保罗·埃伦费斯特Paul Ehrenfest

保罗·埃伦费斯特的父亲西格蒙德埃伦费斯特出身于一个贫穷的犹太家庭。他在摩拉维亚的犹太村庄洛施维茨的一家织布厂工作时，与约翰娜·耶利内克结婚。婚后他们搬到维也纳，在那里开了一家杂货店，生意相当不错。他们有五个存活下来的孩子，埃伦费斯特是最小的，有四个哥哥阿图尔、埃米尔、胡戈和奥托。Johanna Ehrenfest在他们的店里长时间工作，埃伦费斯特在家由保姆照顾。

埃伦费斯特小时候身体不好。他体弱多病，有眩晕发作，还经常流鼻血。他遭受了附近其他孩子的反犹言论，但他的兄弟们大力支持他，在他的童年中扮演了重要角色。埃伦费斯特五岁时，他的大哥已经二十二岁了，正是通过他的兄弟们，埃伦费斯特对教育产生了兴趣。他们给他一些他喜欢解的谜题。

到六岁时，埃伦费斯特已经能读、能写、能算。这些大多是他自学的，母亲帮了一点忙，兄弟们则给予鼓励。在这个年龄，即1886年，他开始上小学，1888年转到另一所小学。他是由兄弟们而非学校引入科学和数学的，他们的态度对他产生了相当大的影响[2]：-

这种早期印象——科学是应当带着喜悦去学习的东西，是应当讨论和争论的东西——被吸收进了埃伦费斯特的最内心深处。

他于1890年完成小学学业，他的学校报告显示，那段时间在学业上非常成功，所有科目都得了最高分，但他的生活已经开始变得不幸。他的母亲已患病一段时间，于1890年死于乳腺癌。埃伦费斯特的父亲也健康状况不佳，患有胃溃疡。约翰娜去世后不久，埃伦费斯特的父亲再婚，第二任妻子是约瑟芬·耶利内克，即他第一任妻子的妹妹。约瑟芬与埃伦费斯特的大哥年龄相仿。

1890年，埃伦费斯特在Akademisches 文理中学（Gymnasium）开始接受中学教育。鉴于他在家里的问题，他在学校的表现大幅下滑，无论是成绩还是行为，或许并不令人意外。他唯一继续擅长的科目是数学。显然，他是一个不快乐的孩子[2]：-

他常常痛苦，深感抑郁，与自己及世界格格不入。

生活并未好转，因为在他十六岁时，父亲因多年逐渐恶化的胃病去世。他的长兄Arthur成为他的监护人，并设法说服埃伦费斯特不要如他所愿离开学校。情况有所改善[2]：-

埃伦费斯特显然能够从抑郁中走出来，这种抑郁有时严重到让他考虑自杀。他的知识兴趣变得更加强烈，或许作为一种自我保护的形式。

1899年夏天，埃伦费斯特成功通过了学校考试，但他的学校经历绝对是负面的，正如他后来生活中所表现的那样，他坚持自己的孩子在家接受教育。埃伦费斯特于1899年10月成为维也纳技术大学的学生。在那里，他与另外三名数学学生Heinrich Tietze、汉斯·哈恩和古斯塔夫·赫格洛茨建立了密切的友谊。他们自称“不可分割的四人”。埃伦费斯特在1899-1900年间参加了路德维希·玻尔兹曼关于热力学理论的讲座。突然间，主要归功于路德维希·玻尔兹曼，他在学校对教育的负面想法被对数学和物理的巨大热爱所取代。

按照当时的惯例，奥地利和德国的学生通常不会在整段本科课程期间只待在一所大学。1901年，埃伦费斯特转学到哥廷根，师从菲利克斯·克莱因和大卫·希尔伯特。在那里，他修读了马克斯·亚伯拉罕关于光的电磁理论的课程，还旁听了Stark、Walther Nernst、卡尔·史瓦西和恩斯特·策梅洛的课程。在旁听菲利克斯·克莱因和大卫·希尔伯特的课程时，埃伦费斯特看到了一位年轻的俄罗斯数学学生塔季扬娜·埃伦费斯特。他纳闷她为什么不来参加数学俱乐部的聚会，随后发现原因是女性不被允许参加。埃伦费斯特对这一规定提出挑战，经过一番斗争，终于使这一规定得以改变。这是他们友谊的开端，最终促成了他们的婚姻。

在哥廷根度过十八个月后，埃伦费斯特回到了维也纳。1904年，他在路德维希·玻尔兹曼的指导下于维也纳获得博士学位，论文题目属于经典力学领域：《刚体在流体中的运动与海因里希·鲁道夫·赫兹的力学》。这篇论文被认为是一项不错的工作，但埃伦费斯特本人从未给予它很高的评价，并在1904年6月23日获得博士学位后选择不将其发表。此后，塔季扬娜·埃伦费斯特从哥廷根来到维也纳与埃伦费斯特会合，他们在克服了信仰不同这一严重问题后结了婚。在获准结婚之前，两人都不得不放弃自己的宗教——婚礼于1904年12月21日举行。

1905年，埃伦费斯特发表了一篇关于马克斯·普朗克的黑体辐射理论的论文。它[2]：-

……显示出埃伦费斯特的真正兴趣、独特才能以及他个人风格的起点。

他留在维也纳，但没有职位。1906年9月，他回到哥廷根，希望那里可能有职位空缺，但没有。然而，他震惊地得知路德维希·玻尔兹曼于9月6日自杀。埃伦费斯特承担了撰写讣告的任务。菲利克斯·克莱因、大卫·希尔伯特、赫尔曼·闵可夫斯基和康斯坦丁·卡拉西奥多里此时都在哥廷根工作，这对埃伦费斯特的研究来说是一个重要时期。菲利克斯·克莱因请他写一篇关于统计力学的文章，如果他愿意，可以与其妻子合写。两位埃伦费斯特开始撰写这篇文章，但直到1911年才付印。

1907年，埃伦费斯特前往圣彼得堡。并不是他在那里有职位，而是他的妻子是俄罗斯人，这次搬迁大概是为了找到一个能让他们感到自在的地方。诚然，鉴于他所遭遇的反犹态度，埃伦费斯特对自己的国家感情复杂。一到圣彼得堡，他就与雅各布·塔马尔金、亚历山大·弗里德曼、弗拉基米尔·安德烈耶维奇·斯捷克洛夫以及其他数学家和物理学家取得了联系。

埃伦费斯特夫妇在圣彼得堡度过了五年。这段时间里，埃伦费斯特深深沉浸于研究问题之中。他与妻子合作撰写了关于统计力学的综述文章，这篇文章的完成时间比预期要长。他与菲利克斯·克莱因通信，后者告诉他，需要的是对该学科所有问题的一份综述，而不是由埃伦费斯特本人给出完整解答。为了希望这能带来一个学术职位，埃伦费斯特尽管已拥有博士学位，仍在圣彼得堡攻读了物理学硕士学位。他成功获得了学位，但并未获得他所期望的学术职位。他写信给许多机构，包括北美的一些机构，试图找到职位，但他的所有询问都没有结果。

1911年，埃伦费斯特在Annalen der Physik上发表了一篇重要论文，论述quantum theory的基本特征。1912年1月，埃伦费斯特出发前往德语世界的各所大学巡访，希望获得一个职位。他访问了柏林，在那里见到了马克斯·普朗克；莱比锡，在那里见到了老朋友赫格洛茨；慕尼黑，在那里遇到了阿诺·索末菲；然后是苏黎世、维也纳和布拉格，在布拉格他第一次遇到了阿尔伯特·爱因斯坦。在旅途中，他得知儒勒·昂利·庞加莱写了一篇关于量子理论的论文，其结果与他Annalen der Physik论文中的结果相似。儒勒·昂利·庞加莱并不知道埃伦费斯特的贡献，因此没有引用他的工作。

埃伦费斯特回到圣彼得堡，令他难过的是，儒勒·昂利·庞加莱的论文已经发表，而他还没来得及向儒勒·昂利·庞加莱指出自己的贡献——他为与圣彼得堡主流研究隔绝付出了代价。然而，他的命运即将改变。亨德里克·洛伦兹正在寻找一个人来继任他在莱顿的讲席。阿诺·索末菲推荐了埃伦费斯特，写道（见[2]）：-

他讲课像一位大师。我几乎从未听过一个人讲话如此引人入胜、才华横溢。意味深长的语句、机智的论点和辩证手法，他都以非凡的方式信手拈来……他知道如何把最困难的东西讲得具体而直观清晰。数学论证经他翻译成易于理解的图像。

1912年9月29日，埃伦费斯特收到一封电报，说他已被任命为莱顿的教授。他在莱顿度过了余下的职业生涯。我们现在来考察他在那里工作期间做出的一些贡献。

1917年和1920年，埃伦费斯特发表论文，研究物理空间的三维性质在多大程度上由基本物理方程的结构所决定，或反映在这些基本方程中这一问题。埃伦费斯特的论证既基于艾萨克·牛顿的天体力学，也基于阿尔伯特·爱因斯坦的相对论。

埃伦费斯特对量子统计的贡献在于理解了光子的性质，以及由马克斯·普朗克辐射定律所蕴含的光子属性。他研究量子理论，并将其应用于旋转物体。他认识到安德烈-马里·安培的分子电流与经典统计力学不相容。他提出了一个扩散模型，以阐明热力学第二定律的统计解释，即封闭系统的熵只能增加。现代非平衡态热力学把路德维希·玻尔兹曼的分子、碰撞观念与埃伦费斯特的统计观念结合起来，给出一种非线性的统计理论。

1933年，埃伦费斯特提出了基于自由能函数导数不连续性的相变分类。

乔治·乌伦贝克是埃伦费斯特的学生，1920年开始攻读硕士学位的研究。他谈到埃伦费斯特的教学风格[9]：-

先有断言，后有证明……他著名的清晰性[不应]与严格性混为一谈。……他从不提出或制造问题；他不相信问题；在他看来，唯一值得考虑的问题是你自己提出的问题。……他基本上一次只与一个学生工作，而且实际上每周几乎每天下午都如此。

关于埃伦费斯特的数学技能，乔治·乌伦贝克写道[9]：-

尽管他懂数学，但对他来说并不简单。他不是计算机。他不能计算。

埃伦费斯特在20世纪20年代初的讲座，10写道：-

埃伦费斯特的研究生讲座由一门为期两年的课程组成：詹姆斯·克拉克·麦克斯韦理论，以电子理论和一些相对论结束，一年；以及统计力学，以原子结构和量子理论结束，另一年。

1925年，当量子力学开始主导理论物理学的工作时，埃伦费斯特感到他有问题[9]：-

我想他一直憎恨它。所有这些年轻人，他们非常轻松地做出了这些计算……而你不需要理解太多。你只是计算，你做这个，你做那个，一切都出来了……因此，有一种以大卫·希尔伯特的基础、用算符构建起来的数学装置，它具有某种抽象性。这如此违背他的信条，我相信他为此感到痛苦。……他完全理解这一切。他说他只是太老了。真正参与其中违背了他的信条。

尼尔斯·玻尔和埃伦费斯特于1918年开始通信。当他们在莱顿7会面时：-

[埃伦费斯特]和尼尔斯·玻尔有许多可以一起谈论的话题——从量子理论的当前问题到冰岛萨迦，从儿童发展的阶段到真正的物理学家与其他人的区别。他们的交流遍及天地，埃伦费斯特向他的新朋友展示了荷兰博物馆的珍宝和球茎田的绚丽色彩。

埃伦费斯特在1921年第三届索尔维会议上介绍了尼尔斯·玻尔的结果。尼尔斯·玻尔因过度劳累没有出席。1921年晚些时候，尼尔斯·玻尔邀请埃伦费斯特去哥本哈根。他回复道：-

亲爱的，亲爱的玻尔，我非常非常想再次和你在一起。

埃伦费斯特对尼尔斯·玻尔和阿尔伯特·爱因斯坦在量子理论上的分歧感到不快。1925年12月，他在莱顿的家中把他们聚在一起，试图让他们达成一致的立场。他们没有达成，埃伦费斯特非常不快，因为他被迫在他两个亲密朋友中的一个站边。他在1927年流着泪说，如果被迫做出选择，他将不得不赞同尼尔斯·玻尔。

1931年5月，埃伦费斯特写信给尼尔斯·玻尔[3]：-

我已完全与理论物理失去联系。我再也读不进任何东西，觉得自己无能，甚至无法对洪水般的文章和书籍中什么才是有意义的有一点最微薄的把握。也许我已根本无可救药。

埃伦费斯特一生都受自卑之苦，这与他的科学家同行对他的高度尊重形成鲜明对比。他的儿子Wassik患有唐氏综合征，在身体和智力上都有严重问题，这也令他极为悲伤。

他最后一封信（从未寄出）是一份令人悲伤的文件（例如见[3]）：-

我亲爱的朋友们：尼尔斯·玻尔、阿尔伯特·爱因斯坦、Franck、赫格洛茨、Joffé、Kohnstamm和Tolman！

我完全不知道在接下来的几个月里如何继续承受我已经无法忍受的生活重担。我再也无法忍受让我的莱顿讲席付诸东流。我必须辞去这里的职位。也许我能在俄罗斯用尽我余下的力量。……然而，如果不能很快明确我能做到这一点，那么几乎可以肯定我会自杀。如果那真的发生，我希望知道我曾平静而不匆忙地写信给你们，你们的友谊在我生命中扮演了如此重要的角色。……

近年来，我越来越难以理解物理学的发展。在越来越疲惫和撕裂的尝试之后，我终于在绝望中放弃了。这让我对生活完全厌倦……我确实感到被判继续活着，主要是出于对孩子们的经济担忧。我尝试了其他事情，但那只短暂地有所帮助。因此我越来越专注于自杀的精确细节。除了自杀，我没有其他实际可能，而且是在先杀死Wassik之后。原谅我……

愿你和你的亲人安好。

这封信，以及他写给学生们的一封类似信件，从未寄出。埃伦费斯特在阿姆斯特丹的沃特林教授研究所的候诊室里枪杀了正在接受治疗的瓦西克。随后他开枪自杀。荷兰报纸只报道了他的突然去世，并长篇累牍地叙述了他的成就。

阿尔伯特·爱因斯坦在2中这样评价埃伦费斯特：-

他不仅是我所认识的本行业中最优秀的教师；他还热切关注着人们的发展和命运，尤其是他的学生们。理解他人，赢得他们的友谊和信任，帮助任何陷入外部或内心挣扎的人，鼓励年轻才俊——所有这些都是他真正的本色，几乎超过了他对科学问题的沉浸。

Paul Ehrenfest's father, Sigmund Ehrenfest, came from a poor Jewish family. He was working in a weaving mill in the Jewish village of Loschwitz in Moravia when he married Johanna Jellinek. After the marriage they moved to Vienna where they set up a grocery business which fared rather well. They had five children who survived birth, and Paul was the youngest, having four older brothers Arthur, Emil, Hugo, and Otto. Johanna Ehrenfest worked long hours in their shop and Paul was looked after at home by a nursemaid.

As a child Paul's health was poor. He was sickly, had dizzy spells, and suffered frequent nosebleeds. He suffered from anti-Semitic comments from other children in the neighbourhood but his brothers supported him strongly and played an important role in his childhood. His oldest brother was twenty-two years old by the time Paul was five and it was through his brothers that Paul became interested in education. They gave him puzzles which he enjoyed solving.

By the time he was six years old Paul could read, write and count. Mostly he had taught himself these things, helped a little by his mother, and encouraged by his brothers. At this age, in 1886, he began to attend primary school, moving to a different primary school in 1888. He was introduced to science and mathematics by his brothers, rather than from his school, and their attitude was one which would have quite an influence on him [2]:-

This early impression of science as something to be learned with joy, something to be discussed and argued about, was absorbed into Ehrenfest's innermost being.

He completed his primary schooling in 1890 and his school reports show that it had been a very successful time academically with top marks in all his subjects, but already his life was becoming unhappy. His mother who had been ill for some time died of breast cancer in 1890. Paul's father was also in poor health, suffering from stomach ulcers. Soon after Johanna's death Paul's father married again, his second wife being Josephine Jellinek, his first wife's younger sister. Josephine was about the same age as Paul's oldest brother.

In 1890 Paul began his secondary education at the Akademisches Gymnasium. Perhaps not surprisingly given his problems at home his performance at school deteriorated greatly, both his marks and his behaviour. The only subject he continued to excel in was mathematics. Clearly he was an unhappy child [2]:-

He was often miserable, deeply depressed and at odds with himself and the world.

Life did not get better, for when he was sixteen years old his father died from the stomach trouble which had got progressively worse for many years. Arthur, his oldest brother, became his guardian and managed to persuade Paul not to leave school as he wished to do. Things got somewhat better [2]:-

Paul was apparently able to work himself out of his depression, which had sometimes been deep enough to make him contemplate suicide. His intellectual interests grew stronger, perhaps as a form of self-protection.

In the summer of 1899 Ehrenfest successfully took his school examinations, but his experiences of school had been decidedly negative as he showed later in life when he insisted that his own children were educated at home. Ehrenfest became a student at the Technische Hochschule in Vienna in October 1899. There he formed a close friendship with three other students of mathematics, Heinrich Tietze, Hans Hahn and Herglotz. They called themselves the 'inseparable four'. Ehrenfest attended Boltzmann's lectures on the mechanical theory of heat during 1899-1900. Suddenly, thanks mainly to Boltzmann, the negative thoughts about education which he had at school were replaced with a great love for mathematics and physics.

As was the custom at the time, students in Austria and Germany did not usually stay at a single university for their whole undergraduate course. In 1901 Ehrenfest moved to Göttingen where he studied under Klein and Hilbert. There he took Max Abraham's course on the electromagnetic theory of light and also attended courses by Stark, Walther Nernst, Schwarzschild and Zermelo. While attending courses by Klein and Hilbert, Ehrenfest saw a young Russian student of mathematics Tatiana Alexeyevna Afnassjewa. He wondered why she did not come to meetings of the mathematics club but 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.

Ehrenfest returned to Vienna after spending eighteen months in Göttingen. He obtained his doctorate from Vienna in 1904, under Boltzmann's supervision, on a topic in classical mechanics The motion of rigid bodies in fluids and the mechanics of Hertz. It was considered a good piece of work but Ehrenfest himself never rated it very highly and chose not to publish it after receiving his doctorate on 23 June 1904. After this Tatiana came from Göttingen to join Ehrenfest in Vienna and they married after overcoming the severe problem of having different faiths. They both had to renounce their religion before the marriage was allowed -- it took place on 21 December 1904.

In 1905 Ehrenfest published a paper on Planck's theory of black-body radiation. It [2]:-

... shows Ehrenfest's real interests and particular talents and the beginning of his personal style.

He remained at Vienna but without a post. He returned to Göttingen in September 1906, hoping there might be a position available but there was not. He was shocked to learn, however, that Boltzmann had committed suicide on 6 September. Ehrenfest took on the task of writing his obituary. Klein, Hilbert, Minkowski and Carathéodory were all working in Göttingen at this time and it was an important period for Ehrenfest's research. Klein asked him to write, jointly with his wife if he wished, an article on statistical mechanics. The two Ehrenfests began working on the article which would not appear in print until 1911.

In 1907 Ehrenfest went to St Petersburg. It was not that he had a post there but his wife was Russian and the move was probably aimed at finding somewhere where they could feel at home. Certainly Ehrenfest had mixed feelings about his own country given the anti-Semitic attitudes he had encountered. Once in St Petersburg he made contact with Tamarkin, Friedmann, Steklov and other mathematicians and physicists.

The Ehrenfests spent five years in St Petersburg. It was a time when Ehrenfest was deeply engrossed in research problems. Together with his wife he worked on the review article on statistical mechanics which took longer to complete than expected. He corresponded with Klein who told him that what was required was a survey, not a complete solution of all the problems of the subject by Ehrenfest himself. In the hope that this might lead to an academic post Ehrenfest, despite holding a doctorate, took the degree of Master of Physics at St Petersburg. He was successful in obtaining the degree but not the academic post for which he hoped. He tried to find a position by writing to many institutions, including some in North America, but nothing came of any of his enquiries.

An important paper was published by Ehrenfest in 1911 in Annalen der Physik on the essential features of quantum theory. In January 1912 Ehrenfest set out on a tour of universities in the German speaking world in the hope of a position. He visited Berlin where he saw Planck, Leipzig where he saw his old friend Herglotz, Munich where he met Sommerfeld, then Zürich, Vienna, and Prague where he met Einstein for the first time. On his travels he learnt that Poincaré had written a paper on quantum theory which gave similar results to those in his Annalen der Physik paper. Poincaré had not known of Ehrenfest's contribution and therefore had not referred to his work.

Ehrenfest returned to St Petersburg saddened that Poincaré's paper had been published before he could point out his own contribution to him -- he was paying the price for being isolated from mainstream research in St Petersburg. However, his fortunes were about to change. Lorentz was looking for someone to succeed to his chair at Leiden. Sommerfeld recommended Ehrenfest, writing (see [2]):-

He lectures like a master. I have hardly ever heard a man speak with such fascination and brilliance. Significant phrases, witty points and dialectic are all at his disposal in an extraordinary manner ... He knows how to make the most difficult things concrete and intuitively clear. Mathematical arguments are translated by him into easily comprehensible pictures.

On 29 September 1912 Ehrenfest received a telegram saying that he had been named professor at Leiden. He remained at Leiden for the rest of his career. We examine now some of the contributions which he made while working there.

In 1917 and 1920 Ehrenfest published papers investigating the problem of the extent to which the three-dimensional nature of physical space is determined by the structure of basic physical equations or is reflected in these basic equations. Ehrenfest's arguments were based both on Newton's celestial mechanics and also on Einstein's relativity theory.

Among Ehrenfest's contributions to quantum statistics was an understanding of the nature of photons, and their properties which were implied by Planck's radiation law. He worked on quantum theory applying it to rotating bodies. He recognised that Ampère's molecular currents are incompatible with classical statistical mechanics. He proposed a model of diffusion in order to illuminate the statistical interpretation of the second law of thermodynamics, that the entropy of a closed system can only increase. The modern theory of nonequilibrium thermodynamics brings together the molecular, collisional ideas of Boltzmann with the statistical ideas of Ehrenfest's to give a nonlinear, statistical theory.

In 1933 Ehrenfest presented a classification of phase transitions based on the discontinuity in derivatives of the free energy function.

Uhlenbeck was a student of Ehrenfest who began research for his Master's degree in 1920. He spoke of Ehrenfest's teaching style [9]:-

First the assertion, then the proof ... His famous clarity [should] not to be confused with rigour. ... He never gave or made problems; he did not believe in them; in his opinion the only problems worth considering were those you proposed yourself. ... He worked with essentially one student at a time, and that practically every afternoon during the week.

As to Ehrenfest's mathematical skills, Uhlenbeck wrote [9]:-

Although he knew mathematics it was not simple for him. He was not a computer. He could not compute.

Pais writes about Ehrenfest's lectures in the early 1920s [10]:-

Ehrenfest's graduate lectures consisted of a two-year course: Maxwell theory, ending with the theory of electrons and some relativity, one year; and statistical mechanics, ending with atomic structure and quantum theory the other.

In 1925 when quantum mechanics began to dominate work in theoretical physics, Ehrenfest felt he had problems [9]:-

I think he always hated it. All these youngsters who had, with great facility, made these calculations ... and you didn't have to understand much. You just computed and you did this and you did that and everything came out ... There was, therefore, a mathematical apparatus built with Hilbert's basis, with operators, which had a sort of abstractness. It was so against his creed that I'm sure he suffered from it. ... he understood it all alright. He said he was just too old. It was against his creed to really take part in it.

Niels Bohr and Ehrenfest began to correspond in 1918. When they met in Leiden [7]:-

[Ehrenfest] and Bohr had much to talk about together -- from the current problems of quantum theory to the Icelandic sagas, from the stages of a child's development to the difference between genuine physicists and the other. Their exchanges ranged over heaven and earth as Ehrenfest showed his new friend the treasures of the Dutch museums and the brilliant colours of the bulb fields.

Ehrenfest presented Bohr's results to the third Solvay conference in 1921. Bohr did not attend through overwork. Later in 1921 Bohr invited Ehrenfest to Copenhagen. He replied:-

Dear, dear Bohr, I would like so terribly much to be with you again.

Ehrenfest was unhappy at the disagreement between Bohr and Einstein over quantum theory. He brought them together at his home in Leiden in December 1925 in an attempt to have them reach an agreed position. They did not and Ehrenfest was very unhappy that he was forced to take sides with one of his two close friends. He said in 1927, while in tears, that forced to make a choice he would have to agree with Bohr.

May 1931 Ehrenfest wrote to Bohr [3]:-

I have completely lost contact with theoretical physics. I cannot read anything any more and feel myself incompetent to have even the most modest grasp about what makes sense in the flood of articles and books. Perhaps I cannot at all be helped any more.

All through his life Ehrenfest had suffered from low self esteem, which was in marked contrast to the high esteem in which he was held by his fellow scientists. He was also greatly saddened by his son Wassik having Down's syndrome and having severe problems both physically and mentally.

His last letter (which was never sent) is a sad document (see for example [3]):-

My dear friends: Bohr, Einstein, Franck, Herglotz, Joffé, Kohnstamm, and Tolman!

I absolutely do not know any more how to carry further during the next few months the burden of my life which has become unbearable. I cannot stand it any longer to let my professorship in Leiden go down the drain. I must vacate my position here. Perhaps it may happen that I can use up the rest of my strength in Russia. .. If, however, it will not become clear rather soon that I can do that, then it is as good as certain that I shall kill myself. And if that will happen some time then I should like to know that I have written, calmly and without rush, to you whose friendship has played such a great role in my life. ...

In recent years it has become ever more difficult for me to follow the developments in physics with understanding. After trying, ever more enervated and torn, I have finally given up in desperation. This made me completely weary of life .. I did feel condemned to live on mainly because of the economic cares for the children. I tried other things but that helps only briefly. Therefore I concentrate more and more on the precise details of suicide. I have no other practical possibility than suicide, and that after having first killed Wassik. Forgive me ...

May you and those dear to you stay well.

This letter, and a similar letter which he wrote to his students, was never sent. Ehrenfest shot Wassik in the waiting room of the Professor Watering Institute in Amsterdam where Wassik was being treated. Then he shot himself. The Dutch papers only reported his sudden death and gave lengthy accounts of his achievements.

Einstein said of Ehrenfest [2]:-

He was not merely the best teacher in our profession whom I have ever known; he was also passionately preoccupied with the development and destiny of men, especially his students. To understand others, to gain their friendship and trust, to aid anyone embroiled in outer or inner struggles, to encourage youthful talent - all this was his real element, almost more than his emersion in scientific problems.