尼古拉·博戈柳博夫Nikolai Bogolyubov

尼古拉·博戈柳博夫的名字也音译为Bogoljubov（或Bogoliubov或Bogoliuboff）。他出生于下诺夫哥罗德（1932年至1990年间称为高尔基），这是莫斯科东南约450公里处的一座大城市。他的父母是博戈柳博夫 Mikhailovich 博戈柳博夫和Olga Nikolaevna。博戈柳博夫 Mikhailovich是俄罗斯东正教会的一名神父，教授神学和哲学，他的妻子Olga是一名音乐教师。1917年十月革命引发了最终导致苏维埃掌权并于1922年创建苏联的事件时，博戈柳博夫 Nikolaevich年仅八岁。由于苏维埃日益占据主导地位，对俄罗斯东正教神父的子女施加了限制，博戈柳博夫 Nikolaevich的父亲越来越难以给儿子提供良好的教育。因此，1921年，全家决定迁往基辅，在那里博戈柳博夫 Nikolaevich可以接受一流的教育。事实上，1922年，尽管他只有十三岁，他就开始参加由Nikolai Mitrofanovich Krylov在基辅大学举办的研究讨论班。

德米特里·格雷夫和Nikolai Krylov都很快意识到了他们这位年轻学生的潜力，并给予了他极大的帮助。1923年，博戈柳博夫在Krylov的协助下开始进行数学研究，并取得了他的第一批原创成果。他于1924年写下了他的第一篇科学论文On the behavior of solutions of linear differential equations at infinity （俄语）。Nikolai Krylov已于1922年被任命为基辅的乌克兰科学院数学物理系主任，并于1925年正式开始指导博戈柳博夫，后者当年已在科学院注册攻读候选学位（相当于博士学位）。在这个阶段，博戈柳博夫还没有本科学位，但由于他已被证明的卓越才能，他被接受进行研究生学习。1928年，他成功答辩了他的学位论文The Application of the Direct Methods of the Calculus of Variations to Investigation of Irregular Cases of a Simplest Problem。随后他开始攻读博士学位（相当于德国的教授资格论文（Habilitation））。Yu A Mitropolskii和S V Tyablikov写道[44]：-

他第一时期的著作，其中一些是他与他的老师N M Krylov合作完成的，涉及变分法的直接方法、殆周期函数理论以及边值微分方程的近似解。已经在这个时期，博戈柳博夫科学天赋的一个特征已经清晰地显现出来；如果可以这样说的话，他是一个专门研究那些无法用通常方法攻克、需要原则上全新的进路的问题的专家。他当时获得的许多结果早已成为经典；博戈柳博夫的数学论文已获得广泛的国际声誉和认可。他的一篇论文于1930年获得了博洛尼亚科学院颁发的奖项（A Merlani奖）。

1930年，博戈柳博夫 由 乌克兰科学院 主席团授予博士学位（成绩优异）。他继续在基辅大学以及基辅的 乌克兰科学院 理论物理研究所工作。两年后，博戈柳博夫 开始与 Nikolai Mitrofanovich Krylov 合作，他们发展了非线性振动理论；他们将自己的课题称为“非线性力学”。博戈柳博夫 找到了对模拟振动系统的非线性方程进行渐近积分的方法 [52]：-

博戈柳博夫 的许多论文涉及对非线性力学渐近方法的严格论证。通过将 儒勒·昂利·庞加莱-李雅普诺夫 理论和 儒勒·昂利·庞加莱-阿尔诺·当茹瓦 理论应用于环面上的轨迹，他考察了在参数足够小的情况下精确平稳解在近似解附近的性质，并证明了关于拟周期解的存在性和稳定性的定理。

他们的工作以俄文发表在专著 Introduction to Non-linear Mechanics（1937年）中，1943年出现了由 所罗门·莱夫谢茨 从俄文翻译的英文版。诺曼·莱文森 的评论开头如下：-

该专著的主要部分是对两位作者一部著作的浓缩，该著作致力于系统处理具有实际意义的问题。其处理方式旨在使工程师或物理学家易于理解。事实上，严谨性完全服从于使材料尽可能广泛可用的目标。书中给出了导致专著中所考虑类型方程的物理系统示例。此外，通过示例的显式解说明了求解方程方法的一般陈述。

他最后写道：-

所罗门·莱夫谢茨 在使 Krylov 和 博戈柳博夫 的这项工作现在得以面世方面做出了相当大的贡献。

转向力学对博戈柳博夫来说是通往理论物理道路上的一步，他在理论物理中做出了许多深刻贡献。然而，他的职业生涯被第二次世界大战打断。1941年6月，德军开始迅速推进到乌克兰，基辅遭到轰炸。7月，苏联人将技术工人疏散到东部，博戈柳博夫被疏散到巴什科尔托斯坦的乌法。在那里，他成为乌法国立航空技术大学数学分析系主任，并在乌法师范学院任教。他留在乌法直到1943年8月前往莫斯科。1943年11月1日，他接受了莫斯科国立大学理论物理系的一个职位，在那里研究随机过程理论。他于1946年出版了重要专著Problems of dynamical theory in statistical physics（俄文）。1946年至1949年间，他担任基辅国立大学力学与数学系主任。1947年，他成为莫斯科弗拉基米尔·安德烈耶维奇·斯捷克洛夫数学研究所新成立的理论物理系主任。该系的主要研究领域是量子场论，特别强调发展必要的数学方法。博戈柳博夫与该系其他研究人员合作，发表了Theory of Quantized Fields（1957年）、Problems of the Theory of Dispersion Relations（1958年）和Axiomatic Approach in Quantum Field Theory（1969年）等论文。1953年1月，他被任命为莫斯科国立大学理论物理负责人。

博戈柳博夫于1956年在杜布纳的联合核研究所创立了理论物理实验室。他成为该实验室的第一任主任，该实验室今天被称为博戈柳博夫理论物理实验室。欧洲核研究组织CERN成立于1954年。1958年，博戈柳博夫以理论物理实验室主任的身份，建议联合核研究所与CERN之间应进行系统性的科学家交流。这一想法在1959年于CERN举行的关于高能加速器领域国际合作的非正式会议上得到了推动，来自美国、苏联和其他西欧国家的顶尖科学家出席了该会议。1966年，他被任命为联合核研究所所长，担任该职务直至1988年。

1957年，博戈柳博夫与Dmitrii V Shirkov合著出版了Introduction to quantum field theory（俄文）。Arthur Wightman对该书的评论开头如下：-

这本书是对量子场论形式体系的介绍。对具体物理问题的应用仅用于说明该理论的基本思想。与所有这类近期努力一样，作者们不得不在数学上严谨的阐述（这将涵盖物理学家认为重要的内容极少）与更形式化的叙述之间做出选择。作者们显然选择了后者。尽管他们付出了相当大的努力以连贯的方式描述该理论，但他们不允许自己奢侈地仅仅因为某些问题在数学上尚未严格定义就忽视它们在物理上的重要性。

国际数学家大会于1958年在爱丁堡举行，博戈柳博夫（与瓦西里·谢尔盖耶维奇·弗拉基米罗夫合作）作了全体会议报告之一On some mathematical problems of quantum field theory。Arthur Wightman也评论了该报告：-

这份报告清晰地阐述了量子场论中，特别是在色散理论中出现的一些分布论和解析函数论问题。所涉及的主题包括分布的乘法、楔边定理及其推广。

这并不是博戈柳博夫与国际数学家大会的唯一联系，因为他是1982年在华沙举行的大会上负责颁发菲尔兹奖的委员会成员。

Yu A Mitropolskii和S V Tyablikov在[44]中给出了博戈柳博夫科学风格的一个例子：-

也许超导理论的例子最清楚地说明了博戈柳博夫科学风格的另一个非常典型的特征。当代理论物理学最重要的问题通常具有异常的数学复杂性。因此，即使理论基础上不存在原则性缺陷，在许多情况下计算困难如此之大，以至于可能转化为原则性困难；特别是，非相对论多体问题的情况就是如此。在解决这类问题时，提供正确解决这些问题所需的严格程度极为重要。正是这种近乎艺术、基于卓越物理和数学直觉的能力，是博戈柳博夫科学创造活动的突出特征。

[23]的作者还描述了博戈柳博夫的科学风格以及他与学生和同事的互动：-

博戈柳博夫培养了一整代数学家和理论物理学家。许多著名科学家尊敬而自豪地称他为老师。数学和物理的有机结合迫使每一个研究博戈柳博夫著作的人回忆起那些精确科学的代表被简单地称为自然哲学家的时代。这就是我们看到科学风格的博戈柳博夫特征的地方：全局评估问题的性质并确定其主要可解性，然后不被困难所阻碍，创建解决这个问题的适当数学工具（这就是我们遇到大卫·希尔伯特的“wir mussen wissen, wir werden wissen”的地方）。所有这些使博戈柳博夫能够建立非线性力学、数学物理和理论物理的大型科学学派。

我们尚未提到的博戈柳博夫工作的一个方面是他在名为Arzamas-16的核研究和核武器生产秘密城市中的活动。瓦西里·谢尔盖耶维奇·弗拉基米罗夫写道[59]（另见[60]）：-

1950年初，苏联政府派博戈柳博夫到设在萨罗夫修道院的一个绝密地点工作，该地点被称为苏联城市建设的伏尔加中央管理办公室，或称KB-11，为当时由I E Tam和A D Sakharov领导的理论物理学家小组提供数学支持，他们当时正在研究氢弹的第一个方案……博戈柳博夫和他的学生在这个地点组织了数学部门。……这个团队必须是先驱者，并且在克格勃的警惕目光下非常迅速地工作。博戈柳博夫的渊博学识和才华派上了大用场！……博戈柳博夫本人完成了一系列关于磁场中等离子体稳定性理论以及动力学方程的理论与应用的出色论文，并开始构建公理化量子场论。RDS-6的成功试验于1953年8月12日进行。博戈柳博夫被派往哈萨克斯坦的草原进行试验。……博戈柳博夫在那个地点工作了三年多；当时他刚过40岁。这是他生命中一段浪漫、非常富有成果和创造力的时期；一方面，那是修道院铁丝网后的生活，伴随着该制度的一切困难和强制；另一方面，是对托付给他的工作负有巨大责任。

博戈柳博夫因其对数学和理论物理的杰出贡献而获得许多荣誉。他于1958年被授予列宁奖：-

……因其对超导微观理论和量子场论的研究。

他曾三次获得苏联国家奖（1947年、1953年、1984年）；1953年的那次是因参与创建苏联第一颗氢弹。他还被授予米哈伊尔·阿列克谢耶维奇·拉夫连季耶夫奖和奖章、美国物理学会和美国物理联合会颁发的Dannie Heineman数学物理奖（1966年），并六次获得列宁勋章。他被授予十月革命勋章和两枚劳动红旗勋章。因杰出服务，博戈柳博夫于1969年被授予社会主义劳动英雄金星奖章，十年后再次获得。他获得了由德国汉堡Alfred Tepfer基金设立的A P Karpinski奖、保罗·狄拉克奖章（1992年）、德国物理学会的马克斯·普朗克金奖（1973年），以及美国费城富兰克林研究所的本杰明·富兰克林金奖（1974年）：-

……因非线性力学中的数学方法。

他被授予苏联科学院的M V Lomonosov金奖（1985年）：-

……因在数学和理论物理学方面的杰出成就。

他当选为乌克兰科学院和苏联科学院的成员，以及世界各地多个科学院的外籍院士。博戈柳博夫不仅因获得许多奖项而受到表彰，还因有多个以他命名的奖项而受到致敬。例如，联合核子研究所颁发博戈柳博夫奖，以表彰对理论物理和应用数学的杰出贡献。该研究所还颁发博戈柳博夫青年科学家奖。Ukrainian Academy of Sciences也颁发博戈柳博夫奖，以表彰对理论物理和应用数学的杰出贡献。

我们注意到，为纪念博戈柳博夫而撰写的若干文章的作者（我们在参考文献中列出）中，有几位曾是他的学生。这些人包括Yurii A Mitropolskii、Dmitry V Shirkov、Mikhail K Polivanov、Sergei V Tyablikov、瓦西里·谢尔盖耶维奇·弗拉基米罗夫和Dmitry N Zubarev。N N 博戈柳博夫（小），即[15]的作者之一，是博戈柳博夫的儿子，他是一位顶尖科学家，从事与其父相似的数学物理领域的工作。

Nikolai Nikolaevich Bogolyubov's name is also transliterated as Bogoljubov (or Bogoliubov or Bogoliuboff). He was born in Nizhny Novgorod (called Gorky between 1932 and 1990), a large city about 450 km south-east of Moscow. His parents were Nikolai Mikhailovich Bogolyubov and Olga Nikolaevna. Nikolai Mikhailovich was a priest in the Russian Orthodox Church who taught theology and philosophy, and his wife Olga was a music teacher. Nikolai Nikolaevich was eight years old when the October Revolution of 1917 started the events which would lead to the Soviets taking power and the creation of the Soviet Union in 1922. It became increasingly difficult for Nikolai Nikolaevich's father to provide a good education for his son since the increasing Soviet domination led to restrictions on children of Russian Orthodox priests. Therefore, in 1921, the family decided to move to Kiev where Nikolai Nikolaevich could receive a top quality education. Indeed in 1922, although he was only thirteen years old, he began attending research seminars at Kiev University run by Nikolai Mitrofanovich Krylov.

Both Dmitry Aleksandrovich Grave and Nikolai Krylov quickly realised the potential of their young student and helped him greatly. In 1923 Bogolyubov began to undertake mathematical research assisted by Krylov and produced his first original results. He wrote his first scientific paper On the behavior of solutions of linear differential equations at infinity (Russian) in 1924. Nikolai Krylov had been appointed chairman of the Mathematical Physics Department of the Ukrainian Academy of Sciences in Kiev in 1922, and in 1925 he formally began to supervise Bogolyubov who had registered for a Candidates Degree (equivalent to a Ph.D.) at the Academy in that year. At this stage Bogolyubov had no undergraduate degree, but he was accepted for postgraduate studies because of his proven exceptional abilities. In 1928 he successfully defended his thesis The Application of the Direct Methods of the Calculus of Variations to Investigation of Irregular Cases of a Simplest Problem. He then began to study for his doctorate (equivalent to the German habilitation). Yu A Mitropolskii and S V Tyablikov write [44]:-

The works of his first period, some of which were carried out by him jointly with his teacher N M Krylov, deal with direct methods of the calculus of variations, to the theory of nearly-periodic functions and approximate solutions of boundary-value differential equations. Already during that period one of the characteristic features of Bogolyubov's scientific gifts had become clearly pronounced; he is, if one may use the expression, a specialist in problems which cannot be attacked by usual methods and require an approach new in principle. A number of results obtained by him at that time have long since become classical; Bogolyubov's mathematical papers have attained widespread international renown and recognition. One of his papers was awarded in 1930 a prize by the Bologna Academy of Sciences (the A Merlani prize).

In 1930 Bogolyubov was awarded his doctorate (with distinction) by the Presidium of the Ukrainian Academy of Sciences. He continued working at Kiev University and also at the Institute for Theoretical Physics of the Ukrainian Academy of Sciences in Kiev. Two years later Bogolyubov began joint work with Nikolai Mitrofanovich Krylov in which they developed a theory of non-linear oscillations; they called their topic 'non-linear mechanics'. Bogolyubov found methods to asymptotically integrate non-linear equations modelling oscillating systems [52]:-

A number of papers by Bogolyubov are concerned with a rigorous justification of the asymptotic methods of non-linear mechanics. By applying the Poincaré-Lyapunov theory and the Poincaré-Denjoy theory on trajectories on a torus, he examined the nature of the exact stationary solution in the vicinity of an approximate solution for a sufficiently small value of the parameter and proved theorems on the existence and stability of quasi-periodic solutions.

Their work was published in Russian in the monograph Introduction to Non-linear Mechanics (1937), and in 1943 an English version appeared, translated from the Russian by Solomon Lefschetz. Norman Levinson begins a review as follows:-

The major portion of the monograph is a condensation of a book by the two authors devoted to a systematic treatment of problems of practical interest. The treatment is so oriented as to be readily available to the engineer or physicist. In fact, rigor is entirely subordinated to the objective of making the material as widely available as possible. Examples of physical systems are given which lead to the type of equation considered in the monograph. Moreover, general statements of methods for solving equations are illustrated by the explicit solution of examples.

He ends by writing:-

Lefschetz has performed a considerable service in making this work of Krylov and Bogolyubov available now.

The move towards mechanics was for Bogolyubov a step on a road which led to theoretical physics where he made many deep contributions. However, his career was interrupted by World War II. In June 1941 German armies began a rapid advance into Ukraine and Kiev was bombed. In July the Soviets evacuated the skilled workers to the east and Bogolyubov was evacuated to Ufa in Bashkortostan. There he became head of the Department of Mathematical Analysis at Ufa State Aviation Technical University and he also taught at the Ufa Pedagogical Institute. He remained at Ufa until August 1943 when he went to Moscow. On 1 November 1943 he accepted a position in the Department of Theoretical Physics at Moscow State University where he worked on the theory of stochastic processes. He published the important monograph Problems of dynamical theory in statistical physics (Russian) in 1946. During years 1946 to 1949 he was dean of the Faculty of Mechanics and Mathematics of Kiev State University. In 1947 he became head of the Department of Theoretical Physics, a new Department at the Steklov Mathematical Institute in Moscow. The main research area in the Department was quantum field theory, in particular there was an emphasis on developing necessary mathematical methods. Bogolyubov, in joint work with other researchers in the Department, published papers such as Theory of Quantized Fields (1957), Problems of the Theory of Dispersion Relations (1958) and Axiomatic Approach in Quantum Field Theory (1969). In January 1953 he was appointed as Head of Theoretical Physics at Moscow State University.

Bogolyubov founded the Laboratory of Theoretical Physics in the Joint Institute for Nuclear Research in 1956 at Dubna. He became the first director of the laboratory which today is called the Bogolyubov Laboratory of Theoretical Physics. CERN, the European Organization for Nuclear Research, was founded in 1954. In 1958 Bogolyubov, in his role as Director of the Laboratory of Theoretical Physics, suggested that there should be systematic exchanges of scientists between the Joint Institute for Nuclear Research and CERN. This idea was given impetus at an informal meeting on international co-operation in the field of high-energy accelerators held at CERN in 1959, which was attended by leading scientists from the United States, the USSR and other western European countries. In 1966 he was appointed as Director of the Joint Institute for Nuclear Research, a role he held until 1988.

In 1957 Bogolyubov published Introduction to quantum field theory (Russian) coauthored with Dmitrii V Shirkov. Arthur Wightman begins a review of the book as follows:-

The book is an introduction to the formalism of the quantum theory of fields. Applications to specific physical problems are described only to illustrate the fundamental ideas of the theory. As in all recent efforts of this kind, the authors have had the choice between a mathematically rigorous exposition which would cover very little of what physicists regard as important or a more formal account. The authors have clearly chosen the latter. Although they make considerable effort to describe the theory in a coherent fashion, they do not permit themselves the luxury of ignoring matters which are physically important merely because they are, as yet, mathematically ill defined.

The International Congress of Mathematicians was held in Edinburgh in 1958 and Bogolyubov (jointly with Vasilii Vladimirov) gave one of the plenary addresses On some mathematical problems of quantum field theory. Arthur Wightman also reviewed the address:-

This address is a clear exposition of some problems of the theory of distributions and analytic functions which have arisen in quantum field theory, especially in dispersion theory. The subjects treated include the multiplication of distributions, and the edge of the wedge theorem and its generalizations.

This was not the only connection Bogolyubov had with the International Congress of Mathematicians, for he was a member of the committee in charge of awarding the Fields medals at the 1982 Congress held in Warsaw.

Yu A Mitropolskii and S V Tyablikov give an example of Bogolyubov's scientific style in [44]:-

Perhaps the example of the theory of superconductivity illustrates most clearly one more feature which is very characteristic of Bogolyubov's scientific style. The most important problems of contemporary theoretical physics are characterized, as a rule, by exceptional mathematical complexity. As a result of this, even if no deficiencies of principle exist in the foundations of the theory, in a number of cases the computational difficulties are so great that they may transcend into difficulties of principle; this, in particular, is the situation in the non-relativistic many-body problem. In solving problems of this type it is exceedingly important to provide the degree of rigor required for the correct solution of these problems. It is just such an ability, bordering on art and based on brilliant physical and mathematical intuition, which is the outstanding characteristic of Bogolyubov's scientific creative activity.

The authors of [23] also describe Bogolyubov's style of science and his interaction with students and colleagues:-

Bogolyubov brought up a whole generation of mathematicians and theoretical physicists. Many famous scientists respectfully and proudly call him their teacher. The organic welding together of mathematics and physics compels everyone who studies the works of Bogolyubov to recall those times when the representatives of the exact sciences were simply called natural philosophers. This is where we see the Bogolyubov trait of scientific style: to globally appraise the character of the problem and to establish its principal solubility, and then, without being held back by difficulties, to create an adequate mathematical apparatus for solving this problem (this is where we come across Hilbert's "wir mussen wissen, wir werden wissen"). All this enabled Bogolyubov to establish large scientific schools of non-linear mechanics, mathematical physics, and theoretical physics.

One aspect of Bogolyubov's work which we have not mentioned yet is his activities in the secret city for nuclear research and nuclear arms production named Arzamas-16. Vladimirov writes [59] (see also [60]):-

At the beginning of 1950 the government of the USSR sent Bogolyubov to work at an ultra-secret site based in the Sarov monastery, known as the Volga Central Administrative Office of Urban Construction of the USSR, or KB-11, to provide mathematical support for the group of theoretical physicists led by I E Tam and A D Sakharov, who were then working on the first variant of the hydrogen bomb ... Bogolyubov and his students organized the mathematical section at this site. ... The team had to be pioneers and to work very quickly under the vigilant eye of the KGB. The enormous erudition and talent of Bogolyubov came in very handy! ... Bogolyubov himself completed a series of brilliant papers on the theory of stability of a plasma in a magnetic field and on the theory and applications of the kinetic equations, and he began his construction of axiomatic quantum field theory. A successful test of the RDS-6 took pace on 12 August 1953. Bogolyubov was sent to the steppes of Kazakhstan for the tests. ... Bogolyubov worked at that site for over three years; he was then just over 40. It was a romantic and very fruitful and creative period in his life; on the one hand, it was life behind barbed wire in a monastery with all the difficulties and impositions of the regime, and on the other hand there was the enormous responsibility for the work entrusted to him.

Bogolyubov received many honours for his outstanding contributions to mathematics and theoretical physics. He was awarded the Lenin Prize in 1958:-

... for his research into the microscopic theory of superconductivity and quantum field theory.

He received the State Prize of the USSR on three occasions (1947, 1953, 1984); that in 1953 was for taking part in the creation of the USSR's first hydrogen bomb. He was also awarded the Lavrent'ev Prize and Medal, the Dannie Heineman Prize for Mathematical Physics from the American Physical Society and the American Institute of Physics (1966), and six times he received an Order of Lenin. He was presented with the Order of the October Revolution, and two Orders of the Red Banner of Labour. For distinguished service Bogolyubov was awarded the Gold Star of Hero of Socialist Labour in 1969 and again ten years later. He received the A P Karpinski Prize established by the Alfred Tepfer Fund of Hamburg, Germany, the Dirac Medal (1992), the Max Planck Gold Medal from the Germany Physical Society (1973), and the Benjamin Franklin Gold Medal from the Franklin Institute, Philadelphia, United States (1974):-

... for Mathematical Methods in Nonlinear Mechanics.

He was awarded the M V Lomonosov Gold Medal of the USSR Academy of Sciences (1985):-

... for outstanding achievements in mathematics and theoretical physics.

He was elected to membership of the Ukrainian Academy of Sciences and the USSR Academy of Sciences as well as to foreign membership of academies around the world. Not only was Bogolyubov honoured by receiving many prizes, he has also been honoured by having several prizes named for him. For example the Joint Institute for Nuclear Research awards the Bogolyubov Prize for outstanding contributions to theoretical physics and applied mathematics. It also awards a Bogolyubov Prize for Young Scientists. The Ukrainian Academy of Sciences also awards a Bogolyubov Prize for outstanding contributions to theoretical physics and applied mathematics.

We note that several of the authors of articles written as a tribute to Bogolyubov (which we list in the references) had been his students. These include Yurii A Mitropolskii, Dmitry V Shirkov, Mikhail K Polivanov, Sergei V Tyablikov, Vasilii S Vladimirov, and Dmitry N Zubarev. N N Bogolyubov (Jr), an author of [15], is Bogolyubov's son who is a leading scientist, working in similar areas of mathematical physics as his father.