朗道写给物理学生的信 | 科学思维的价值

任何物理学家都应该从事他最感兴趣的工作，而不是出于虚荣而从事他的科学工作。

——朗道

■ 作者  栗弗席兹

■ 编译  廖玮

■ 编者按  

本文原文以俄语发表于 Nauka i zhizn’ No. 9, 14-22, 1971; 英文翻译发表于American Journal of Physics 45, No. 5,415-422,1977，translated by J. G. Adashk；收录于 Landau The Physicist and the Man: Recollections of L D. Landau,ed. by I. M. Khalatnikov, translated from Russian by J. B. Sykes, Pergamon Press 1989。

如文中所述，朗道有很强的写作障碍，他长期依靠合作者把其工作和物理思想表述整理成论文，即便其单独完成的研究工作也是如此。朗道长期依靠栗弗席兹（E.M. Lifshitz）为其写作论文，朗道口述，栗弗席兹按照朗道的口述表述整理成文字。

现在（1976年）距离列夫·达维多维奇·朗道的辉煌事业因一场悲惨的事故而结束已经快15年了。那些选择从事理论物理事业的人，再也不能从这位对在科学领域向其寻求建议的任何人敞开大门的人那里收到告别了。这个非同寻常的人的思维方法也在过去消退，并被传说所笼罩。即使那些有幸成为他的学生和朋友的人的最生动的回忆，也无法充分描述他人格的独特、光辉和魅力。

任何回忆都必定是主观的，其中包括叙述者个性的一部分。只有没有被记录者转述的真实的话语和直接的说话方式，才能让人洞察到一个人的灵魂。

根据一个人死后留下的信件，可以推断出他生前的生动惯用语言。但是列夫·达维多维奇写信非常困难，而且很少写。他很难把自己的想法写下来（因此，当有人建议他写一篇通俗文章时，他的回答是:“你可能听说过我完全没有写作天赋，我所有的作品都是和别人合著的。”）。他甚至很难在一篇他独自完成科学工作的文章中（没有合作者）做出语言论述，他所有的科学论文多年来都是别人为他写成的。他对表达的简洁和清晰有着难以克服的渴望，这迫使他在每一个短语的选择上都花费了大量的时间，以至于最终写任何东西，无论是科学文章还是私人信件，都成一种折磨。

因此极显其高度责任感的突出特色是, 列夫·达维多维奇总是（虽然不总是立即）回答向他寻求建议或帮助的人（“我推迟了我的回答，不是因为任何根本性的原因,但仅仅因为对我来说写下文字是困难的,因此我需要很长时间才能抽出时间写信”；又说:“抱歉耽搁了，由于我对书信体艺术的极度厌恶”）。

多年来，他直接向物理问题研究所办公室的打字员口述这些信件，他在地板上踱步，小心翼翼地说出每一个短语。我们感谢尼娜·德米特里耶夫娜·洛什卡列娃（Nina Dmitrievna Loshkareva），她多年来一直担任研究所的秘书。她保存了这些信件的副本，尽管这些信件是“私人的”而不是“官方的”。

关于朗道不仅是一位天才的物理学家而且也是一位天生的教师这一事实，人们已经写了很多。在科学史上，一个人同时具备这两种品质的情况并不常见。在这方面，有理由将朗道与他自己的老师，伟大的尼尔斯·玻尔，做比较。尽管他们在情感构成和性格特征上几乎没有什么共同之处——玻尔的极端温和与朗道的热情和严厉一点也不相似——但他们确实有一些更深刻的共同点：在科学问题上绝对拒绝妥协，对人怀有善意，随时准备帮助任何试图在科学上找到自己的道路的人，以及为他人的才能和他人的科学成功而喜悦的能力。

因此，很自然地，回答年轻人的问题，即如何学习和学习什么，在朗道的信件中占据了一个突出的位置。这些回答不仅展示了朗道灵魂的品质，而且反复地反映了他对训练未来的物理学家的看法。这些观点应该会引起新一代年轻科学家的兴趣。

一个在奔萨（Penza）的技术学院的学生写给列夫·达维多维奇，抱怨他花了太多时间在物理实验室里以及在数学和理论物理的自我教育上，但在发现自己仍然面临的大量学习材料时感到很失落：我只是在开始我的旅程，我也看不出明确的导向科学的路径，我请求你帮助我组织自己，选择正确的方向。您可以非常简单地但极大地帮助我：请寄给我一份大纲，某种告诉我该学什么、按什么顺序学习的大纲。朗道的回答是：

亲爱的B同志

你显然很认真地对物理感兴趣，我急切地想要帮助你。你很好地懂得，在科学领域工作，你需要学习很多东西。

至于你应该学什么，这在很大程度上取决于你未来的计划。关键是现代物理学家分为两类——理论家和实验家。理论家们用笔在纸上写下公式，实验家们在实验室里用仪器工作。很自然，这两个专业所需要的教育是不同的。很明显，理论家需要一个更彻底和深刻的理论基础，尽管实验家当然也必须知道很多。

因此，考虑一下这个问题，写信告诉我你的意愿。我很乐意寄给你合适的大纲，在你学习完这些材料之后，我想你就会做好准备开始工作了。

致以最良好的祝愿

朗道

工人L写信给列夫·达维多维奇：“一周后我将离开莫斯科，如果你能给我一些建议，告诉我必须学习什么以及如何学习才能成为一名理论物理学家，以及我是否值得为此而努力，我将非常感激……我所接受的训练大致相当于在莫斯科大学的力学和数学专业三年的训练，但我已经25岁了，必须工作。”他写了他试图解决的问题，理解物理理论原理的困难，以及他如何试图绕过这些困难；他还提到他觉得学外语很难。“我请求你，列夫·达维多维奇，请告诉我，我是否有希望成为一名物理学家。如果是这样的话，除了寄给我你著名的大纲和你可能给我的任何建议外，请告诉我完成你的大纲通常需要多长时间，以便我再次评估自己的能力。我知道，列夫·达维多维奇，你的时间是多么宝贵，如果你能回答我，我将认为这是莫大的荣幸。”

列夫·达维多维奇写道：

亲爱的L同志

我将尽力回答你的问题。

事先评价你在理论物理领域的能力当然是困难的。但烧制陶器的并不是神。我相信，如果你真的愿意，你一定能在理论物理领域取得成功。最重要的是，这项工作必须是你真正感兴趣的。对于虚荣的考虑绝不能取代真正的兴趣。

显然，你必须首先正确地掌握理论物理的技巧。这本身并不太难，因为你已经接受了部分数学训练，而数学技巧是我们的科学的基础。二十五岁并不算太老(我的年龄是你的两倍，也无意辞职)，而工人的劳动，无论如何也不会对你造成任何伤害。

你唯一不能做的就是把精力都集中在解决重大科学问题上。如果你继续有系统地工作，问题的解决最终会自然而然地到来。当然，经济困难可能是一个障碍，因为空腹或非常疲劳时不容易工作。不幸的是，外语是必不可少的。但是不要忘记，你不需要特别的能力来掌握它们，因为即使是非常笨的英国人也对英语有相当的了解。你得出了正确的结论，你必须少考虑基本的东西。最重要的是要掌握工作的技巧，对微妙要点的理解会自然而然地得到。

总之，我可以说，如果你有真正的兴趣和工作能力，你会成为一个理论家。我把大纲附在这封信之后。至于所涉及的时间，这将取决于你对其他事情的负担程度，以及你目前实际知道多少。实际情况是，时间跨越从Pomeranchuk的两个半月（他一开始就几乎知道了一切），到其他同样成功情况的几年时间。

致以最美好的祝愿，你的，朗道

一所技术学院的一个学生也写道，他被理论物理所吸引，而当面对许多他仍然觉得难以理解的书籍和文章时，他变得多么恼怒。他讲述了自己曾经在物理问题研究所（Institute of Physical Problems）参加过朗道的研讨会（该研究所对所有人开放），但他什么也听不懂，也无法让自己与朗道说话。下面是列夫·达维多维奇的回答：

亲爱的R同志。

如果你真的对理论物理感兴趣，我将很乐意帮助你从事这门在我看来诱人的科学。

你会自然地被大量的材料弄糊涂，不知道从哪里开始。很明显，一个理论研讨会目前对你来说是难以理解的，你参加它还为时过早。我寄给你的是“理论最低标准”大纲，如果你愿意，你可以由我或我的同事逐节测试。

你必须从数学开始，你知道，它是我们科学的基础。测试范围已在大纲中说明。记住，所谓的“数学知识”，我们指的不仅仅是各种各样的定理，而是一种实际的做积分以及求解常微分方程等等的能力。

我的电话号码也列在大纲上。你不必怕我——我从不咬人。

祝你成功

朗道

又一个向列夫·达维多维奇的请求是：“爱因斯坦一度没有拒绝帮助他的学生因菲尔德（Infeld），因此我决定给你写信，希望你不会拒绝我的小小的请求。我也是一名学生，只是在无线电工程系的二年级，但我非常喜欢理论物理。你可能很忙，但如果你能抽出几分钟给我，我将不胜感激。对我来说，掌握理论物理的大多数分支的深刻而全面的知识是绝对必要的，因此也必须掌握必要的高等数学……请原谅我打扰你，但对我来说，这是非常重要的，尽管可能不太合适。但在生活中，如果事情变得艰难，就不会有总是合适的余地。”列夫·达维多维奇在新年前夜回答道:

亲爱的K同志

我很高兴给你回信。你完全正确地认为，要从事理论物理工作，必须首先掌握这一领域的知识。我很乐意帮你。

正如你自己所理解的，一个理论家首先必须了解他的数学。我们需要的并不是数学家们大肆赞扬的各种存在性定理，而是数学技巧，即解决具体数学问题的能力。

我推荐下面的课程。首先，学会正确地(而且尽可能快地)做微分、积分、解常微分方程;学习矢量分析和张量代数(即如何使用张量指标)。在这里，起主要作用的不应该是教科书，而应该是一本包含一系列问题的书——哪本书并不重要，只要它包含的问题足够多就行。

做完这些后，请给我打电话(最好在上午九点半到十点半之间，那时我几乎总是在家，但如果有必要，也可以在一天中的其他时间)，来见我。我将测试你，并为你提供进一步学习的大纲。如果你通过了整个大纲(根据你的知识和勤奋程度，这将需要一到三年的时间)，那么我将认为你已经为科学工作做好了充分的准备，如果你愿意的话，我会尽力帮助你，为你的科学工作做出安排。这就是全部。

祝新年快乐，并致以良好的祝福。

你的，朗道

由于莫斯科居民总是能够直接与列维·达维多维奇沟通，所以很自然地，信件主要来自其他城市。许多人问：既不去专门的物理研究所学习，也不去大学学习，能够成为理论物理学家吗? 他们发现自己面临着一个困境：他们应该继续在自己的大学学习，还是应该试图离开它，继续独立学习?

朗道对一个教育学院一位心存疑虑的学生的回答是：

在我看来，你给自己制造了一个不必要的困境。你将从教育学院毕业的事实无论如何都会派上用场，继续在学院学习几乎不会影响你的工作。如果你有足够的意愿，你可以独立学习理论物理——毕竟，它只需要书本和纸张。

另一所教育学院的一名学生收到了对类似问题的如下答复：

你热切地想从事物理学是很好的，因为对科学的热爱是通向成功的第一个通行牌。幸运的是，理论物理是一门完全不需要强制学生上大学的科学。我在这封信里附上了一个大纲。遵照这个大纲，你将获得足够的理论物理知识，使你能够进一步独立工作。记住，精通数学是特别重要的。数学的主要分支在大纲的导言部分提到。

如果您能够并且愿意的话，请到莫斯科来，我的同事或我可以从大纲的各个部分(共有九个部分，包括数学)对你进行考察。如果你成功了，我希望能帮助你找到一个从事理论物理工作的机会，即使你不是从莫斯科大学毕业，而是从图拉教育学院毕业。

确切地说，这就是全部。我衷心祝愿你成功。记住，在科学中最重要的是工作，其余的自然会来到。 

列夫·达维多维奇最看重的是对科学的热爱，一种不受外来动机驱使的热情，而这些特点总是能引起他的同情和帮助的愿望。然而，如果他不能立即看出交流中的激情，他回答的语气就会变得不那么富有同情心。因此，一名外地大学的毕业生表示希望在物理问题研究所的理论部工作，但在这方面只报告说他能够获得莫斯科居留证，他得到的答复如下：

不幸的是，我不能大大地鼓励你。我们不敢草率行事，只在通过理论物理的“理论最低标准”考试后才选择研究生。适当的大纲已经附上。考试可以在任何时间进行。如果你成功地通过了这道障碍，那么你可能会在没有莫斯科居住证的情况下被录取，因为俄罗斯科学院为外地研究生提供宿舍。

这些信件中提到的理论物理最低标准大纲最早由朗道在20世纪30年代在哈尔科夫的乌克兰物理技术研究所提出，当时学生们开始聚集在他身边，他的理论物理学校开始形成。该大纲后来不断修订，但其所依据的教学原则没有改变。

列夫·达维多维奇反对肤浅和业余浅涉：独立的科学工作只有在对科学原理进行了充分全面的研究之后才能进行。他深信理论物理学是一门统一的、不可分割的科学，有统一的方法。他坚持认为，凡是希望成为他学生的人，首先要掌握理论物理学所有分支的原理。这些原理包含在理论最低标准的七个相继部分中（力学、场论、量子力学、统计物理、连续介质力学、宏观电动力学和相对论量子理论）。

朗道自己的科学创造力的一个特点是其几乎前所未有的广度；它涵盖了所有的理论物理——从流体力学到量子场论。在我们这个不断变窄的专业化时代，这种多才多艺正在成为一种例外；随着朗道的去世，物理学可能失去了最后一位伟大的普遍主义者。当然，他并不要求任何人成为像他一样的普遍主义者。但他认为，所有理论物理学分支的知识——至少是在“理论最低标准”范围内的知识——都是所有理论家必须具备的，不管他们的专业是多么狭窄。他一遍又一遍地重复:

至于你提出的关于学习理论物理的问题，我只能说，有必要学习它的所有主要分支，而学习的顺序是由它们的相互关系决定的。作为一种学习方法，我只能强调，你必须自己完成所有的计算，而不能把它留给你所读过的书的作者。

有趣的是，列夫·达维多维奇同时认为，一个人不可能同时兼顾物理学的理论和实验工作。对一群提出真正的理论物理学家也应该是实验家的学生，列夫·达维多维维奇写道：

那些相信理论物理学家也可以是实验家的人显然把理论物理学家想象成超人。理论物理学和实验物理学现在已经大不相同了，一个人不太可能同时从事这两项工作。在过去的几十年里，唯一的例外是费米，但是，我们认识到他是一个天才，这个例外只是证实了这一规律。理论物理学家和实验物理学家从事物理学的不同方面，两者相互补充，相互联系，但任何一方都不指导另一方。

“理论物理最低标准”的考试，可以说总是很有效：这种考试并不需要推导出什么理论公式，而只需要运用自己的知识去解决一个具体的问题。起初，列夫·达维多维奇亲自批改所有的考试。后来，当申请人的数量变得太大时，这些职责被分配给了他最亲密的合作者。但是第一次考试，第一次与每一个新来的年轻人相识，列夫·达维多维奇总是让自己去做。为了这个目的，任何人都可以和他见面——其所要做的就是打电话表达他的意愿。

当然，并非所有从事理论物理最低标准学习的人都有能力和毅力去完成它;有许多人中途退出。从1934年到1961年，通过这个考验的人的名单（列夫·达维多维奇亲自保存了这份名册）只包括43个名字。这个选拔的效率至少可以从以下正式数据来评估:通过的人中有8人已经成为科学院的院士，另有16人是科学博士。

从所引用的信件中可以看出，列夫·达维多维奇对掌握数学技巧有多么重视。这种精通的程度必须是这样的：如果可能的话，数学上的困难不应该转移理论家对问题的物理困难的注意力——至少在涉及标准数学程序时是这样。这只有通过充分的培训才能做到。然而，经验表明，目前的大学课程和教育方法往往不能提供这种程度的训练。经验还表明，如果一个物理学家在开始独立研究之后才开始学习数学，他会觉得数学太“枯燥”。因此，列夫·达维多维奇首先对每位考生进行数学“实用”和计算方面的测试。测试要求具备以下能力:计算任意不定积分（可以用初等函数表示）和解任意标准型常微分方程的能力，以及矢量分析和张量代数的知识。第二次数学考试包括复变函数理论的原理（余数理论、拉普拉斯方法）。其中的设想是，像张量分析、群论等的训练，将与它们所应用的理论物理分支一起学习。

在一所教授物理的大学为数学课程向其征求意见时，朗道在其回应中非常清楚地陈述了其对物理学家的数学教育的看法。他以其特有的直率提出了这样的观点：这些教程的制定必须充分考虑到物理系的要求，并听取那些在物理科学工作的日常经验中知道这项工作需要什么的人的建议。他写道：

不幸的是，你们的教程和所有通常的数学教程一样，都有同样的缺点，这些缺点使物理学家研究数学的一半时间变成了令人厌烦的浪费。尽管数学对物理学家很重要，但众所周知，他们真正需要的是计算分析数学。另一方面，数学家们，由于令人费解的原因，把逻辑练习当作交易中的强制性股票推给我们。在这个特别的教程中，这以特别的开场白的形式直接强调了这一点。在我看来，是时候教物理学家们他们自己需要的东西了，而不是去拯救他们的灵魂，而不管他们自己的意愿。我不想去反驳中世纪学者的令人尊敬的观点，即通过学习不必要的科目，人们不知何故学会了如何进行逻辑思考。

我断然认为，有必要在为物理学家设计的数学课程中排除一切存在定理、过分严格的证明等。因此，我不会停下来与你单独讨论教程中与这一观点强烈抵触的所有众多条目。我只补充几句话。

矢量分析是作为多重积分研究的一部分在你们的课程中教授的。我并不反对这样的并置，但我希望这样做不会损害关于向量分析公式的绝对必要的形式知识。

处理级数的教程中有很多不必要的东西，这些东西淹没了一些有用的资料，这些资料对于傅里叶级数和傅里叶积分来说是绝对必要的。

在我看来，把所谓的数学物理作为一门选修课是正确的。我们不应该要求实验物理学家能够处理这样的主题。

开设概率论课程的必要性值得怀疑。物理学家在量子力学和统计物理的课程中学习所有他们需要知道的关于概率的知识。

因此，我认为对数学教学进行一次最严肃的改革的时机已经成熟。那些承担这一最重要和最困难的任务的人，将会得到已经受过训练的物理学家们的真诚感谢，尤其是来自未来世代的众多成员的感谢。

列夫·达维多维奇一生都对教学问题非常感兴趣，他梦想着撰写各种层次的物理书籍——从中小学校教科书到对专家的理论物理教程。事实上，《理论物理教程》的几乎所有卷都是在他有生之年完成的，《普通物理教程》和《对所有人的物理学》的第一卷也是如此。以他的思想为基础的《理论物理简明教程》在他去世后开始出版。他还计划为物理学家编写数学教科书，按照他的想法，这些教科书应该是教授数学在物理学中的实际应用的“操作手册”。他没能活着实现这个计划。

他也没有抽出时间写中小学教科书，尽管他对中小学有着强烈的兴趣，而且很乐意给中小学学生们做演讲，给他们回信。

因此，图拉一所学校的少先队员写道：“我们知道你的空闲时间很少，但我们仍然希望你能抽出几分钟来回答我们的问题。我们班的少先队员并不都明白他们为什么需要接受教育，所以我们希望组织一次以“教育是财富，劳动是财富的钥匙”为主题的聚会。他们中的许多人没有系统地学习功课，只是为了获得及格分数。我们希望收到您的来信，因为您的话将对我们的少先队员很有说服力。”列夫·达维多维奇的回答是：

亲爱的孩子们,

要对显而易见的东西写出些什么是非常困难的。毕竟，你们很清楚现在的教育对任何职业都是必不可少的。没有受过教育的人永远是二流的。

在这种情况下，我非常苦恼地发现你们的信中有一个语法错误。这说明你们小孩子读书很少，你们甚至连自己的母语都不熟练。因此，多读书吧——毕竟，读书也是有乐趣的——要记住，你们受教育不是为了学校，而是为了你们自己，受教育一点也不枯燥，相反，还很有趣。

致以最良好的祝愿。

朗道

列夫·达维多维奇还回答了很多那些不幸的人，他们相信有可能在没有知识或能力的情况下实现科学革命（包括对相对论的反驳）。然而，在这种情况下，列夫·达维多维奇认为在表达他的反对意见时，没有必要表现出任何同情和含糊其辞。以下是一些这样的回答：

我得说你的手稿毫无趣味可言。现代物理学是一门巨大的科学，它主要以大量的实验事实为基础。显然，你对这门科学几乎一无所知，你试图用毫无意义的词句来解释你所知甚少的物理现象。很明显，它什么也不能产生出来。如果你真的对物理学感兴趣，你不应该急于从事发现，而应该首先对这门学科至少有一点了解。

现代物理学是一门复杂而困难的科学，要想在这门科学上有所成就，就必须知道得很多。要提出任何新思想，就更需要知识。从你的信中可以明显看出，你的物理知识很有限。你所谓的新思想只不过是一个没有受过良好教育的人的胡言乱语;这就好像一个以前从未见过电动机器的人来找你，并在这个问题上提出新的想法。如果你真的对物理学感兴趣，首先要花时间学习这门科学。过一段时间，你自己就会明白从你的打字机里打出的这些废话是多么可笑。

不幸的是，你提出的论点荒谬到了极点。甚至很难解释你信中的错误在哪里。看在神的份上，在你开始解释宇宙之前，至少要具备阅读物理文献的最基本能力;你现在所做的就是把自己置于一个荒谬的境地。

你的话都是些毫无意义的天真话。很明显，如果你想在这一领域工作，你要做的还有很多——要熟悉这一门学科。没学会开车的人是不会开车的。物理决不会比这个更简单。

对列夫·达维多维奇的信件的这个简短抽样，恰如其分地以关于真正的科学家的工作动机的一段话而结束。在某种程度上，对任何科学家而言，对其工作的成果的承认都是重要的；这对列夫·达维多维奇当然也很重要。然而，毫无疑问，他内心最大的动力不是对名声的渴望，而是永不枯竭的好奇心，一种了解自然的强烈热情。他最看重的也是别人身上的这种激情。因此，他总是谴责只研究“重要”问题的倾向:    

你问我该从事什么，理论物理的哪个分支是最重要的。我必须说，我认为这种对问题的陈述是荒谬的。一个人如果只把科学中“最重要的”问题看作值得自己感兴趣的问题，那他的不谦虚一定是相当可笑的。在我看来，任何物理学家都应该从事他最感兴趣的工作，而不是出于虚荣的考虑而从事他的科学工作。当然，人们必须小心避免那些表述不明智、因而缺乏科学兴趣的问题。 

一个人绝不能为了别有用心的动机，为了名利，为了有什么伟大的发现而工作，这样做是不会有什么结果的。朗道从不放过任何一个机会来复述这个简单的真理。

■ 附录 

英文翻译(取自Landau The Physicist and the Man: Recollections of L D. Landau)

Landau's plain talk to students of physics

E.M. Lifshitz

It is now (1976) almost fifteen years since a tragic accident put an end to the brilliant activity of Lev Davidovich Landau. Those choosing to embark on a career in theoretical physics can no longer receive a valediction from the man whose door was open to anyone seeking his advice in science. The cast of this unusual man's mind also recedes in the past and becomes shrouded with legends. Even the most vivid recollections of those who were fortunate to be included among his close pupils and friends cannot give a full account of the uniqueness, lustre, and fascination of his personality.

Any remembrance is bound to be subjective and include some part of the personality of the narrator. Only the actual words, the direct manner of speaking, unparaphrased by the chronicler, are capable of giving an insight into a man's soul.

A man's vivid idiom can be deduced after his death from his letters. But Lev Davidovich wrote letters with great difficulty, and infrequently. It was difficult for him to set his thoughts down in writing (thus, his answer to one of the suggestions that he write a popular article was: 'You have probably heard that I have utterly no aptitude for writing, and all my writings are with co-authors'). It was even difficult for him to discourse in an article on scientific work he did alone (without co-workers!), and all his scientific papers were written for him for many years by others. His insuperable desire for brevity and clarity of expression forced him to devote so much time to the choice of each phrase, that ultimately the task of writing anything, be it a scientific article or a personal letter, became a torment.

It is therefore all the more remarkable and characteristic of his high sense of duty, that Lev Davidovich always (albeit not always immediately) answered anyone who turned to him for advice or help ('I have delayed my answer not for any fundamental reason, but simply because it is difficult for me to write letters and it therefore takes me a long time to get round to it'；and again: 'Excuse the delay, due to my extreme antipathy to the epistolary art').

For many years he dictated these letters directly to a typist at the office of the Institute of Physical Problems, pacing the floor and carefully delivering each phrase. We are indebted to Nina Dmitrievna Loshkareva, for many years the secretary of the Institute, for preserving copies of these letters, although they were 'personal' rather than 'official'.

Much has been written about the fact that Landau was not only a genius as a physicist, but also a born teacher. The combination of both qualities in one person to such a degree is not a frequent occurrence in the history of science. In this respect, there are grounds for comparing Landau with his own teacher, the great Niels Bohr. Although they had little in common in their emotional make-up and traits of character—Bohr's extreme gentleness was not at all similar to Landau's ebullience and harshness—they did share something much more profound: absolute refusal to compromise when it comes to science, combined with good will towards people, readiness to help anyone trying to find his way in science, and the ability to rejoice in someone else's talent and someone else's scientific success.

It is therefore natural that a prominent place in Landau's correspondence is occupied by answers to young people's questions how and what to study. These answers not only demonstrate the quality of Landau's soul, but repeatedly reflect his views on the training of future physicists. These views should be of interest to the new generation of young scientists.

A student of one of the technical colleges in Penza writes to Lev Davidovich complaining that he spends much time in the physics laboratory and on self-education in mathematics and theoretical physics, but finds himself at a loss when confronting the vast material that is still to be learned: I am only at the start of my journey, I do not see clearly the paths that lead to science, and I beg of you to help me get organized, to choose the right direction. You can help me very simply and very greatly: please send me a plan, some sort of programme that tells me what to study and in what sequence.' Landau answers:

Dear Comrade B.

You are apparently seriously interested in physics, and I am very anxious to help you. It is very well that you understand that to work in science there is much for you to learn.

As to what you should study, this depends very strongly on your future plans. The point is that modern physicists come in two classes—theoreticians and experimenters. The theoreticians use pens to write formulae on paper, and experimenters work with instruments in laboratories. Naturally, the education required for these two specialities differs. It is clear that the theoreticians need a much more thorough and profound theoretical foundation, although experimenters, of course, must also know quite a lot.

Therefore, think over this question and write to me of your intentions. I shall be glad to send you appropriate programmes, and after you have studied this material, I think you will be ready enough to start.

With best wishes,

L. Landau

Worker L. writes to Lev Davidovich: 'In a week I shall be leaving Moscow, and will be extremely grateful if you could give me some advice as to what and how I must study to become a theoretical physicist, and whether it is worth while for me to aim at this . . . My training corresponds to approximately three years of the Mechanics and Mathematics Division of the Moscow State University, but I am already 25 years old, and have to work.' He writes of the problems he had tried to solve, the difficulties in the understanding of the principles of physical theories, and how he attempted to get round these difficulties; he mentions also that he finds it difficult to learn foreign languages. ‘I beg of you, Lev Davidovich, please write to me if there is any hope of my becoming a physicist. And if this is the case, besides sending your famous programme and any advice you may wish to give me, please tell me how long it usually takes to complete your programme, so as to enable me to assess once more my own capabilities. I know, Lev Davidovich, how precious your time is, and I shall consider it a great honour if you answer me.’

Lev Davidovich writes:

Dear Comrade L.          
     I shall attempt to answer your questions.

It is of course difficult to evaluate beforehand your ability in the field of theoretical physics. But it is not the Gods who fire pottery. I believe that you will be able to work successfully in the field of theoretical physics if you really want to. It is most important that this work be your real interest. Vanity considerations can in no way replace real interest.

Obviously you must first master properly the techniques of theoretical physics. This by itself is not too difficult, since you already went through part of the mathematical training, and mathematical techniques are the foundations of our science. Twenty-five is not too old (I am twice as old and have no intention of quitting), and a worker's labour, in any case, could not do you any harm.

The only thing you must not do is to direct your effort to a solution of major scientific problems. If you just keep on working systematically, the solution of the problem will eventu- ally come by itself. Financial difficulties, of course, can be a hindrance, for it is not easy to work on an empty stomach or when you are very tired. Foreign languages, unfortunately, are essential. But don't forget that you need no special ability to master them, for even very dim- witted Englishmen have a fair knowledge of English. You have reached the correct conclusion that you must think less of the fundamentals. The most important thing to master is the technique of working, and the understanding of the fine points will come by itself.

To sum up, I can say that you will become a theoretician if you have a real interest and an ability to work. I am attaching the programme to this letter. As to the time involved, this will depend on the extent to which you are burdened with other matters, and on how much you actually know at present. In practice the time ranges from two and a half months in the case of Pomeranchuk, who practically knew everything at the outset, to several years in other also successful cases.

With best wishes, yours, Landau

A student of one of the technical colleges also writes of being attracted to theoretical physics, and how exasperated he becomes when faced with the many books and articles which he still finds it difficult to understand. He tells how he once attended Landau's seminar at the Institute of Physical Problems (admission to which was always open to all), but understood nothing, and could not bring himself to address Landau. Here is Lev Davidovich's answer:

Dear Comrade R.

If you are seriously interested in theoretical physics, I shall gladly help you engage in what I also regard as an alluring science.

Naturally, you are bewildered by the tremendous mass of material and don't know where to start. It is clear that a theoretical seminar would at present be unintelligible to you and it is still too early for you to attend it. I am sending you the 'theoretical minimum' programme in which you can, if you wish, be examined section by section, by myself or by my associates.

You must start with mathematics which, you know, is the foundation of our science. The scope is indicated in the programme. Bear in mind that by 'knowledge of mathematics' we mean not just all kinds of theorems, but a practical ability to integrate and to solve in quadra- tures ordinary differential equations, etc.

My telephone numbers are also indicated in the programme. You need not be afraid of me— I never bite.

With all wishes for your success

L. Landau

One more appeal to Lev Davidovich: 'At one time Einstein did not refuse to help his student Infeld, and I therefore decided to write to you in the hope that you will not refuse my small request. I, too, am a student, only in the second year of the Radio Engineering Department, but I am very fond of theoretical physics. You are probably very busy, but if you can spare a few minutes for me, I shall be most grateful. It is absolutely essential for me to acquire a profound and comprehensive knowledge of most branches of theoretical physics, and therefore also of the necessary higher mathematics.. .Forgive me for troubling you,but for me it is very important and, although it is perhaps not quite proper, but it happens in life, if the going gets rough, that there is not always room for propriety.' Lev Davidovich answers on New Year's Eve:

Dear Comrade K.

I am glad to answer your letter. You are quite correct in believing that to work in theoretical physics you must first acquire knowledge of this field. I shall gladly help you with this.

As you have yourself understood, a theoretician must above all know his mathematics. What is needed is not all kinds ofexistence theorems, on which mathematicians lavish so much praise, but mathematical techniques, that is, the ability to solve concrete mathematical problems.

I would recommend the following course of study. First, learn to be able to perform correctly (and as rapidly as possible) differentiation, integration, solution of ordinary differential equations in quadratures; study vector analysis and tensor algebra (i.e. how to operate with tensor indices). The principal role should be played here not by the textbook but by a book containing a set of problems—it does not much matter which book, so long as it contains enough problems.

After you have done this, please phone me (best between 9.30 and 10.30 a.m., when I am almost always at home, but if necessary at some other time of the day), and come and see me. I shall examine you and supply you with a programme for further study. If you pass this entire programme (this will take from one to three years, depending on your knowledge and dili- gence), then I shall consider you to be fully prepared for scientific work, and will attempt to help you, if you so desire, with arrangements for this purpose. This is all.

With wishes for a happy New Year,

yours, Landau

Since Moscow residents were always able to communicate with Lev Davidovich directly, it is natural that letters came to him mainly from other cities. Many asked: Is it possible to become a theoretical physicist by studying neither in a special Physics Institute nor in a University? They found themselves confronted by a dilemma: should they continue to study in their own college or should they attempt to leave it and continue their studies independently?

Landau's answer to one such doubting student of a Pedagogical Institute is:

It seems to me that you are creating an unnecessary dilemma for yourself. The fact that you will graduate from the Pedagogical Institute will in any case come in handy, and continuing your studies at the Institute will hardly interfere with your work. If you have enough will, you can study theoretical physics independently—after all, it requires nothing but books and paper.

A student from another pedagogical institute received, to an analogous query, the following reply:

The fact that you ardently want to engage in physics is very good, for ardent love of science is the first token of success. Fortunately, theoretical physics is a science for which attendance at a university is not at all obligatory. I am enclosing in this letter a programme, which when followed will provide you with enough knowledge of theoretical physics to permit further independent work. Bear in mind that a mastery of mathematics is especially important. The main branches of mathematics are mentioned in the introductory part of the programme.

If you can and want to, come to Moscow, where my co-workers or I can examine you in the various divisions of the programme (there are altogether nine, including mathematics). If you are successful, I hope to be able to help you find an opportunity to work in theoretical physics even in the event that you graduate not from the Moscow State University, but only from the Tula Pedagogical Institute.

This, properly speaking, is all. I sincerely wish you all success. Remember, that most important in science is work, the rest will come by itself. 

A passionate attachment to science, an enthusiasm not impelled by some extraneous motives, was valued by Lev Davidovich more than anything else, and these characteristics invariably aroused his sympathy and desire to help. The tone of his replies, however, becomes less sympathetic if he does not discern immediately this passion in the communication. Thus, a gradu- ate of an out-of-town university, who expressed a desire to work at the Theoretical Department of the Institute of Physical Problems, but reported in this connection only that he is able to obtain a Moscow residence permit, received the following answer:

Unfortunately, I cannot encourage you greatly. We are afraid to buy a pig in a poke, and choose graduate students only after they pass their theoretical physics examinations in the form of the 'Theoretical Minimum'. The appropriate programme is attached. The examination can be taken at any time. If you crawl successfully through the potential barrier, then you could prob- ably be accepted without a Moscow residence permit, since the Academy of Sciences provides hostels for out-of-town graduate students. 

The Theoretical Minimum' programme referred to in all these letters was first developed by Landau back in the 1930s, while at the Ukrainian Physicotechnical Institute in Kharkov, when students started to gather around him and his school of theoretical physics came into being. This programme was subsequently continuously revised, but the pedagogical principles on which it was based remained unchanged.

Lev Davidovich was the enemy of any superficiality and dilettantism: independent scientific work can be undertaken only after a sufficiently comprehensive study of the principles of science. In accordance with his deep conviction that theoretical physics is a unified and indivisible science with unified methods, he insisted that those who wish to become his pupils master first the principles of all the branches of theoretical physics.These principles were contained in seven successive sections of the Theoretical Minimum' (mechanics, field theory, quantum mechanics, statistical physics, mechanics of continuous media, macroscopic electrodynamics, and relativistic quantum theory).

A characteristic feature of Landau's own scientific creativity was its almost unprecedented breadth; it encompassed all of theoretical physics— from hydrodynamics to quantum field theory. In our era of ever-narrowing specialization, such versatility is becoming an exception; with the passing of Landau, physics has lost possibly one of the last great universalists. Of course, he did not demand of anyone to be a universalist to the same degree that he himself was. But he regarded knowledge of all the branches of theoretical physics—at least within the scope of the 'Theoretical Minimum'—as mandatory for all theoreticians, regardless of their narrow specialization. Again and again he repeats:

As to your question concerning the study of theoretical physics, I can state only that it is necessary to learn ALL its main branches, and the sequence of study is dictated by their mutual relationship. As a method of study, I can only emphasize that you must perform all the calcu- lations by yourself, and must not leave it to the authors of the books you have read.

It is interesting that at the same time Lev Davidovich believed that one person is incapable of simultaneously doing justice to both theoretical and experimental work in physics. To a group of students who advanced the opinion that a real theoretical physicist should be also an experimentalist, Lev Davidovich wrote:

Those who believe that theoretical physicists can also be experimenters apparently imagine that theoreticians are supermen. Theoretical and experimental physics are now so greatly dif- ferent, that one person cannot possibly engage in both. The only exception of the last few decades was Fermi but, recognizing that he was a genius, this exception only confirms the rule. Being engaged in different aspects of physics, theoreticians and experimenters supplement each other and are mutually related, but neither guides the other.

The examination on the Theoretical Minimum was always, if we can say so, efficacious: it was not necessary to derive some theoretical formula, but to be able to use one's knowledge to solve a posed concrete problem. At first, Lev Davidovich marked all the examinations himself. Later, when the number of applicants became too large, these duties were distributed among his closest collaborators. But the first examination, the first acquaintance with every new young person, Lev Davidovich always left to himself. Anyone could meet him for this purpose—all he had to do was to phone and express his wish.

Of course, not all those who undertook the study of the Theoretical Mini- mum' had the ability and the persistence to complete it; there were many drop-outs. The list of those who passed this trial from 1934 to 1961 (Lev Davidovich kept this roster personally) contains only 43 names. The efficiency of this selection can be assessed at least from the following formal data: eight of those who passed have already become members of the Academy of Sciences, and sixteen more are Doctors of Science.

It is seen from the cited letters what great significance Lev Davidovich attached to mastery of the mathematical techniques. The degree of this mastery must be such that mathematical difficulties should, if possible, not divert the theoretician's attention from the physical difficulties of the problem—at least when it came to standard mathematical procedures. This can be accomplished only by sufficient training. Yet experience shows that the present university curricula and approaches frequently fail to provide this degree of training. Experience shows also that, if a physicist begins to study mathematics after he has started independent research, he finds it too 'dull'. Therefore, Lev Davidovich first subjected every examinee to a test in mathematics in its 'practical', computational aspects. The following was required: ability to evaluate any indefinite integral (expressible in terms of elementary functions) and to solve any ordinary differential equation of standard type, and knowledge of vector analysis and tensor algebra. The second examination on mathematics included the principles of the theory of functions of complex variables (residue theory, the Laplace method). The assumption was that such disciplines as tensor analysis, group theory, etc., will be studied together with those divisions of theoretical physics in which they find application.

Landau's views on the mathematical education of physicists were set forth by him with great clarity in response to a request for his opinion on the mathematics programme in one of the colleges teaching physics. With his characteristic directness, he advances the opinion that these programmes must be planned with full account taken of the requirements of the physics departments—and with the advice of those who know, from their daily experience with scientific work in physics, what is required for this work. He writes:

Unfortunately, your programmes suffer from the same shortcomings as all usual programmes on mathematics, which turn half the study of mathematics by physicists into a tiresome loss of time. For all the importance of mathematics to physicists, what they really need, as is well known, is computational analytic mathematics. Mathematicians, on the other hand, for inexplicable reasons, palm off on us logical exercises as a mandatory stock in trade. In this particular programme this is directly emphasized in the form of a special introductory remark. It seems to me that the time has long come to teach physicists what they need for themselves, and not save their souls despite their own desires. I do not care to dispute the venerable medieval scholastic opinion, that by studying unnecessary subjects people somehow learn how to think logically.

I believe categorically that it is necessary to exclude from the mathematics courses designed for physicists all existence theorems, excessively rigorous proofs, etc. I shall therefore not stop to discuss separately all the numerous items in your programme which strongly contradict this point of view. I shall make only a few supplementary remarks.

Vector analysis is taught in your programme as part of the study of multiple integrals. I have nothing against such a juxtaposition, but I hope that this is not done to the detriment of the absolutely essential formal knowledge of the formulae of vector analysis.

The programme dealing with series is particularly overburdened with unnecessary things, which drown out those few useful data that are absolutely essential to know concerning the Fourier series and the Fourier integral.

It would be correct in my opinion, to make the so-called mathematical physics an optional course. One should not require experimental physicists to be able to handle such topics.

The need for a course in probability theory is quite doubtful. Physicists learn all they need to know about probability in courses of quantum mechanics and statistical physics.

Thus, I believe that the teaching of mathematics is ripe for a most serious reform. Those who undertake this most important and difficult task will deserve the sincere gratitude of the already trained physicists, but in particular of the numerous members of future generations.

Being deeply interested all his life in problems of teaching, Lev Davidovich dreamt of writing books on physics at all levels—from school textbooks to a course on theoretical physics for specialists. Actually, almost all the volumes of Course of Theoretical Physics* were completed in his lifetime, as well as the first volumes of Course of General Physics and Physics for Everyone. The Shorter Course of Theoretical Physics, which is based on his ideas, started being published after his death. He also planned to write textbooks of mathematics for physicists, which should be, in accordance with his ideas, 'operating manuals' for teaching the practical application of mathematics to physics. He did not live to realize this programme.

Nor did he get round to writing school textbooks, although he was vividly interested in schools, and willingly addressed schoolchildren, and answered their letters.

Thus, the Pioneers [boy and girl scouts] of one of the schools in Tula wrote: 'We know how little free time you have, but we hope nevertheless that you will find a few minutes to answer us. We wish to organize a gathering on the topic, "Education is a treasure, labour is a key to it", since not all the Pioneers of our class understand why they need an education. Many of them study their lessons not systematically, but only to get a pass mark. We would like a letter from you, since your words will be very convincing for our Pioneers.' Here is Lev Davidovich's answer:

Dear children,

It is very difficult to write of the obvious. After all, you know perfectly well that education is now

essential for any occupation. The uneducated man will always be something second-rate.

In this context, I was very distressed to find a grammatical error in your letter. This shows that you children read very little, that you are not versed suitably even in your own native tongue. Therefore read much more—it is, after all, also entertaining—and remember that you need education not for the school but for yourselves, and that being educated is far from dull,but on the contrary, interesting. With best wishes,

L. Landau

Lev Davidovich answered also those unfortunately too numerous persons who believe it possible to revolutionize science (including refutation of relativity theory) without having either knowledge or abilities for this purpose. In such cases, however, Lev Davidovich did not consider it necessary to show any sympathy and to mince words when expressing his disapproval. Here are a few examples of such answers:

I must say that your manuscript is lacking in any interest. Modern physics is a tremendous science, based primarily on a large number of experimental facts. You are patently almost completely unacquainted with this science, and you attempt to explain physical phenomena, about which you know little, with meaningless phrases. It is clear that nothing can come out of it. If you are seriously interested in physics, you should not engage in discoveries, but first learn at least a little about the subject.

Modern physics is a complicated and difficult science, and in order to accomplish anything in it, it is necessary to know very much. Knowledge is all the more needed in order to advance any new ideas. It is obvious from your letter that your knowledge of physics is very limited. What you call new ideas is simply prattle of an ill-educated person; it is as if someone who never saw an electric machine before were to come to you and advance new ideas on this subject. If you are seriously interested in physics, first take time to study this science. After some time you yourself will see how ridiculous is this nonsense that came out of your typewriter.

The arguments advanced by you are unfortunately absurd to the highest degree. It would even be difficult to explain where the errors lie in your letter. For God's sake, before you start expounding on the universe, acquire at least the most elementary ability to read a physics text; all you do now is put yourself in a ridiculous situation.

Your remarks consist of naivetes that are of no interest whatever. It is clear, that if you wish to work in this field, there is much study ahead of you—to become acquainted with the subject. You would hardly sit behind the wheel of a car without knowing how to drive. Physics is by no means easier.

This brief sampling from Lev Davidovich's letters is appropriately concluded with a passage on the motives for work of a real scientist. Recognition of the results of his work to one degree or another is important to any scientist; it was important, of course, also to Lev Davidovich. There is no doubt, however, that the greatest inner incentive for himself was not a desire for fame, but inexhaustible curiosity, an all-consuming passion to know nature. And such a passion he valued primarily also in others. For this reason he always condemned the tendency to work only on 'important' problems:

You ask in what to engage, in the sense of which branches of theoretical physics are the most important. I must say that I regard such a statement of the question as absurd. One must have a rather ridiculous immodesty to regard only 'the most important' problems of science as worthy of one's interest. In my opinion, any physicist should engage in what interests him the most, and not embark on his scientific work from considerations of vanity. Of course, one must take care to avoid problems that are not wisely formulated and are therefore devoid of scientific interest.

One must never work for the sake of ulterior motives, for fame, with an aim at making a great discovery—nothing will come out of it anyway. Landau never missed an opportunity to repeat this simple truth.

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