亚历山大·弗里德曼Alexander Friedmann

亚历山大·弗里德曼的出生日期常被记为6月29日。然而这是一个错误，源于将俄国的“旧历”日期转换为“新历”日期时，需要加上12天。相当奇怪的是，弗里德曼错误地将自己的出生日期转换成了6月17日（本应是4 + 12 = 16）。然后，他没有意识到自己给出的日期已经被转换过，于是又转换了一次（17 + 12 = 29）。

弗里德曼的父亲是一名芭蕾舞演员，母亲是一名钢琴家。然而，在弗里德曼九岁时父母离婚了。记录显示，教会站在父亲一边，弗里德曼留在了父亲身边，父亲很快再婚。弗里德曼于1897年8月进入第二圣彼得堡文理中学，他的记录显示起初学业表现相当普通。但很快弗里德曼就成了班上两名最优秀的学生之一。另一位出色的学生是雅各布·塔马尔金，也是一位非凡的数学家，两个男孩是亲密的朋友，在中学和大学期间几乎总是形影不离。

1905年，弗里德曼和雅各布·塔马尔金写了一篇关于伯努利数的论文，并将论文提交给大卫·希尔伯特，拟在Mathematische Annalen上发表。论文被接受，并于1906年付印。1905年对弗里德曼来说不仅是在科学上极为重要的一年，也是他在政治上极其活跃的一年。弗里德曼和雅各布·塔马尔金是学校罢工的学生领袖，抗议政府对学校的镇压措施。

弗里德曼于1906年从中学毕业，并于同年8月进入圣彼得堡大学。在那里，他深受弗拉基米尔·安德烈耶维奇·斯捷克洛夫的影响，后者在弗里德曼入学那年接受了圣彼得堡的任命，并与弗里德曼持有相同的政治观点。弗里德曼也受到保罗·埃伦费斯特的影响，后者于1906年搬到圣彼得堡。到1907年，保罗·埃伦费斯特已经建立了一个现代物理学讨论班，参加者包括若干年轻物理学家以及两位年轻数学家弗里德曼和雅各布·塔马尔金。这个小组讨论了quantum theory、相对论和统计力学。

弗里德曼 在圣彼得堡读本科时，他的父亲去世了。1910年他完成学业后，他的科学导师 弗拉基米尔·安德烈耶维奇·斯捷克洛夫 为 弗里德曼 写了一封推荐信，以便他继续深造。弗里德曼 父亲的去世显然带来了经济上的影响，正如推荐信中所指出的，见 [3]：-

弗里德曼 没有经济来源，在大学期间靠私人辅导、校对和赚取微薄薪水谋生。

弗拉基米尔·安德烈耶维奇·斯捷克洛夫 还写到了 弗里德曼 在本科最后一年所做的数学工作：-

在大学最后一年，他正在撰写一篇我布置的课题论文：‘找出所有正交替换，使得 Laplace equation 在新变量下变换后，允许以两个函数乘积形式出现的特解，其中一个函数只依赖于一个变量，另一个函数依赖于另外两个变量’。我在我的博士论文中触及过这个问题，但没有详细处理。鉴于 弗里德曼 先生与他同龄人相比具有出色的工作能力和知识，我建议他尝试解决这个问题。今年一月，弗里德曼 先生向我提交了一份约130页的详尽研究，其中他给出了该问题相当令人满意的解答。……

弗里德曼 开始攻读硕士学位，并于1911年参与了一个为研究数学分析和力学而成立的小组。除了 弗里德曼，该小组的其他成员还包括 雅各布·塔马尔金、弗拉迪米尔·斯米尔诺夫、Petelin、Shokhat，稍后 阿布拉姆·萨莫伊洛维奇·贝西科维奇 也加入了该小组。弗里德曼 讲授了 阿尔弗雷德·克莱布什 关于弹性的工作以及其他主题，包括 爱徳华·古尔萨 的著作。在攻读硕士学位期间，弗里德曼 在矿业学院讲课，在那里与 Nikolai Krylov 合作，他还在铁路工程学院任教。通过这项工作，弗里德曼 对航空学产生了兴趣，并于1911年发表了一篇综述该领域的文章，特别描述了 尼古拉·叶戈罗维奇·茹科夫斯基 和 谢尔盖·阿列克谢耶维奇·恰普雷金 的贡献。

到1913年，弗里德曼 已经完成了硕士学位所需的考试，考试由 马尔可夫、弗拉基米尔·安德烈耶维奇·斯捷克洛夫 等人主持。1913年2月，他被任命到圣彼得堡郊区巴甫洛夫斯克的高空气象观测站工作，在那里研究气象学。1914年，弗里德曼 前往莱比锡，跟随当时领先的理论气象学家 威廉·皮耶克尼斯 学习。弗里德曼 于1914年夏天离开莱比锡，并参加了数次飞艇飞行以进行观测。

1914年6月弗朗茨·斐迪南大公遇刺后，奥地利向塞尔维亚发出最后通牒，俄罗斯支持塞尔维亚，因此德国支持奥地利。第一次世界大战于1914年8月1日爆发，弗里德曼 很快向天文台台长申请加入志愿航空队。他开始驾驶飞机，并很快参与了轰炸袭击。他继续研究数学，通过信件与 弗拉基米尔·安德烈耶维奇·斯捷克洛夫 写作并交流数学思想。在1915年2月5日写给 弗拉基米尔·安德烈耶维奇·斯捷克洛夫 的一封信中，弗里德曼 写道，见 [3]：-

我的生活相当平稳，除了诸如二十英尺外弹片爆炸、半英尺内奥地利炸弹爆炸（结果几乎算幸运）以及脸和头朝下摔倒（导致上唇破裂和头痛）之类的事故。但当然，人会习惯这一切，尤其是看到周围千倍更可怕的事情。

同样在这封信中，他征求弗拉基米尔·安德烈耶维奇·斯捷克洛夫关于积分他从理论上模拟炸弹下落所得方程的建议。此时，俄军正在封锁由奥地利军队防守的普热梅希尔镇，而弗里德曼在该镇上空执行轰炸任务。他运用自己的数学技能，加上弗拉基米尔·安德烈耶维奇·斯捷克洛夫的建议，计算炸弹的轨迹。在1915年2月28日的一封信中，他写道：-

我最近有机会在飞越普热梅希尔时验证我的想法；炸弹几乎按照理论预测的方式落下。为了获得理论的確凿证明，我将在几天后再次飞行。

弗里德曼因在普热梅希尔上空的飞行而荣获乔治十字勋章。1915年夏天，俄军在其西南前线撤退。弗里德曼被派往基辅，在那里为飞行员讲授航空学。1916年3月，他被任命为基辅中央航空站站长。在基辅，弗里德曼加入了数学学会，其成员包括Ch T Bialobzeski、P V Voronets、鲍里斯·德劳内、德米特里·格雷夫、A P Kotelnikov、V P 尤里·弗拉基米罗维奇·林尼克（尤里·弗拉基米罗维奇·林尼克的父亲）和奥托·尤利耶维奇·施密特。1917年4月，中央航空站迁至莫斯科，弗里德曼也随之迁往那里。

1917年十月革命变得不可避免，当时总理弗里德曼克伦斯基派兵关闭两家布尔什维克报纸。一直藏匿的列宁公开露面，告诉布尔什维克推翻政府。10月26日上午，几乎未流血，列宁宣布苏维埃掌权。此后，中央航空站的工作停止，弗里德曼开始寻找另一职位，但他不确定该走什么方向，尤其是因为战争使他的健康受损。他写信给弗拉基米尔·安德烈耶维奇·斯捷克洛夫说：-

我非常沮丧；我常常痛悔参与战争；似乎我实现了既定目标，但现在这一切有什么用呢？

1918年4月13日，弗里德曼被选为彼尔姆大学数学与物理系的编外教授。他在那里共事的年轻同事包括A S 阿布拉姆·萨莫伊洛维奇·贝西科维奇、I M 伊万·维诺格拉多夫、N M 埃德蒙·冈特和R O Kuzmin。在彼尔姆，弗里德曼建立了一个力学研究所，并成为新成立的彼尔姆大学物理数学学会期刊编委会成员。

俄罗斯民族陷入了内战。红军于1918年2月成立，托洛茨基为其领导人。红军对抗由前帝国军官领导的反共分子组成的白军。事实上，弗里德曼于1918年4月27日在彼尔姆对红军发表了评论，他写道：-

彼尔姆出奇地平静，城里一切事务都以家庭方式妥善进行，甚至红军的训练也是如此，其兵力为30至40人。

然而，在1918年12月20日，他写道：-

彼尔姆交上了厄运。正在进行迅速、全面且相当混乱的疏散。大学处于第二线疏散，但迄今未提供运输工具或包装材料，疏散陷入停滞。……我个人不愿离开这座城市……

一周后，白军占领了彼尔姆。他们控制该城直到1919年8月红军再次夺取控制权。当红军逼近时，弗里德曼和所有教职员，除阿布拉姆·萨莫伊洛维奇·贝西科维奇外，都已离开大学。弗里德曼写道：-

唯一保持冷静并保全了剩余财产的人是阿布拉姆·萨莫伊洛维奇·贝西科维奇，他显然不仅在数学上是A A 马尔可夫的弟子，在果断、精确明确的行动方面也是如此。

1920年春天，内战仍在激烈进行，弗里德曼回到圣彼得堡（当时已更名为彼得格勒），到主地球物理观测台任职。弗里德曼从不是一个贪图安逸的人，1920年他在彼得格勒接受了数量惊人的职务。他开始在彼得格勒大学讲授数学和力学，成为彼得格勒工学院物理数学系的教授，在彼得格勒铁道工程学院应用航空学系工作，在海军学院工作，并在光学研究所的原子委员会从事研究。

1922年，在完成该硕士学位考试九年后，弗里德曼提交了他的硕士论文。论文题为The Hydromechanics of a Compressible Fluid，分为两部分，第一部分关于涡旋运动学，第二部分关于可压缩流体的动力学。正是这项工作激发了佩拉格亚·波鲁巴里诺瓦-科奇纳后来的流体动力学工作。

弗里德曼回到彼得格勒后不久便产生了一个新的兴趣。阿尔伯特·爱因斯坦的广义相对论虽然发表于1915年，但由于第一次世界大战和内战，在俄国并不为人所知。到1920年底，弗里德曼在给保罗·埃伦费斯特的一封信中写道：——

我一直在研究相对性原理的公理化，从两个基本命题出发：
（1）对于匀速运动的世界，匀速运动保持为匀速；
（2）光速是常数（在运动世界和静止世界中相同），并且已经得到了一维空间世界的公式，这些公式比亨德里克·洛伦兹的变换更为一般……

弗里德曼将文章On the curvature of Space寄给了Zeitschrift für Physik，该刊于1922年6月29日收到。在论文中弗里德曼证明了宇宙的曲率半径可以是时间的增函数或周期函数。弗里德曼稍后在一本书中论述该论文的结果时，将这些结果描述如下：——

稳恒型宇宙只包含阿尔伯特·爱因斯坦和de 威廉·德西特所考虑的两种情况。变化型宇宙则代表多种多样的情形；这种类型可以有世界曲率半径……随时间不断增大的情形；也可以有曲率半径周期性变化的情形……

阿尔伯特·爱因斯坦迅速回应了弗里德曼的文章。他的回复于1922年9月18日被Zeitschrift für Physik收到：-

关于非静态世界的结果，包含在[弗里德曼的]工作中，在我看来可疑。实际上，其中给出的解并不满足场方程。

12月6日，弗里德曼写信给阿尔伯特·爱因斯坦：-

考虑到非静态世界的可能存在具有一定的意义，我允许自己在此向您提交我所做的计算……以供验证和批判性评估。[计算给出]……如果您发现我信中呈现的计算正确，请告知《物理学杂志》的编辑；或许在这种情况下，您将发表对您陈述的更正，或提供机会发表此信的一部分。

然而，当信件到达柏林时，阿尔伯特·爱因斯坦已经出发前往日本。他直到三月才回到柏林，但他似乎仍未阅读弗里德曼的信。只有当克鲁特科夫，作为来自彼得格勒的弗里德曼的同事，于1923年5月在莱顿的保罗·埃伦费斯特家中遇到阿尔伯特·爱因斯坦，并告诉他弗里德曼信中包含的细节时，阿尔伯特·爱因斯坦才承认自己的错误。他立即写信给Zeitschrift für Physik：-

在我之前的笔记中，我批评了[弗里德曼的工作《论空间的曲率》]。然而，正如克鲁特科夫先生转达给我的弗里德曼的信使我确信的那样，我的批评基于我计算中的错误。我认为弗里德曼先生的结果是正确的，并提供了新的见解。

1923年7月，弗里德曼离开彼得格勒前往德国和挪威。在德国，他访问了柏林、汉堡、波茨坦和哥廷根。在挪威，他访问了克里斯蒂安尼亚（奥斯陆）。他讨论了气象学、航空学和力学。在哥廷根，他与路德维希·普朗特和大卫·希尔伯特交谈，并与大卫·希尔伯特讨论他在相对论方面的工作。第二年，即1924年，弗里德曼再次出行，这次是参加在代尔夫特举行的第一届国际应用数学大会。他写道关于这次大会：-

大会一切顺利，对俄罗斯人的态度非常好；特别是，我被列入召集下一次会议委员会的成员之中。... 来自哥廷根的理查·科朗特对雅各布·塔马尔金的工作产生了兴趣。奥托·布卢门塔尔、西奥多·冯·卡门和图利奥·列维-齐维塔对我和我同事的工作产生了兴趣。

1925年7月，弗里德曼乘坐气球升至7400米，进行气象和医学观察，创下了纪录。他回到列宁格勒（彼得格勒于1924年更名为列宁格勒）。1925年8月底，弗里德曼开始感到不适。他被诊断患有伤寒，并被送往医院，两周后在那里去世。

在3中，弗里德曼的贡献被总结如下：-

... 弗里德曼被视为一位深刻、独立思考和勇敢的思想家，他摧毁科学偏见、神话和教条；他的智慧看到别人看不到的东西，并且不会看到别人认为显而易见但在现实中毫无根据的东西。他拒绝了几百年的传统，这种传统在任何经验之前就选择认为宇宙是永恒且永远不变的。他在科学中实现了一场真正的革命。正如尼古拉·哥白尼使地球绕太阳转，弗里德曼使宇宙膨胀。

Alexander Friedmann's date of birth is often given as 29 June. However this is an error which came about in converting the "Old Style" Russian date to the "New Style" date, which requires an addition of 12 days. Rather strangely Friedmann wrongly converted his own date of birth to 17 June (it should have been 4 + 12 = 16). Then, not realising that the date he gave had already been converted, it was converted again (17 + 12 = 29).

Friedmann's father was a ballet dancer and his mother was a pianist. However the parents divorced when Alexander was nine years old. Records show that the church sided with the father and Alexander stayed with his father who soon remarried. Alexander entered the Second St Petersburg Gymnasium in August 1897 and his record shows a quite ordinary school performance at first. Soon however Friedmann became one of the top two pupils in his class. The other outstanding pupil was Yakov Tamarkin, also an extraordinary mathematician, and the two boys were close friends, almost always together during their years at school and university.

In 1905 Friedmann and Tamarkin wrote a paper on Bernoulli numbers and submitted the paper to Hilbert for publication in Mathematische Annalen. The paper was accepted and appeared in print in 1906. The year 1905 was not only one of great scientific importance for Friedmann, it was also one where he was extremely active politically. Friedmann and Tamarkin were student leaders of strikes at the school in protest at the government's repressive measures against schools.

Friedmann graduated from school in 1906 and entered the University of St Petersburg in August of that year. There he was strongly influenced by Steklov who had taken up an appointment at St Petersburg in the year Friedmann entered and shared Friedmann's political views. Friedmann was also influenced by Ehrenfest who moved to St Petersburg in 1906. By 1907 Ehrenfest had set up a modern physics seminar which was attended by a number of young physicists and by the two young mathematicians Friedmann and Tamarkin. This group discussed quantum theory, relativity and statistical mechanics.

While Friedmann was an undergraduate at St Petersburg his father died. After he completed his studies in 1910 his scientific advisor, Steklov, wrote a reference for Friedmann to continue his studies. The death of Friedmann's father clearly had financial implications as the reference indicated, see [3]:-

Mr Friedmann is without means and when at the University made his living by private tutoring, proof-reading and earning a small salary.

Steklov also wrote of Friedmann's mathematical work in his final year as an undergraduate:-

In his last year at the University he was working on an essay on the subject I assigned: 'Find all orthogonal substitutions such that the Laplace equation, transformed for the new variables, admits particular solutions in the form of a product of two functions, one of which depends only on one, and the other on the other two variables'. I touched on this problem in my doctoral thesis, but did not treat it in detail.. I suggested that Mr Friedmann should try to solve this problem, in view of his outstanding working capacity and knowledge compared with other persons of his age. In January of this year, Mr Friedmann submitted to me an extensive study of about 130 pages, in which he gave a quite satisfactory solution of the problem. ...

Friedmann began to study for his Master's Degree and, in 1911, became involved with a circle formed to study mathematical analysis and mechanics. In addition to Friedmann, other members of the circle included Tamarkin, Smirnov, Petelin, Shokhat and, a little later, Besicovitch joined the circle. Friedmann lectured on Clebsch's work on elasticity and other topics including Goursat's books. While studying for his Master's Degree Friedmann lectured at the Mining Institute, cooperating there with Nikolai Krylov, and he also taught at the Railway Engineering Institute. Through this work Friedmann became interested in aeronautics and in 1911 he published an article surveying the area describing, in particular, the contributions of Zhukovsky and Chaplygin.

By 1913 Friedmann had completed the necessary examinations for the Master's Degree having been examined by Markov, Steklov and others. In February 1913 he was appointed to a position in the Aerological Observatory in Pavlovsk, a suburb of St Petersburg, where he was to study meteorology. In 1914 Friedmann went to Leipzig to study with Vilhelm Bjerknes, the leading theoretical meteorologist of the time. Friedmann left Leipzig in the summer of 1914 and took part in several flights in airships to make observations.

When Austria gave Serbia an ultimatum after the June 1914 assassination of Archduke Francis Ferdinand, Russia supported Serbia, so Germany came to the support of Austria. World War I broke out on 1 August 1914 and Friedmann soon sought permission from the Head of the Observatory to join the volunteer aviation detachment. He began flying aircraft and was soon involved in bombing raids. He continued to study mathematics, writing and exchanging mathematical ideas with Steklov by letter. In a letter to Steklov written on 5 February 1915 Friedmann writes, see [3]:-

My life is fairly even, except such accidents as a shrapnel explosion twenty feet away, the explosion of an Austrian bomb within half a foot, which turned out almost happily, and falling down on my face and head, which resulted in a ruptured upper lip and headaches. But one gets used to all this, of course, particularly seeing things all around which are a thousand times more awful.

Also in this letter he asked Steklov's advice on integrating equations he had obtained from theoretically modelling bombs dropping. At this time the Russians were blockading the town of Przemysl, which was defended by Austrian troops, and Friedmann flew bombing missions over the town. He had used his mathematical skills, together with a suggestion from Steklov, to compute the trajectory that the bomb would take. In a letter of 28 February 1915 he wrote:-

I have recently had a chance to verify my ideas during a flight over Przemysl; the bombs turned out to be falling almost the way the theory predicts. To have conclusive proof of the theory I'm going to fly again in a few days.

Friedmann was awarded the George Cross for bravery with his flights over Przemysl. In the summer of 1915 the Russian army retreated on its south west front. Friedmann was sent to Kiev and there he gave lectures on aeronautics for pilots. In March 1916 he was appointed Head of the Central Aeronautical Station in Kiev. In Kiev, Friedmann joined the Mathematical Society which had among its members Ch T Bialobzeski, P V Voronets, B N Delone, D A Grave, A P Kotelnikov, V P Linnik (I V Linnik's father) and O Yu Schmidt. In April 1917 the Central Aeronautical Station moved to Moscow, and Friedmann moved there.

The Revolution of October 1917 became inevitable when Alexander Kerensky, the prime minister, sent troops to close down two Bolshevik newspapers. Lenin, who had been in hiding, made a public appearance telling the Bolsheviks to overthrow the Government. On the morning of October 26, after hardly any bloodshed, Lenin proclaimed that the Soviets were in power. After this, the work of the Central Aeronautical Station was stopped and Friedmann began to look for another post, but he was unsure of the direction he should take, particularly since his health had suffered as a result of the war. He wrote to Steklov saying:-

I'm very depressed; I often bitterly regret taking part in the war; it seems I achieved what I set out to do, but what's the use of it all now?.

On 13 April 1918 Friedmann was elected an extraordinary professor in the Department of Mathematics and Physics at the University of Perm. Among the young colleagues he had there were A S Besicovitch, I M Vinogradov, N M Gunter and R O Kuzmin. At Perm Friedmann set up an Institute of Mechanics and became a member of the editorial board of the Journal of the newly founded Physico-Mathematical Society of Perm University.

The Russian nation was plunged into civil war. The Red Army had been formed in February 1918 with Trotsky as its leader. The Reds opposed the White Army formed of anticommunists led by former imperial officers. In fact Friedmann had commented on the Red Army in Perm on 27 April 1918 when he wrote:-

Perm is surprisingly calm, and everything is done in the city in family fashion, in a good way, even the training of the Red army, which is 30-40 strong.

However, on 20 December 1918, he wrote:-

Perm has come under an unlucky star. There is a rapid, overall and fairly chaotic evacuation. The University is in the second line of evacuation, but no transport or packing materials have been supplied so far, and the evacuation is at a standstill. ... I personally am not inclined to leave the city ...

A week later the White Army occupied Perm. They controlled the town until August 1919 when the Red Army took control again. As the Red Army had approached Friedmann and all the staff, except Besicovitch, had left the University. Friedmann wrote:-

The only person who kept his head and saved the remaining property was Besicovitch, who is apparently A A Markov's disciple not only in mathematics but also with regard to resolute, precise definite actions.

In the spring of 1920, with the Civil war still raging, Friedmann returned to St Petersburg (now named Petrograd) to take up a post at the Main Geophysical Observatory. Friedmann was never one to take life easy and he took up an impressive number of appointments in 1920 in Petrograd. He began teaching mathematics and mechanics at Petrograd University, became a professor in the Physics and Mathematics Faculty of the Petrograd Polytechnic Institute, worked in the Department of Applied Aeronautics at Petrograd Institute of Railway Engineering, worked at the Naval Academy and undertook research at the Atomic Commission at the Optical Institute.

In 1922, nine years after completing the examinations for this Master's Degree, Friedmann submitted his Master's dissertation. The dissertation was entitled The Hydromechanics of a Compressible Fluid and was in two parts, the first on the kinematics of vortices and the second on the dynamics of a compressible fluid. It was this work which stimulated the later work on hydrodynamics by Kochina.

Friedmann had taken up a new interest soon after returning to Petrograd. Einstein's general theory of relativity, although published in 1915, was not known in Russia due to World War I and the Civil War. By late 1920, Friedmann wrote in a letter to Ehrenfest:-

I have been working on the axiomatics of the relativity principle, proceeding from two underlying propositions:
(1) uniform motion remains uniform for the uniformly moving world and
(2) the velocity of light is constant (identical in the moving and stationary world), and have obtained formulae for a world with one space dimension which are more general than Lorentz's transformations ...

Friedmann sent the article On the curvature of Space to Zeitschrift für Physik and it was received by the journal on 29 June 1922. In the paper Friedmann showed that the radius of curvature of the universe can be either an increasing or a periodic function of time. Friedmann, writing about the results of the paper in a book a little later, describes the results as follows:-

The stationary type of Universe comprises only two cases which were considered by Einstein and de Sitter. The variable type of Universe represents a great variety of cases; there can be cases of this type when the world's radius of curvature ... is constantly increasing in time; cases are also possible when the radius of curvature changes periodically ...

Einstein quickly responded to Friedmann's article. His reply was received by Zeitschrift für Physik on 18 September 1922:-

The results concerning the non-stationary world, contained in [Friedmann's] work, appear to me suspicious. In reality it turns out that the solution given in it does not satisfy the field equations.

On 6 December Friedmann wrote to Einstein:-

Considering that the possible existence of a non-stationary world has a certain interest, I will allow myself to present to you here the calculations I have made ... for verification and critical assessment. [The calculations are given] ... Should you find the calculations presented in my letter correct, please be so kind as to inform the editors of the Zeitschrift für Physik about it; perhaps in this case you will publish a correction to your statement or provide an opportunity for a portion of this letter to be published.

However by the time the letter reached Berlin, Einstein had already left on a trip to Japan. He did not return to Berlin until March but he still did not seem to have read Friedmann's letter. Only Krutkov, when a colleague of Friedmann's from Petrograd, met Einstein at Ehrenfest's house in Leiden in May 1923 and told him of the details contained in Friedmann's letter did Einstein admit his error. He wrote immediately to Zeitschrift für Physik :-

In my previous note I criticised [Friedmann's work On the curvature of Space]. However, my criticism, as I became convinced by Friedmann's letter communicated to me by Mr Krutkov, was based on an error in my calculations. I consider that Mr Friedmann's results are correct and shed new light.

In July 1923 Friedmann left Petrograd to visit Germany and Norway. In Germany he visited Berlin, Hamburg, Potsdam and Göttingen. In Norway he visited Christiania (Oslo). He discussed meteorology, aeronautics and mechanics. In Göttingen he talked to Prandtl and Hilbert, talking to Hilbert about his work in relativity. The following year, 1924, Friedmann was travelling again, this time to the First International Congress for Applied Mathematics held at Delft. He wrote about the congress:-

Everything went well at the congress, the attitude towards the Russians was wonderful; in particular, I was included among the members of the committee for convening the next conference. ... Courant from Göttingen got interested in Tamarkin's work. Blumenthal, Kármán and Levi-Civita got interested in my and my colleagues work.

In July 1925 Friedmann made a record-breaking ascent in a balloon to 7400 metres to make meteorological and medical observations. He returned to Leningrad (Petrograd had been renamed Leningrad in 1924). Near the end of August 1925 Friedmann began to feel unwell. He was diagnosed as having typhoid and taken to hospital where he died two weeks later.

In [3] Friedmann's contributions are summed up as follows:-

... Friedmann is seen as a profound, independent-minded, and daring thinker who destroys scientific prejudices, myths and dogmas; his intellect sees what others do not see, and will not see what others believe to be obvious but for which there are no grounds in reality. He rejects the centuries-old tradition which chose, prior to any experience, to consider the Universe eternal and eternally immutable. He accomplishes a genuine revolution in science. As Copernicus made the Earth go round the Sun, so Friedmann made the Universe expand.