organised an informal physics colloquium which met:-

... every other week, usually at Ehrenfest's home, for reports on work published recently in the physics literature. Occasionally one of the participants would have some current work of his own to report on. Discussions were lively and vigorous, often extending until midnight or even later.

It was a time when Paul Ehrenfest was deeply engrossed in research problems and Tatiana became involved in a project to reform mathematics teaching in Russia. Tatiana, along with her husband, also worked on the review article on statistical mechanics which took longer to complete than expected. They corresponded with Klein who told them that what was required was a survey, not a complete solution of all the problems of the subject by the Ehrenfests themselves.

From 1907 to 1912 the Ehrenfest's lived and worked in St Petersburg. Their second child, Anna (often called Galya or Galinka) was born in July 1910. With no paying position the family were very poor, now with two children to care for. In 1912 the major article Begriffe Grundlagen der statischen Auffassung in der Mechanik Ⓣ which Klein had requested, was published in Encyclopädie der mathematische Wissenschaften. An English translation under the title The conceptual foundations of the statistical approach in mechanics appeared in 1959 (and was reprinted in 1990). N G van Kampen writes in a review:-

This is the first English translation of the celebrated encyclopedia article of Paul and Tatiana Ehrenfest, published in 1912. It consists of a critical discussion of the foundations of (classical) statistical mechanics, in particular, the use of the concept 'probability', Boltzmann's H-theorem, the objections of Loschmidt and Zermelo and the various attempts to overcome them, and the difference between the approaches of Boltzmann and Gibbs. Since the theory of irreversible processes has become an important branch of statistical mechanics, this discussion has gained new interest. Many English-speaking readers will be able to profit from the critical attitude of the authors and the thorough way in which they recognize and analyze the difficulties, rather than hide them in some streamlined formalism.

On 29 September 1912 Ehrenfest received a telegram saying that he had been named professor at Leiden and the family moved there. In 1915 their third child Paul was born, then in August 1918 a second son Vassily was born [1]:-

Sometime during the twenties, Ehrenfest-Afanassjewa returned to Russia, where she taught mathematics and continued to publish papers, although the couple still met occasionally.

Paul Ehrenfest through his life had suffered from low self esteem, but now began to suffer from depression. He was also greatly saddened by his youngest son Vassily who suffered from Down's syndrome and had severe problems both physically and mentally. On 25 September 1933 Ehrenfest shot Vassily in the waiting room of the Professor Watering Institute in Amsterdam where Vassily was being treated. Then he shot himself. The Dutch papers only reported his sudden death and gave lengthy accounts of his achievements. Ehrenfest-Afanassjewa returned to Leiden where she remained for the rest of her life. Not only did she lose her husband and youngest son in such a tragic way, but a few years later, in 1939, her eldest son Paul was killed by an avalanche while skiing in the French Alps.

Tatiana Ehrenfest played an important role in mathematical education in the Netherlands. A discussion with E J Dijksterhuis on the intuitive approach to teaching geometry in 1924 led to the appearance of a magazine for the didactics of mathematics, published under the name 'Euclid.' The intuitive approach was characterised by contemplating obvious spatial concepts and phenomena. From 1936 Tatiana Ehrenfest was the driving force behind the Mathematics Working Group of the Association of Education for Innovation and Education. The Working Group produced many decisive contributions to the development of teaching math in the Netherlands, especially after the end of World War II. She also continued to publish works such as Die Grunglagen der Thermodynamik Ⓣ (1956) and On the use of the notion of 'probability' in physics published in the American Journal of Physics in 1957.

Tatiana's eldest daughter, Tatiana Pavlovna Ehrenfest, attended the University of Leiden where she studied mathematics and physics. Like her mother, she was more interested in mathematics than in physics and taught mathematics at the University of Leiden. In mathematics she has done important work in collaboration with Nicolaas Govert de Bruijn, Cedric Smith and Bill Tutte. She married the surgeon Dr van Aardenne.