姆斯季斯拉夫·克尔德什Mstislav Keldysh

姆斯季斯拉夫·克尔德什出生于里加。他的父亲Vsevolod Mikhailovich 克尔德什（1878-1965）是一名军事建筑工程师，毕业于里加理工学院。Vsevolod Mikhailovich在里加与Mariya Aleksovna Skvortsova（1879-1953）结婚。她致力于抚养他们的孩子。值得记录的是，再往前一代，Mariya Aleksandrovna的父亲是一名炮兵将军，将军之子，因此出身贵族。Vsevolod Mikhailovich的父亲是一名军医，军衔为将军，因此也出身贵族。克尔德什 Vsevolodovich一直为自己的贵族出身感到自豪，尽管这在共产主义俄罗斯给他带来了麻烦。这个家庭相当富裕，而且由于Vsevolod Mikhailovich的工作性质，他往返于许多不同的城镇之间。他在不同的技术学院讲课，后来参与了莫斯科地铁和莫斯科-伏尔加运河的设计和建设。克尔德什 Vsevolodovich是他父母七个孩子之一。所有孩子都由母亲教授德语和法语，母亲还让他们热爱音乐。在他的六个兄弟姐妹中，我们特别提到Lyudmila Vsevolodovich Keldysh，生于1904年，后来成为著名数学家，本档案中有其传记，以及Yurii Vsevolodovich Keldysh，后来成为音乐学家。

到1909年，全家已迁居里加，Vsevolod Mikhailovich在理工学院授课，克尔德什 Vsevolodovich就出生在这座城市。1915年，德军入侵拉脱维亚，里加理工学院的教职员被疏散到莫斯科。克尔德什一家在莫斯科没有亲戚可以帮忙，生活相当艰难。他们有好几年住在城郊的Losinoostrovskaya，但父母喜爱古典音乐，常去城里听音乐会。音乐会结束后，他们别无他法，只能步行回家，要走好几英里。在Losinoostrovskaya有过艰难的日子，例如孩子们记得1917年有一天，母亲给全家吃的只有炸洋葱，没有别的食物。1918年底，全家搬到莫斯科东北约250公里的伊万诺沃-沃兹涅先斯克，Vsevolod Mikhailovich开始在那里的理工学院任教——这所学院并入了里加理工学院。不过，他常回莫斯科从事工程项目。

1923年，全家搬到了莫斯科的一套公寓，当时十二岁的克尔德什就读于克里沃阿尔巴茨基巷的第7学校。这套公寓位于大楼的地下室，有五个房间，还有一间原本为仆人设计的小第六间房。克尔德什、尤里和另一个兄弟共用一间狭长的大房间，里面有三张铁床、一张大写字台和一架钢琴[17]：-

房间里总是烟雾缭绕、拥挤、嘈杂而有趣。妹妹们有时不被允许进去。尤里是唯一不抽烟、不吵闹的人。他会在钢琴前坐上几个小时，完全沉浸在音乐中，没有注意到周围发生的事情。……克尔德什在外表和举止上是个“吉普赛小子”，在所有兄弟中格外顽皮，也好争吵。

克尔德什为自己的贵族出身感到自豪，尽管如果他隐藏这一点，日子可能会好过些。他在填写正式表格时总是写上“社会出身——贵族”，并因此在1927年因社会阶级原因被土木工程师学院拒收。然而，在姐姐Lyudmila Vsevolodovich Keldysh的劝说下，他违背父亲的意愿（父亲希望他成为工程师）学习数学。他进入了莫斯科国立大学的物理数学系，在那里师从米哈伊尔·阿列克谢耶维奇·拉夫连季耶夫，于1931年7月24日毕业。此后，在米哈伊尔·阿列克谢耶维奇·拉夫连季耶夫的强力推荐下，他被任命到尼古拉·叶戈罗维奇·茹科夫斯基中央空气流体动力学研究所任职。该研究所由尼古拉·叶戈罗维奇·茹科夫斯基和谢尔盖·阿列克谢耶维奇·恰普雷金于1918年建立，提供了非凡的研究环境。当时，该研究所由谢尔盖·阿列克谢耶维奇·恰普雷金领导（尼古拉·叶戈罗维奇·茹科夫斯基已于数年前去世），米哈伊尔·阿列克谢耶维奇·拉夫连季耶夫是该研究所的顶尖科学家之一。正是在该研究所[20]：-

……他在那里遇到了比他年长三岁的列昂尼德·T·谢多夫，并开始了科学合作和亲密友谊，这在他余生中成为巨大力量和支持的源泉。

此处一段未译出，以下为英文原文 Keldysh worked on aerohydrodynamics, publishing a series of papers on the topic between 1934 and 1937. One problem that was particularly important during the 1930s was that of 'flutter', strong vibrations which would suddenly begin and sometimes be so violent as to cause the aircraft to destroy itself. Keldysh's theoretical work on this was a highly significant factor in overcoming the problem. But this was not the only research that Keldysh was undertaking at the time, for Ivan Matveevich Vinogradov invited him to undertake research for a doctorate at the V A Steklov Mathematical Institute of the USSR Academy of Sciences after the Institute had moved from Leningrad to Moscow in 1934. Keldysh submitted his doctoral thesis Functions of Complex Variable and Harmonic Functions Representation with Polynomial Series to the Steklov Mathematical Institute in 1937 - the degree was awarded in the following year [20]:-

获得博士学位后不久，他开始在莫斯科国立大学任教。他成功地讲授了常规本科课程和高度专业化的研究生课程，并指导研究生。克尔德什的研究讨论班很快在莫斯科的数学生活中占据了重要地位，影响了许多年轻数学家的发展，无论是纯数学还是应用数学方向，他们如今都已成为杰出的研究工作者。

克尔德什继续他的研究，经常与他的前老师米哈伊尔·阿列克谢耶维奇·拉夫连季耶夫合作。例如，克尔德什发表了：Conformal mappings of multiply connected domains on canonical domains（1939），一篇关于近期发展的综述；（与米哈伊尔·阿列克谢耶维奇·拉夫连季耶夫合作）Sur une évaluation pour la fonction de Green（1939）；（与米哈伊尔·阿列克谢耶维奇·拉夫连季耶夫合作）Sur un problème de M Carleman（1939）；以及独著论文Sur l'approximation en moyenne quadratique des fonctions analytiques（1939）。在评论最后提到的这篇论文时，S E Warschawski写道：-

作者构造了不属于康斯坦丁·卡拉西奥多里类的区域的例子，由此推断，所有多项式系统在其中封闭的区域类不能由拓扑性质来刻画，而是依赖于这些区域的度量性质。

克尔德什此时最感兴趣的课题之一是约翰·彼得·古斯塔夫·勒热纳·狄利克雷问题。作为他在这一领域工作的一个例子，我们引用对克尔德什的论文On the solubility and the stability of Dirichlet's problem（俄文）（1941）的一篇评论。雅各布·塔马尔金开始了详细的评论如下：-

这篇论文非常清晰简洁地阐述了关于约翰·彼得·古斯塔夫·勒热纳·狄利克雷问题可解性以及当区域边界变化时解的稳定性的各种近期结果。在第一章中，作者阐述了约翰·彼得·古斯塔夫·勒热纳·狄利克雷问题在诺伯特·维纳意义下的广义解，并讨论了正则点和非正则点的概念。在第二章中，他讨论了容量的概念。第三章致力于诺伯特·维纳关于点正则性的判别准则，以及讨论解在非正则点处的行为。第四章包含调和测度和广义解的积分表示的阐述。这些章节包含一些新结果，许多已知结果的证明以新的形式呈现。最后一章第五章似乎主要包含新结果。

彼得·诺维科夫在访谈[11]中总结了他叔叔克尔德什的贡献：-

克尔德什 在复变函数论和微分方程方面也是一位非常有才华的数学家。他对空气动力学的应用分支做出了特别基础的贡献。他是政府的首席理论顾问，并在1940-1960年代组织了与喷气机和太空相关的计算工作。他在苏联社会中是一位广为人知的人物。关于这类人工作的所有信息都被保密，没有反映在世界媒体上。M 克尔德什 长期担任 科学院 of USSR 的主席。

让我们更详细地看看 克尔德什 职业生涯中的这些方面。首先让我们注意到，飞机“颤振”问题只是他研究的第一类问题。下一个相关的问题是“摆振”，即飞机用三个轮子着陆时经常发生的极端振动。在这里，他能够利用解决颤振问题的经验，他对摆振的解决方案，连同给工程师关于如何克服这个问题的详细指示，在 Shimmy of the front gear of the three wheels undercart (1945) 中描述。除了在 尼古拉·叶戈罗维奇·茹科夫斯基 中央空气流体动力学研究所从事这类工作外，他还继续在 弗拉基米尔·安德烈耶维奇·斯捷克洛夫 数学研究所工作，从1944年4月成立到1953年领导力学系。他在这期间发表的论文例子说明了他在 弗拉基米尔·安德烈耶维奇·斯捷克洛夫 研究所所做的工作：Sur l'approximation en moyenne par polynomes des fonctions d'une variable complexe (1945)、Sur l'interpolation des fonctions entières (1947)、On the characteristic values and characteristic functions of certain classes of non-self-adjoint equations (俄语) (1951) 和 On a Tauberian theorem (俄语) (1951)。值得注意的是，尽管这些论文研究抽象数学，但 克尔德什 对这些问题的许多兴趣源于在实际应用数学情境中遇到的想法 [20]：-

例如，他在1951年发表的一篇关于在边界上退化的椭圆型方程边值问题的论文，引起了俄罗斯和外国数学家的极大关注，其起源在于他在空气动力学方面所做的工作。

克尔德什 越来越多地转向管理苏联正在进行的重大科学研究项目。1946年，他离开 尼古拉·叶戈罗维奇·茹科夫斯基 中央空气流体动力学研究所，成为喷气推进研究所的负责人。他担任这个职位九年。他在1961-62年期间担任 苏联科学院 的副主席，然后从1962年到1975年担任其主席。在此期间，他在1971年庆祝了自己的60岁生日（见 [18]），在官方生日庆祝会上，克尔德什 谈到他对离开学术研究、完全忙于管理和行政感到遗憾。然而，他在苏联核武器的发展以及太空研究计划中发挥了重要作用。例如，他是1954年提出苏联太空卫星计划建议的三位科学家之一，1955年他成为苏联卫星委员会负责人，该委员会成立以监督该计划。1957年首次成功发射卫星标志着密集太空研究计划的开始，克尔德什 通过他领导的多个不同组织如应用数学系参与其中。1959年成立了跨部门科学与工程委员会，克尔德什 被任命为委员会负责人。

在他担任 苏联科学院 主席期间，他引入了重大改革。有一个领域特别值得评论，因为它说明了共产主义意识形态与科学研究之间的紧张关系。共产党人拒绝了现代遗传学理论，因为它们不符合他们的意识形态，而是支持特罗菲姆·李森科的“政治正确”但科学上愚蠢的观点。事情在1964年达到顶点，在 克尔德什 担任主席期间，李森科的同事尼古拉·努日丁被提议为科学院正式院士。在讨论他的提议的会议上，克尔德什 在核武器开发中的同事之一安德烈·萨哈罗夫发言反对说：-

科学院章程对其成员在科学价值和公民责任方面设定了非常高的标准。通讯院士尼古拉·努日丁不符合标准。他与李森科院士一起，对苏联生物学特别是遗传学的可耻落后、伪科学观点的传播、冒险主义、学术的退化以及许多真正科学家的诽谤、解雇、逮捕甚至死亡负责。

克尔德什的候选资格被拒绝，他继续在科学院内建立了一个结构，使遗传学科学能够在没有政治干预的情况下得到适当研究——在当时苏联存在的政治局势下，这是一件极其困难的事情。Ian Sneddon在[20]中写到克尔德什作为科学院院长的角色：-

科学院院长一职带有许多特权；似乎给克尔德什带来最大乐趣的是作为杰出外国科学家的官方东道主和苏联科学代表团的领导人。他是一个极具个人魅力且智力兴趣广泛的人，这为这些访问的成功做出了很大贡献。他率领一个代表团于1965年2月访问了爱丁堡皇家学会，那些有幸参加我们主席、已故教授J N Davidson为他举行的晚宴的人，会记得他当时的讲话给听众留下的印象——特别是即兴部分关于Scott对俄罗斯文学的影响，这是因为他（仅在那天晚上）发现Scott曾是学会主席。

克尔德什因健康原因于1975年辞去科学院院长职务。有迹象表明他的健康恶化，部分原因是过度工作，部分原因是当科学被用作政治斗争的主要工具时，一个爱国的俄罗斯人在捍卫科学理想时所承受的压力。

克尔德什获得了来自本国和外国的许多荣誉。他因在颤振方面的工作而获得国家奖（1942年）和劳动红旗勋章（1943年）。1946年，他又因在摆振方面的工作而获得另一项国家奖。1943年，他当选为苏联科学院通讯院士，三年后当选为正式院士。1956年，他因解决国防问题而被授予社会主义劳动英雄称号，并于次年获得列宁奖。1961年，他再次被授予社会主义劳动英雄称号，这次是因为他在火箭以及世界上第一艘载人飞船东方号方面的工作，该飞船由尤里·加加林驾驶。1971年，他因组织苏联科学工作而被授予镰刀与锤子奖章。他六次获得列宁勋章，还获得过数枚奖章。他当选为许多科学院院士：蒙古科学院（1961年）、Polish Academy of Sciences（1962年）、Czech Academy of Sciences（1962年）、Romanian Academy of Sciences（1965年）、German Academy of Sciences（1966年）、莱比锡萨克森科学院（1966年）、American Academy of Arts and Sciences（1966年）、Bulgarian Academy of Sciences（1966年）、Hungarian Academy of Sciences（1970年），并于1968年7月1日当选为爱丁堡皇家学会荣誉外籍会士。他还获得了华沙大学的名誉理学博士学位。

最后我们注意到，他于1961年当选为苏联共产党中央委员会委员，并于1962年当选为最高苏维埃代表。此外，月球上的一座环形山以他的名字命名，1973年发现的一颗小行星也是如此。

Mstislav Vsevolodovich Keldysh was born in Riga. His father, Vsevolod Mikhailovich Keldysh (1878-1965), was a military construction engineer who had graduated from the Polytechnic Institute in Riga. Vsevolod Mikhailovich married Mariya Aleksandrovna Skvortsova (1879-1953) in Riga. She devoted herself to bringing up their children. It is worth recording that, going back one more generation, Mariya Aleksandrovna's father was an artillery general, the son of a general, and so from the nobility. Vsevolod Mikhailovich's father was an army doctor with the rank of general so also from the nobility. Mstislav Vsevolodovich was always proud of his noble roots even though this gave him problems in Communist Russia. The family were quite well off and, because of the nature of Vsevolod Mikhailovich's work, he travelled between many different towns. He lectured at different Technical Institutes and later was involved in the design and construction of the Moscow Metro and the Moscow-Volga canal. Mstislav Vsevolodovich was one of his parents' seven children. All the children were taught German and French by their mother who also gave them a love of music. Of his six brothers and sisters we mention in particular Lyudmila Vsevolodovich Keldysh, born in 1904, who became a famous mathematician and has a biography in this archive, and Yurii Vsevolodovich Keldysh who became a musicologist.

By 1909 the family were in Riga, where Vsevolod Mikhailovich lectured at the Polytechnic Institute, and it was in that city that Mstislav Vsevolodovich was born. In 1915 the German army invaded Latvia and the staff at the Riga Polytechnic Institute were evacuated to Moscow. The Keldysh family had no relations to help them in Moscow and they suffered considerable hardship. For several years they lived in Losinoostrovskaya, just outside the city, but the parents loved classical music and often attended concerts in the city. After these concerts, they had no alternative but to make their way home on foot, a journey of several miles. There were difficult times in Losinoostrovskaya, for example the children remembered one day in 1917 when their mother fed the whole family just fried onions, having no other food. The family moved to Ivanovo-Voznesensk, a city about 250 km northeast of Moscow, towards the end of 1918 when Vsevolod Mikhailovich began teaching at the Polytechnic Institute there - this Institute was joined to the Riga Polytechnic Institute. However, he often returned to Moscow to work on engineering projects.

In 1923 the family moved to an apartment in Moscow and Mstislav, who was twelve years old at this time, attended School No 7 in Krivoarbatsky lane. The apartment, in the basement of the building, had five rooms and a tiny sixth room which had been originally designed for a servant. Mstislav, Yuri and one other brother shared a large narrow room containing three iron beds, a large writing desk and a piano [17]:-

The room was always smoky, crowded, noisy and fun. Younger sisters were sometimes not allowed in there. Yuri was the only one not smoking and not noisy. He sat for hours at the piano, completely immersed in music, not noticing what was happening around him. ... Mstislav, in appearance and behavior a "Gypsy Kid," was out of all the brothers especially mischievous, and quarrelsome.

Mstislav Keldysh was proud of his noble origins even through he might have had an easier time if he had hidden them. He always filled in official forms with "social origin - nobility" and he was refused entrance to the Institute of Civil Engineers in 1927 because of his social class. However, he was persuaded by his older sister Lyudmila Vsevolodovich Keldysh to study mathematics, against the wishes of his father (who wanted him to become an engineer). He gained entry to the Physics and Mathematics department of Moscow State University where, after being taught by Mikhail Alekseevich Lavrent'ev, he graduated on the 24 July 1931. Following this, with a strong recommendation from Lavrent'ev, he was appointed to a position at the N E Zhukovsky Central Aero-Hydrodynamic Institute. This Institute, set up by Nikolai Egorovich Zhukovsky and Sergei Alekseevich Chaplygin in 1918, provided a remarkable research environment. It was, at this time, directed by Chaplygin (Zhukovsky had died several years before) and the Institute had Lavrent'ev as one of its leading scientists. It was at the Institute [20]:-

... where he met Leonid T Sedov, three years his senior, and began a scientific collaboration and close friendship which were to be a source of great strength and support to him for the whole of the rest of his life.

Keldysh worked on aerohydrodynamics, publishing a series of papers on the topic between 1934 and 1937. One problem that was particularly important during the 1930s was that of 'flutter', strong vibrations which would suddenly begin and sometimes be so violent as to cause the aircraft to destroy itself. Keldysh's theoretical work on this was a highly significant factor in overcoming the problem. But this was not the only research that Keldysh was undertaking at the time, for Ivan Matveevich Vinogradov invited him to undertake research for a doctorate at the V A Steklov Mathematical Institute of the USSR Academy of Sciences after the Institute had moved from Leningrad to Moscow in 1934. Keldysh submitted his doctoral thesis Functions of Complex Variable and Harmonic Functions Representation with Polynomial Series to the Steklov Mathematical Institute in 1937 - the degree was awarded in the following year [20]:-

Shortly after the award of the doctorate he began to teach at Moscow State university. He delivered with great success both regular undergraduate and highly specialised graduate courses of lectures and he supervised research students. Keldysh's research seminars soon came to assume a prominent role in the mathematical life of Moscow and influenced the development of many young mathematicians, both pure and applied, now distinguished research workers.

Keldysh continued his research, often collaborating with his former teacher, Mikhail Lavrent'ev. For example Keldysh published: Conformal mappings of multiply connected domains on canonical domains (1939), a survey of recent developments; (with Lavrent'ev) Sur une évaluation pour la fonction de Green (1939); (with Lavrent'ev) Sur un problème de M Carleman (1939); and the single-authored paper Sur l'approximation en moyenne quadratique des fonctions analytiques (1939). Reviewing this last mentioned paper, S E Warschawski writes:-

The author constructs examples of regions, not of Carathéodory class, from which he infers that the class of all regions in which the system of all polynomials is closed cannot be characterized by topological properties but that this class depends on metrical properties of these regions.

One of the topics that most interested Keldysh around this time was the Dirichlet problem. As an example of his work in this area we quote from a review of Keldysh's paper On the solubility and the stability of Dirichlet's problem (Russian) (1941). Jacob David Tamarkin begins a detailed review as follows:-

The paper gives a very clear and concise exposition of various recent results concerning the solvability of Dirichlet's problem and also the stability of the solution when the boundary of the domain varies. In Chapter I the author gives an exposition of the generalized solution of Dirichlet's problem in the sense of Wiener, and discusses the notions of regular and irregular points. In Chapter II he discusses the notion of capacity. Chapter III is devoted to Wiener's criterion for regularity of a point, and to discussion of the behaviour of the solution at an irregular point. Chapter IV contains an exposition of the harmonic measure and integral representation of the generalized solution. These chapters contain some new results and many proofs of known results are presented in a new form. The last chapter V appears to contain mostly new results.

Sergei Novikov, in the interview [11], sums up the contributions of his uncle Mstislav Keldysh:-

Mstislav Keldysh, was also a very talented mathematician in the theory of functions of a complex variable and in differential equations. An especially fundamental contribution was made by him to applied branches of aerodynamics. He was a Chief Theoretician-adviser of the government and an organizer of computational work related to jets and space in 1940-1960s. He was a widely known person in the Soviet society. All information on the work of such people was classified and not reflected in the world press. M Keldysh was the President of the Academy of Sciences of USSR for a long time.

Let us look in a little more detail at some of these aspects of Keldysh's career. First let us note that the problem of airplane 'flutter' was only the first such problem that he worked on. The next, related, problem was that of 'shimmy', that is the extreme vibrations which often occurred in the nose leg of a plane landing on three wheels. Here he was able to use his experience in solving the flutter problem and his solution to shimmy, together with detailed instructions to engineers on how to overcome the problem, was described in Shimmy of the front gear of the three wheels undercart (1945). As well as undertaking this type of work at the Zhukovsky Central Aero-Hydrodynamic Institute, he continued to work at the Steklov Mathematical Institute, heading the Department of Mechanics from its foundation in April 1944 until 1953. Examples of papers he published during this period illustrate the work he undertook at the Steklov Institute: Sur l'approximation en moyenne par polynomes des fonctions d'une variable complexe (1945), Sur l'interpolation des fonctions entières (1947), On the characteristic values and characteristic functions of certain classes of non-self-adjoint equations (Russian) (1951), and On a Tauberian theorem (Russian) (1951). It is worth noting that, although these papers studied abstract mathematics, much of Keldysh's interest in these problems arose through meeting the ideas in practical applied mathematical situations [20]:-

For instance a paper he published in 1951 on boundary value-problems for elliptic equations that degenerate on the boundary, that attracted much attention from Russian and foreign mathematicians had its origins in work he was doing in aerodynamics.

After World War II, Keldysh turned increasingly to managing the major scientific research projects that were being carried out in the USSR. In 1946 he left the Zhukovsky Central Aero-Hydrodynamic Institute to become head of the Jet-Powered Research Institute. He held this position for nine years. He served as vice-president of the USSR Academy of Sciences during 1961-62, then served as its president from 1962 to 1975. During this period be celebrated his 60th birthday in 1971 (see [18]) and at the official birthday celebration, Keldysh spoke of his regret at leaving his academic research behind when he became fully occupied with management and administration. However, he had played an important role in the development of nuclear weapons by the Soviets as well as in their space research programme. For example, he was one of three scientists to make a proposal in 1954 for the Soviet space satellite programme and in 1955 he became head of the USSR Commission on the Satellite which was set up to oversee the programme. The first successful satellite launch in 1957 marked the beginning of an intensive programme of space research and Keldysh was involved in this through a number of different organisations such as the Department of Applied Mathematics which he headed. In 1959 the Interdepartmental Scientific and Engineering Council was established and Keldysh was appointed head of the Council.

During his period as president of the USSR Academy of Sciences he introduced major reforms. One area in particular is worth commenting on because it illustrates the tension between Communist ideology and scientific studies. The Communists had rejected modern theories of genetics because they did not fit their ideology and instead supported the "politically correct" but scientifically foolish views of Trofim Lysenko. Matters came to a head in 1964, during Keldysh's presidency, when Nikolai Nuzhdin, an associate of Lysenko, was proposed for full membership of the Academy. At the meeting where his proposal was discussed, Andrei Sakharov, one of Keldysh's colleagues in the development of nuclear weapons, spoke against saying:-

The Academy's Charter sets very high standards for its members with respect to both scientific merit and civic responsibility. Corresponding member Nikolai Nuzhdin does not satisfy the criteria. Together with Academician Lysenko, he is responsible for the shameful backwardness of Soviet biology and of genetics in particular, for the dissemination of pseudo-scientific views, for adventurism, for the degradation of learning, and for the defamation, firing, arrest, even death of many genuine scientists.

Nuzhdin's candidacy was rejected and Keldysh went on to build a structure within the Academy in which the science of genetics could be properly studied without political interference - an exceptionally difficult thing to achieve in the political situation that existed in the USSR at the time. Ian Sneddon writes about Keldysh in his role of president of the Academy in [20]:-

The office of President of the Academy carries with it many privileges; the one which seemed to give Keldysh the most pleasure was that of acting as official host to distinguished foreign scientists and as the leader of scientific delegations from the USSR. He was a person of great personal charm and wide intellectual sympathies, which contributed much to the success of these visits. He led a delegation which visited the Royal Society of Edinburgh in February 1965 and those who were privileged to attend the dinner which our President, the late Professor J N Davidson, gave in his honour, will recall the impression which his speech on that occasion made on his audience - especially an impromptu part on the influence of Scott on Russian literature occasioned by his discovery (of only that evening) that Scott had been President of the Society.

It was for health reasons that Keldysh stepped down as president of the Academy in 1975. There are suggestions that his health deteriorated, partly because of overwork, partly because of the strain caused by the difficulties that a patriotic Russian was put under defending scientific ideals when science was being used as the main tool in a political struggle.

Keldysh received many honours both from his own country and from foreign countries. He was awarded a State Prize (1942) and the Red Banner of Labour (1943) for his work on flutter. Another State Prize was awarded in 1946 for his work on shimmy. He was elected a corresponding member of the USSR Academy of Sciences in 1943 and a full academician three years later. He was named Hero of the Socialist Labour in 1956 for his solution to defence problems and received the Lenin Prize in the following year. In 1961 he again was named Hero of the Socialist Labour, this time for his work on rockets and on Vostok, the world's first manned spaceship piloted by Yuri Gagarin. In 1971 he was awarded the Sickle and Hammer for his organisation of Soviet science. Six times he received the Order of Lenin and he also was awarded several medals. He was elected to many academies: the Mongolian Academy of Sciences (1961), the Polish Academy of Sciences (1962), the Czech Academy of Sciences (1962), the Romanian Academy of Sciences (1965), the German Academy of Sciences (1966), the Saxony Academy of Sciences in Leipzig (1966), the American Academy of Arts and Sciences (1966), the Bulgarian Academy of Sciences (1966), the Hungarian Academy of Sciences (1970), and was elected an Honorary Foreign Fellow of the Royal Society of Edinburgh on 1 July 1968. He also received an honorary D.Sc. from the University of Warsaw.

Finally we note that he was elected to the Central Committee of Communist Party of the USSR (1961) and as a Deputy of the Supreme Soviet (1962). In addition a crater on the Moon was named for him, as was a minor planet discovered in 1973.