伊戈尔·沙法列维奇Igor Shafarevich

伊戈尔·沙法列维奇被普遍认为是俄罗斯当代主要数学家之一。他生于1923年，是罗斯季斯拉夫·斯捷潘诺维奇沙法列维奇和尤利娅·雅科夫列夫娜·瓦西里耶娃的儿子。罗斯季斯拉夫·斯捷潘诺维奇曾就读于莫斯科国立大学，在那里获得力学学位。他在多所不同的高等教育机构教授理论力学，例如莫斯科工程学院（莫斯科技术大学）。然而，在沙法列维奇罗斯季斯拉沃维奇出生前的那些年里，他经历过一些极其艰难的时期。谈到他父亲的经历时，沙法列维奇说（见[1]）：-

例如，[那里]有被处决的威胁。……仅仅是因为某个党派来到城里，或者有人被扣作人质，或者只是为了以防万一，或者因为你穿着靴子。我父亲说，他曾两次被拉去处决。有一次，事情最终以他受到检查而告终。他们检查了能从他那里拿走什么，以及是否值得枪毙他。当他们看到他有鞋子——不是靴子——时，就把他放了。[那里有]饥饿、斑疹伤寒、大批人死亡。

罗斯季斯拉夫·斯捷潘诺维奇年轻时曾想过进修道院，但内战的事件使他变得不那么虔诚了。沙法列维奇的母亲尤利娅·雅科夫列夫娜拥有圣彼得堡别斯图热夫女子学院的语言学学位。她是一位有才华的音乐家，曾师从特奥菲尔·里希特学习钢琴，后者是一位管风琴家和作曲家，也是20世纪主要钢琴家之一斯维亚托斯拉夫·特奥菲洛维奇·里希特（1915-1997）的父亲。里希特一家是沙法列维奇一家的亲密朋友，沙法列维奇和斯维亚托斯拉夫在成长过程中有很多时间在一起。

在沙法列维奇出生时，他的父亲在莫斯科工作，一家人住在那里一间公共公寓的房间里。尤利娅·雅科夫列夫娜的父亲是日托米尔国家银行的董事，日托米尔是尤利娅·雅科夫列夫娜曾居住的城镇。他在镇上有一套大公寓，尤利娅·雅科夫列夫娜回到父母家生孩子。斯维亚托斯拉夫·里希特和沙法列维奇一样，出生在日托米尔，那里是里希特家族的家乡。沙法列维奇和他的母亲很快回到他们在莫斯科公寓的房间，沙法列维奇就是在莫斯科长大的。小时候，沙法列维奇由父母教导，所以到了上学的年龄，他已经能读会写，因此直接被安排进了二年级。

沙法列维奇最初的爱好是历史和文学。他对文学的热爱始于童年读寓言的时候。他读过希腊传说、俄罗斯寓言和格林兄弟的德国寓言。这些不仅使他对文学产生了热爱，还赋予了他国际视野。对沙法列维奇来说阅读很容易，因为他父母的公寓里有很多书。读一本历史书让他想到要成为一名历史学家（见[1]或[15]）：-

我最初想成为的是历史学家。一本历史书落到了我手里。甚至不是那么有趣。一本从德语翻译过来的、供文法学校用的古代史。突然间我感到，世界并不局限于我周围的事物，而是在时间和空间上向四面八方延伸。我第一次为自己发现，我和我周围的人只是无尽世代链条中的一环。我立刻爱上了历史，甚至到了沉浸其中的地步。

突然，在他大约十二岁时，他对历史的热情突然转变，发展出了对数学的热情。我们当然不是说他对历史失去了兴趣，因为他一生中除数学之外的主要兴趣就是历史和音乐。他突然意识到自己想献身于数学的原因，是他从未完全理解的[15]：-

我试图回忆我是如何转向数学的，却想不起其中的逻辑或理由，尽管我认为当时从事历史研究确实会很困难。它被视为一门意识形态学科，选择各种观点的可能性非常有限。作为一个10到12岁的男孩，我几乎不可能理解这一点，但也许我潜意识里感觉到了。

他在这个幼小的年纪就展现出了数学天赋，这种天赋得到了他父母的培养。他独立阅读数学教科书，但不确定自己是否真正理解了它们。1938年，他决定向大学寻求帮助，于是找到了莫斯科大学的院长并说明了自己的情况。院长意识到面前是一个非常有才华的年轻人，便建议可以让沙法列维奇作为校外生注册，尽管他仍然是个小学生。然后他把沙法列维奇送到鲍里斯·德劳内那里，鲍里斯·德劳内考了他解析几何。接着他去了亚历山大·热纳季耶维奇·库罗什那里，亚历山大·热纳季耶维奇·库罗什考了他代数，最后他去了伊斯拉埃尔·盖尔范德那里，伊斯拉埃尔·盖尔范德考了他分析[15]：-

他们对我非常亲切和友善，和我一起做了大量工作，也就是说，在要求的内容之外还给了我很多文献阅读。……我把鲍里斯·德劳内和亚历山大·热纳季耶维奇·库罗什视为我的老师。他们不仅代表了两种不同的数学类型，而且是两种截然相反的数学类型。鲍里斯·德劳内是彼得堡学派的经典代表。他感兴趣的是非常经典类型的丢番图分析。……但亚历山大·热纳季耶维奇·库罗什恰恰相反，是个激进派。他告诉我，数学可以分为两部分：哲学和记账。所有公式、积分——那就是记账。而二十世纪之前存在的一切都已经失去了意义。……这种两方面的影响在某种意义上帮助我找到了中间道路。……鲍里斯·德劳内给了我两条特别好的建议：一是读大卫·希尔伯特的'Zahlbericht'Ⓣ（数论报告），二是读卡尔·弗里德里希·高斯。

这些著作对他未来的数学活动产生了持久的影响。现在沙法列维奇的父母担心，如果他把所有时间都花在大学水平的数学上，他的学校学业会受到影响，因此他们只同意他进行这些数学研究，条件是他用英语学习几何，用德语学习代数。沙法列维奇在1939年完成九年级后离开学校，从未参加高中文凭考试，但已经参加了大部分大学考试，直接进入莫斯科大学本科最后一年。他在1940年十七岁生日前后获得了大学文凭，并开始在伊斯拉埃尔·盖尔范德和亚历山大·热纳季耶维奇·库罗什的指导下进行研究。

德国和苏联之间的莫洛托夫-里宾特洛甫互不侵犯条约意味着第二次世界大战的最初几年对莫斯科的生活影响不大，特别是对沙法列维奇的本科年和作为研究生的第一年没有影响。然而，1941年6月22日，德国撕毁互不侵犯条约并入侵苏联，情况发生了巨大变化。沙法列维奇回忆了接下来发生的事情（例如见[1]）：-

……所有研究生被召集在一起，宣布我们被征入所谓的‘人民民兵’。他们告诉我们，我们首先被送到军营，在那里接受短期训练，然后我们或许可以住在家里，但定期值班守卫莫斯科的各种目标。然后我的老师鲍里斯·德劳内和亚历山大·热纳季耶维奇·库罗什给区委员会写了一封信（民兵是由区委员会组建的），呼吁让我回到研究生院，我被延期了。很快我被动员到博罗季诺地区挖反坦克壕。这项工作持续了两个多月，直到从莫斯科方向可以听到炮击声。我们被命令转移到莫扎伊斯克，从那里，在德国飞机的轰炸下，我们乘火车返回莫斯科。

他于1941年10月15日返回莫斯科，得知德国军队已经进入城市郊区。回到家中，他遇到了仍住在那里的斯维亚托斯拉夫·里希特，他们决定一起去探险，并乘火车旅行。离开火车后，他们在离莫斯科约40公里处行走时，被一群农民拦住。里希特解释了发生的事情（例如见[1]）：-

[农民们]把我们当作希特勒派来的破坏者或间谍，把我们押送到最近的警察局。他们在我的身份证上发现了‘德国人’这个词。当警察局长看到沙法列维奇的身份证时，无法掩饰他的惊讶：‘这是怎么回事？十九岁就已经在大学二年级了？……我试图解释：“因为他非常有天赋。……”沙法列维奇觉得这太有趣了，突然大笑起来。一直极具威胁性的警察局长突然放松了：‘你知道你要做什么吗？立即乘第一班火车回家。’……当我们最终回到沙法列维奇家时，已经是凌晨两点，我当时就住在那里。

大学被疏散到乌兹别克斯坦的塔什干，所以沙法列维奇去了那里。这可能是幸运的，因为1941年底，住在沙法列维奇家的斯维亚托斯拉夫·里希特的父亲被逮捕并作为德国合作者被枪决。当沙法列维奇家被搜查时，他们发现了沙法列维奇学习过的德国数学书，并作为证据带走，但后来被归还，沙法列维奇家没有受到秘密警察的严重问题。莫斯科大学的主要部分后来在阿什哈巴德运作，再后来在斯维尔德洛夫斯克。沙法列维奇在这两个地方都待过，特别是在1942年大学在阿什哈巴德期间，他获得了副博士学位（相当于博士学位）。在他研究的后期阶段，他没有伊斯拉埃尔·盖尔范德作为导师，因为他搬到了另一个城市，所以他唯一的导师是亚历山大·热纳季耶维奇·库罗什。

到1944年，沙法列维奇已开始在莫斯科大学力学与数学系（Meh-Mat）任教。他于1946年21岁时获得科学博士学位，并成为苏联科学院弗拉基米尔·安德烈耶维奇·斯捷克洛夫研究所的副研究员。然而，1949年他连同许多同事一起被解雇[15]：-

似乎如果一位教师有很多学生，那被认为是不好的。人们希望采用更官僚化的方式。所有人都应该有相同数量的学生。许多有兼职职位的人被解雇了。并不是说我们被剥夺了工作。……我继续在斯捷克洛夫研究所工作。外国数学家打电话问我是否能养家糊口。情况从来不是那样。1949年没有规定你不能在其他地方任教，但许多在其他地方工作同时又在Meh-Mat任教的人被解雇了。

沙法列维奇于1953年复职。然而，他的生活和事业与前苏联遭遇的政治动荡密不可分。他的学生伊利亚·皮亚特茨基-沙皮罗描述了他对1955年前后政治局势的态度（例如，见[1]）：-

我记得我们的谈话不限于数学，在结束数学讨论后，我们经常转向政治。沙法列维奇，一位教授的儿子，是一个受过良好教育的人，懂法语和德语。即使在那时，他也明确表示他不喜欢十月革命。当然，他没有明说，那会很危险。那时，在斯大林统治下，没有人能梦想成为持不同政见者。然而，我很清楚沙法列维奇对共产主义有负面情绪。当然，他从未加入共产党。更有趣的是，他原则上反对所有革命运动。那时，陀思妥耶夫斯基的俄语作品不容易获得，但沙法列维奇引用了著名小说《群魔》中对革命的非常负面的描绘。

1972年，他成为持不同政见者团体的积极参与者，索尔仁尼琴是该团体的主要成员。结果，他于1975年被莫斯科大学解雇。他描述了围绕这一事件的情况（例如，见[15]）：-

我出版了一本关于社会主义的书和一系列非数学文章。我与索尔仁尼琴合作，与萨哈罗夫合作。而我，一个大学教授，教学生！这当然是一个奇怪的现象。……[我没有更早被解雇]纯粹是因为伊万·彼得罗夫斯基。他会对我说：“你知道他们向我索要你的血。”我会回答：“该怎么办。他们索要——那就洒出来吧。”“不，不，不。你知道，我使用诡计。我告诉他们学生们喜欢你，谁知道如果你被解雇会发生什么，在学年中间这样做不方便。……到年底，他们就忘记了。”那是我与伊万·彼得罗夫斯基的最后一次谈话。……他的继任者霍赫洛夫也设法推迟了一段时间。

1980年，他出版了一本名为The Socialist Phenomenon的书。这是对他最初发表于题为From under the Rubble的文集中的文章的扩展。他继续参与政治活动，于1989年出版了名为Russophobia的书。这本书被许多读者视为含有种族主义成分而感到冒犯，并引发了广泛的讨论和谴责。他写了一篇辩护，捍卫自己自由表达思想的权利。

他的数学研究得到了普遍认可。他对伽罗瓦理论的逆问题以及类域论做出了重大贡献，从而解决了一些长期悬而未决的猜想。最近，他在代数几何方面取得了重要进展。也许对他数学贡献的最好总结是沙法列维奇 Dolgachev对[2]的评论。我们引用其中一段：-

……一位数学家的著作对数学进展的影响与他发表论文列表的长度无关。在他漫长的数学生涯中，沙法列维奇发表的研究论文不超过50篇，但其中许多对数论、群论和代数几何的发展的影响难以估量。沙法列维奇对这些领域贡献的亮点可以简要总结如下。在数论方面：数域的p-扩张理论、一般互反律的显式形式、可解群的逆埃瓦里斯特·伽罗瓦问题的解决（1946-1954）、类域塔问题的解决（与Evgenii Solomonovich Golod合作，1964）、数域上椭圆曲线算术的工作（1957-1967）。在群论方面：与Golod和Aleksei Ivanovich Kostrikin关于群的上同调的工作（1957-64）、与Kostrikin和Alexei N Rudakov关于正特征域上的埃利·嘉当伪群和李代数的工作（1966-69）。在代数几何方面：函数域上阿贝尔簇的主齐性簇理论（1961）、椭圆曲面理论、对意大利代数几何学派关于代数曲面分类结果的重建（与他的学生合作）（1964-65）、K3曲面的周期与算术（与伊利亚·皮亚特茨基-沙皮罗合作，1970-73）、正特征域上的K3曲面（与Alexei N Rudakov合作，1976-1984）。

他的书和文章都被广泛阅读和赞誉。关于他一些书的评论和序言的摘录，见THIS LINK。

他作为讲师和教师表现卓越，他的数学著作因其清晰和犀利而受到赞誉。他的学生们报告说，与沙法列维奇的交往和在他的指导下学习是他们职业生涯中最幸福的经历之一。

事实上，他的工作在国外得到了认可，1974年被任命为美国国家科学院的外籍成员。除了当选为美国国家科学院成员外，沙法列维奇还当选为科学院 of the USSR、American Academy of Arts and Sciences、Royal Society of London、German Academy Leopoldina、Italian Accademia dei Lincei和塞尔维亚科学与艺术学院的成员。在他获得的众多奖项中，我们提到列宁奖和哥廷根科学院的海涅曼奖。他被授予伦敦数学会荣誉成员。巴黎大学授予他荣誉博士学位。

我们已经指出，沙法列维奇热爱历史、文学和音乐。我们还应该提到的一个爱好是徒步旅行。他年轻时喜欢在山中徒步，这一热情源于鲍里斯·德劳内 [1]的影响：-

鲍里斯·德劳内本人回忆道，他、"还是个男孩"的沙法列维奇以及一位名叫Sergei Mikhailovich Nikolskii的数学家曾一口气走了整整110公里，中途只短暂休息吃饭和游泳。

沙法列维奇的妻子是Nina Ivanova，她在莫斯科国立工程物理学院任教。他们有一个儿子Andrei Igorevich 沙法列维奇，生于1963年，是一位物理学家。他们还有一个女儿。

Igor Rostislavovich Shafarevich is generally regarded as one of the leading contemporary mathematicians of Russia. He was born in 1923, the son of Rostislav Stepanovich Shafarevich and Yulia Yacovlevna Vasileva. Rostislav Stepanovich had attended Moscow State University where he obtained a degree in mechanics. He taught theoretical mechanics in a number of different higher education institutions, for example the Moscow Engineering Institute (Technical University of Moscow). However, he had gone through some extremely difficult times in the years before Igor Rostislavovich was born. Speaking about his father's experiences, Igor said (see [1]):-

[There] was threat of execution, for example. ... Simply, because some party came to town, or hostages were taken, or just in case, or because you had boots. My father was twice taken to be shot, he said. And once it all ended up in him being inspected. They checked what they could take from him and whether it was worth shooting him. And when they saw that he had shoes - not boots - he was let go. [There was] hunger, typhus, death of people in masses.

As a young man Rostislav Stepanovich had thought about entering a monastery but the events of the civil war had made him become less religious. Igor's mother, Yulia Yacovlevna, had a degree in philology from the Bestuzhev Institute for Women in St Petersburg. She was a talented musician who had studied the piano under Theophil Richter, an organist and composer, the father of Sviatoslav Theophilovich Richter (1915-1997), one of the leading pianists of the 20th century. The Richter family were close friends of the Shafarevich family, and Igor and Sviatoslav spent much time together as they were growing up.

At the time that Igor was born, his father was working in Moscow and the family lived in a room in a communal apartment there. Yulia Yacovlevna's father was the director of the State Bank in Zhytomyr, the town where Yulia Yacovlevna had lived. He had a large flat in the town and Yulia Yacovlevna had returned to her parents' home for the birth of her child. Sviatoslav Richter, like Igor, was born Zhytomyr which was the Richter's home town. Igor and his mother soon returned to their room in the Moscow apartment and it was in Moscow that Igor was brought up. As a child, Igor was taught by his parents so when it came time for him to attend school he could already read and write, so was put straight into the second class.

Shafarevich's first love was history and literature. His love of literature began when he read fables as a child. He read of the Greek legends, the Russian fables and the German fables of the brothers Grimm. These not only gave him a love of literature but also an international perspective. Reading was easy for Shafarevich since his parents had many books in their apartment. Reading a history book made him think of becoming an historian (see [1] or [15]):-

What I wanted to be at first was a historian. Some book on history came into my hands. Not even all that interesting. A translation from German on history of antiquity for grammar schools. And suddenly I felt that the world was not limited to what is around me but extended in all directions in time and space. I discovered for the first time for myself that I and those surrounding me are only one link in an endless chain of generations. I instantly fell in love with history, up to the point of immersing myself in it.

Suddenly, when he was around twelve years old, his passion for history suddenly changed and he developed a passion for mathematics. By this we certainly don't mean to suggest that he lost his interest in history, for all his life his main interests other than mathematics were history and music. The reason for suddenly realising that he wanted to devote his life to mathematics was something that he never fully understood [15]:-

I tried to remember how I turned to mathematics and could not recall the logic or reason for it, though I think that to work on history then would really have been hard. It was considered an ideological discipline, and the possibility of choice of various points of view was very limited. I could hardly have understood that as a 10-12-year-old boy, but maybe I felt it subconsciously.

He demonstrated mathematical gifts at this early age, a gift which was nurtured by his parents. He read mathematical textbooks independently but was unsure whether he had really understood them. In 1938, he decided that he would seek help from the university so he approached the dean at Moscow University and explained his position. The dean, realising that he had a very talented youngster in front of him, suggested that he could enrol Shafarevich as an external student even though he was still a schoolboy. He then sent Shafarevich to Boris Nikolaevich Delone who examined him in analytic geometry. Next he went to Aleksandr Gennadievich Kurosh who examined him in algebra, and finally he went to Israil Moiseevic Gelfand who examined him in analysis [15]:-

They were very cordial and good towards me, they worked a great deal with me, i.e., gave me a lot of literature to read on top of what was required. ... I consider Delone and Kurosh my teachers. They represented not just two different, but two diametrically opposite mathematical types. Delone was a classical representative of the Petersburg school. He was interested in Diophantine analysis of a very classical type. ... But Kurosh was, on the contrary, a radical. He told me that mathematics can be divided into two parts: philosophy and accounting. All formulae, integrals - that was accounting. And everything that existed before the twentieth century had already lost its interest. ... This two-sided influence helped me in some sense to find a middle road. ... Delone gave me two particularly good pieces of advice: one was to read Hilbert's 'Zahlbericht' Ⓣ, and the second to read Gauss.

These works were to have a long-lasting influence on his future mathematical activities. Now Shafarevich's parents worried that his school studies would suffer if he spent all his time on university level mathematics so they only agreed to him undertaking these mathematical studies on the condition that he studied geometry in English and algebra in German. Shafarevich left school in 1939 after completing the ninth grade and never took the examinations for his high school diploma but, having taken most of the university examinations, went straight into the final undergraduate year at Moscow University. He graduated with his university diploma in 1940 around the time of his seventeenth birthday and began undertaking research advised by Gelfand and Kurosh.

The Molotov-Ribbentrop non-aggression pact between Germany and the Soviet Union meant that the initial years of the World War II had little effect on life in Moscow and, in particular, none on Shafarevich's undergraduate year and his first year as a research student. However, things changed dramatically on 22 June 1941 when Germany broke the non-aggression pact and invaded the Soviet Union. Shafarevich recalled what happened next (see for example [1]):-

... all the postgraduate students were called together and it was announced that we were being enlisted in the so-called 'People's Militia'. They told us that we were first being sent to the barracks, where we would go through a short training course, and then we would perhaps live at home but be periodically on duty guarding various objects in Moscow. Then my teachers B N Delone and A G Kurosh wrote a letter to the district committee (the militia was being formed by the district committees) with an appeal to let me return to graduate school and I was deferred. Soon I was mobilized to dig antitank ditches in the district of Borodino. This work continued for more than two months, until an artillery barrage could be heard from the direction of Moscow. We were ordered to move to Mozhaisk, and from there, under bombing by German planes, we returned by train to Moscow.

He returned to Moscow on 15 October 1941 to learn that the German army was already into the outskirts of the city. Back in his home he met up with Sviatoslav Richter who was still living there and they decided to go for an expedition together and took a train journey. Leaving the train, they were walking about 40 km from Moscow when they were stopped by a group of peasants. Richter explained what happened (see for example [1]):-

[The peasants] took us to be saboteurs or spies sent by Hitler and bundled us off to the nearest police station. They discovered the word 'German' on my ID card. And when he saw Shafarevich's, the chief of police couldn't conceal his surprise: 'What's all this, then? Nineteen and already in your second year at university? ... I tried to explain: 'It's because he's very gifted. ...' Shafarevich found this irresistible and burst out laughing. The police chief, who had been extremely threatening until now, suddenly relaxed: 'You know what you're going to do? Get on the first train home without delay.' ... it was two in the morning when we finally got back to the Shafareviches', where I was staying at the time.

The university was evacuated to Tashkent in Uzbekistan, so Shafarevich went there. This may have been fortunate since late in 1941 Sviatoslav Richter's father, who was living at the Shafarevichs' home, was arrested and shot as a German collaborator. When the Shafarevichs' home was searched, they found German mathematics books that Shafarevich had studied and took them away as evidence but later they were returned and the Shafarevichs had no serious problems from the secret police. The main part of Moscow University later operated in Ashkhabad and still later in Sverdlovsk. Shafarevich spent time in both these places, in particular during the time that the university was in Ashkhabad in 1942 he was awarded his candidate's degree (equivalent to a Ph.D.). During this latter stage of his research, he had not had Gelfand as an advisor as he had moved to a different city, so his only advisor had been Kurosh.

By 1944 Shafarevich had begun teaching in the Mechanics and Mathematics Department (Meh-Mat) of Moscow University. He was awarded the Doctor of Science degree in 1946 at the age of 21 and became an associate at the Steklov Institute of the USSR Academy of Sciences. However, in 1949 he, along with a number of his colleagues, was fired [15]:-

It seems that if a teacher had many students, that was considered bad. The desire was for a more bureaucratic way. All should have the same number of students. Many that had part-time positions were fired. It is not as though we were stripped of our jobs. ... I continued to work in the Steklov Institute. Foreign mathematicians phoned me asking whether I couldn't feed my family. That was never the case. In 1949 there was no rule that you couldn't teach somewhere else, but many of those who worked somewhere else and also taught at Meh-Mat were fired.

Shafarevich was reinstated in 1953. His life and career, however, are inextricably bound with the political upheaval that befell the Former Soviet Union. His attitude to the political situation around 1955 is described by his student Ilya Piatetski-Shapiro (see, for example [1]):-

I remember that our conversations were not restricted to mathematics, and after finishing our mathematical discussions we frequently turned to politics. Shafarevich, a son of a professor, was a well-educated man who knew French and German. Even then, he made it clear that he disliked the October Revolution. Of course, he did not say it explicitly, which would have been dangerous. At that time, during Stalin's rule, no one could dream of being a dissident. However, it was clear to me that Shafarevich had negative feelings for Communism. Of course, he never was a member of the Communist Party. More interestingly, he was against all revolutionary movements in principle. At that time, Dostoevskii was not easily available in Russian, but Shafarevich quoted the very negative depiction of revolution from the famous novel 'Devils'.

In 1972, he became an active participant in the group of dissidents of which Solzhenitsyn was a leading member. As a consequence, he was dismissed from the University of Moscow in 1975. He described the events surrounding this (see for example [15]):-

I published a book on socialism and a series of nonmathematical articles. I collaborated with Solzhenitsyn, with Sakharov. And me, a university professor, teaching students! It was of course a strange phenomenon. ... [That I wasn't dismissed sooner] was purely due to Ivan Georgievich Petrovsky. He would say to me: "You know they ask me for your blood.'" And I would answer: "What's to be done. They ask - so spill it." "No, no, no. You know, I use ruses. I tell them that the students like you, who knows what would happen if you were dismissed, it isn't convenient to do it in the middle of the academic year. ... By the end of the year, they have forgotten." That was my last conversation with Petrovsky. ... his successor, Khokhlov, also managed to delay it for some time.

In 1980, he published a book entitled The Socialist Phenomenon. This was an elaboration of his essay which first appeared in the collection titled From under the Rubble. He continued his political involvement by publishing the book entitled Russophobia in 1989. This proved offensive to many readers who saw in it elements of racism and it provoked extensive discussion coupled with censure. He wrote a defence of his right to express his ideas freely.

His mathematical research has been universally recognized. He made major contributions to the inverse problem of Galois theory as well as to class field theory, thereby solving some long outstanding conjectures. More recently he made important advances to algebraic geometry. Perhaps the best summary of his mathematical contributions is Igor Dolgachev's review of [2]. We quote an extract:-

... the impact of a mathematician's work on the progress of mathematics has nothing to do with the length of the list of his published papers. During his long mathematical life Shafarevich published no more than 50 research papers, but the influence of many of them on the development of number theory, group theory and algebraic geometry is difficult to overestimate. The highlights of Shafarevich's contribution to these fields can be briefly summarized as follows. In number theory: the theory of p-extensions of number fields, explicit forms of general reciprocity law, solution of the inverse Galois problem for solvable groups (1946-1954), solution of the class field tower problem (with Evgenii Solomonovich Golod, 1964), the work on the arithmetic of elliptic curves over number fields (1957-1967). In group theory: the work with Golod and Aleksei Ivanovich Kostrikin on the cohomology of groups (1957-64), the work with Kostrikin and Alexei N Rudakov on Cartan pseudogroups and Lie algebras over fields of positive characteristic (1966-69). In algebraic geometry: the theory of principal homogeneous varieties of abelian varieties over function fields (1961), the theory of elliptic surfaces, a reconstruction of the results of the Italian school of algebraic geometry on classification of algebraic surfaces (with his students) (1964-65), the periods and arithmetic of K3 surfaces (with Ilya Piatetski-Shapiro, 1970-73), K3 surfaces over fields of positive characteristic (with Alexei N Rudakov, 1976-1984).

Both his books and articles are widely read and acclaimed. See THIS LINK for extracts from reviews and Prefaces of some of his books.

He was outstanding as a lecturer and teacher and his mathematical writings are praised for their clarity and incisiveness. His students report that their association and supervision by Shafarevich were among the happiest of their professional careers.

Indeed his work was recognized abroad by his appointment as a foreign member of the National Academy of Sciences of the USA in 1974. In addition to his election to membership of the National Academy of Sciences of the USA, Shafarevich has been elected to the Academy of Sciences of the USSR, the American Academy of Arts and Sciences, the Royal Society of London, the German Academy Leopoldina, the Italian Accademia dei Lincei and the Serbian Academy of Sciences and Arts. Among the many prizes he has received, we mention the Lenin Prize and the Heinemann Prize of the Göttingen Academy of Sciences. He has been made an honorary member of the London Mathematical Society. The University of Paris awarded him an honorary doctorate.

We have already indicated that Shafarevich loved history, literature and music. One hobby that we should also mention is that of hiking. When he was younger he loved hiking in the mountains, a passion which was due to the influence of Delone [1]:-

Delone himself reminisced how he, Shafarevich who was "still a boy", and a mathematician named Sergei Mikhailovich Nikolskii once walked a full 110 kilometres in one go, making just short breaks for eating and swimming in the middle.

Shafarevich was married to Nina Ivanova, who taught at the Moscow State Engineering Physics Institute. They had a son Andrei Igorevich Shafarevich, born in 1963, who is a physicist. They also had a daughter.