让-皮埃尔·塞尔Jean-Pierre Serre

让-皮埃尔·塞尔的父母，Jean Serre和阿黛尔·迪特，都是药剂师。他的母亲阿黛尔曾是蒙彼利埃大学的药学学生，她修了一门微积分课程（她说，只是为了好玩，因为她喜欢数学）。1932年，塞尔在沃韦尔学校开始了他的小学教育。正是在七八岁的时候，他开始喜欢做数学。1937年，他从沃韦尔学校转到尼姆的阿方斯-多德中学学习。他的母亲保留了她在上蒙彼利埃大学数学课程时买的微积分书籍，塞尔开始从这些书中学习数学[9]：-

当我14或15岁时，我常常看这些书，并研究它们。这就是我学习导数、积分、级数等的方式（我以纯粹形式化的方式做这件事——可以说是莱昂哈德·欧拉的风格：我不喜欢，也不理解，ε和δ。）

此时数学并不是他唯一喜欢的科目。尽管他对物理学从未有过太大兴趣，但他喜欢化学，这是他的父母作为药剂师非常了解的一个领域。特别是他父亲有许多化学书籍，塞尔在十五六岁时读过这些书。事实上，他非常喜欢其中一本书，以至于保留了一本——这就是Jacques Duclaux（1877-1978）所著的《Les colloïdes》，Gauthier-Villars，1922年。然而，随着他对化学的深入研究，他对这门学科的热情逐渐减退，并越来越确信数学才是适合他的领域。

他在[9]中谈到了他在尼姆的Lycée Alphonse-Daudet的时光：-

在高中时，我常常做更高级别的题目。当时我住在尼姆的一所寄宿公寓里，和比我大的孩子们住在一起，他们常常欺负我。所以为了安抚他们，我常常帮他们做数学作业。这是一种很好的训练。

1943-44学年在尼姆的Lycée，他有一位优秀的数学老师，因为留着胡子而被昵称为“Le Barbu”。他是[9]：-

……非常清晰，而且严格；他要求每个公式和证明都写得整洁。

他辅导塞尔参加1944年的Concours General数学考试，并获得了第一名。同样在1944年，他参加了Concours General物理考试，但由于他在整个六小时的考试中使用了错误的公式，成绩很差。塞尔于1944年获得了他的路易·巴舍利耶 ès sciences et ès lettres，但留在Lycée直到1945年，准备参加进入巴黎École Normale Supérieure的入学考试。在Lycée期间[9]：-

我原本不知道一个人可以靠当数学家谋生。直到后来我才发现，做数学是可以得到报酬的！我起初以为我会成为一名高中教师：这在我看来很自然。然后，在我19岁时，我参加了进入巴黎高等师范学校的竞赛，并且成功了。一旦我进入了“高师”，就清楚了我想成为的不是高中教师，而是一名研究数学家。

从1945年到1948年，塞尔在巴黎高等师范学校学习，并于1948年获得数学科学教师资格。此时，他成为尼古拉·布尔巴基数学家小组中最年轻的成员。这个小组包括自20世纪30年代中期以来就参与其中的成员，如亨利·嘉当、谢瓦莱、让·戴尔萨特、让·迪厄多内和安德烈·韦伊。大约在塞尔加入尼古拉·布尔巴基小组的时候，其他人如罗杰·戈德芒、皮埃尔·萨米埃尔和雅克·迪克斯米耶也加入了。

塞尔于1948年8月10日与Josiane Heulot（1922-2004）结婚；他们有一个孩子，一个女儿Claudine，出生于1949年11月29日。Josiane是一位有机化学家，在塞夫勒的女子高等师范学校工作。

从1948年到1954年，塞尔在巴黎的国家科学研究中心任职，先是作为助理，然后是研究员。在1948-49年，他参加了亨利·嘉当的讨论班，讨论班的内容是关于代数拓扑学和层论的。同年参加亨利·嘉当讨论班的还有谢瓦莱、让·戴尔萨特、让·迪厄多内、罗杰·戈德芒、洛朗·施瓦茨和安德烈·韦伊。塞尔的同学之一是亚历山大·格罗滕迪克，他也参加了这个讨论班。亚历山大·格罗滕迪克和塞尔在这个时候成为了朋友。塞尔的导师是亨利·嘉当，但是[18]：-

……埃利·嘉当没有给他的学生建议研究课题：他们必须自己找到一个；之后他会帮助他们。这就是发生在我身上的事。我发现让·勒雷的理论（关于纤维空间及其谱序列）可以应用于比人们认为可能的更多情况，并且这种扩展可以用来计算同伦群。

他于1951年从索邦大学获得博士学位，学位论文是Homologie singulière des espaces fibrés. ApplicationsⓉ（纤维空间的奇异同调：应用）。1952年，他去了普林斯顿，在那里讲授他学位论文中的结果，以及作为这项工作延续的$C$理论。在普林斯顿期间，他参加了关于类域论的埃米尔·阿廷-约翰·泰特讨论班。回到巴黎后，他再次参加了亨利·嘉当讨论班，那一年讨论班正在讨论多复变函数和埃利亚斯·施泰因流形。他在这个讨论班中遇到的想法激发了他研究方向。在1953-54年，他是国家科学研究中心的研究导师。

1954年，塞尔去了南锡大学，在那里工作到1956年。从1956年起，他在法兰西学院担任代数学与几何学讲席，直到1994年退休，成为荣誉教授。他在[16]中描述了他 在法兰西学院的就职演讲：-

我到达法兰西公学院时还是个年轻人，大约30岁。就职演讲几乎就像一场口试，面对的是教授、家人、数学家同行、记者等。我试图准备，但一个月后我只写了半页。演讲那天到来时，气氛相当紧张。我开始朗读我准备好的那半页，然后即兴发挥。

几个月后，他被告知就职演讲会被出版，并要求他提供一份文字稿。由于演讲是即兴的，他没有文字稿，但试图通过对着录音机即兴演讲，然后将磁带交给秘书打字来重现它。然而，秘书说录音听不清。塞尔于是放弃了，他的就职演讲从未出版。这使得它独一无二，因为法兰西公学院所有其他已出版的就职演讲都出版了。

他还谈到了他在法兰西公学院的教学经历（例如见[16]）：-

在公学院教学既是一种奇妙又充满挑战的特权。奇妙是因为可以自由选择主题，以及听众水平很高：国家科学研究中心的研究人员、来访的外国学者、来自巴黎和奥赛的同事——许多常客已经来了5年、10年甚至20年。这也充满挑战：每年都必须讲授新课程，要么关于自己的研究（我更喜欢这样），要么关于他人的研究。由于一年课程的系列讲座大约20小时，这相当多。

他在法兰西公学院的永久职位使塞尔能够花大量时间进行研究访问。特别是，他在普林斯顿高等爱德华·斯图迪研究所（1955年、1957年、1959年、1961年、1963年、1967年、1970年、1972年、1978年、1983年、1999年）和哈佛大学（1957年、1964年、1974年、1976年、1979年、1981年、1985年、1988年、1990年、1992年、1994年、1995年、1996年）度过了一段时间。以下是塞尔讲授课程的大学列表（按字母顺序）：阿尔及尔（1965年、1966年）、波恩（1976年）、加州理工学院（1997年）、尤金（1998年）、日内瓦（1999年）、哥廷根（1970年）、麦吉尔（1967年）、墨西哥（1956年）、莫斯科（1961年、1984年）、普林斯顿（1952年、1999年）、新加坡（1985年）、加州大学洛杉矶分校（2001年）、乌得勒支（1974年）。

塞尔的早期工作是研究谱序列。谱序列是一种类似于正合序列的代数构造，但更难以描述。塞尔并没有发明谱序列，谱序列是由法国数学家让·勒雷发明的。然而，在1951年，塞尔将谱序列应用于研究纤维化中纤维、全空间和底空间的同调群之间的关系。这使他能够发现空间的同调群与同伦群之间的基本联系，并证明关于球面同伦群的重要结果。

塞尔的工作使拓扑学家认识到谱序列的重要性。塞尔谱序列提供了一种有效处理纤维化同调的工具。由于在谱序列方面的工作以及用层论发展复变函数论的工作，塞尔在1954年国际数学家大会上被授予菲尔兹奖。塞尔定理不仅在同伦论中，而且在代数拓扑和同调代数中普遍带来了快速进展。作为塞尔解决问题方法的一个例子，我们引用采访[9]。在这里，塞尔正在回答一个关于灵感重要性的问题：-

我不知道“灵感”到底意味着什么。定理和理论以奇怪的方式出现。有时，你只是对现有的证明不满意，然后去寻找更好的证明，这些证明可以应用于不同的情况。对我来说，一个典型的例子是我研究波恩哈德·黎曼-Roch定理时（大约1953年），我把它看作一个“莱昂哈德·欧拉-儒勒·昂利·庞加莱”公式（当时我不知道小平邦彦-唐纳德·斯宾塞也有同样的想法）。我的第一个目标是证明代数曲线的情形——这个情形已知大约有一个世纪了！但我想要一种特殊风格的证明；当我设法找到它时，我记得从那里到二维情形（刚由小平邦彦完成）只花了我一两分钟。六个月后，完整的结果由弗里德里希·希策布鲁赫建立，并发表在他著名的教授资格论文（Habilitation）学位论文中。很多时候，你并不是真的试图通过正面攻击来解决一个具体问题。相反，你有一些想法，你觉得它们应该有用，但你不确切知道它们对什么有用。所以，你四处寻找，并尝试应用它们。这就像有一串钥匙，然后试着用它们开几扇门。

多年来，塞尔出版了许多极具影响力的著作，涵盖了广泛的数学领域。这些著作展示了塞尔所研究过的主题，它们是Homologie singulière des espaces fibrés Ⓣ（纤维空间的奇异同调）（1951），Faisceaux algébriques cohérents Ⓣ（一致的代数束）（1955），Groupes d'algébriques et corps de classes Ⓣ（代数群与体类）（1959），Corps locaux Ⓣ（局部环）（1962），Cohomologie galoisienne Ⓣ（埃瓦里斯特·伽罗瓦上同调）（1964），Algèbre Locale. Multiplicités Ⓣ（局部代数：重数）（1965），Lie Algebras and Lie Groups（1965），Algèbres de Lie semi-simples complexes Ⓣ（复半单李代数）（1966），Abelian l-adic representations and elliptic curves（1968），Représentations linéaires des groupes finis Ⓣ（有限群的线性表示）（1968），Cours d'arithmétique Ⓣ（算术教程）（1970），Représentations linéaires des groupes finis Ⓣ（有限群的线性表示）（1971），Arbres, amalgames Ⓣ（树，融合），$SL_{2}$（1977），Lectures on the Mordell-Weil theorem（1989），Topics in Galois theory（1992），Exposés de Séminaires Ⓣ（研讨会报告）1950-1999（2001），Correspondance Grothendieck-Serre Ⓣ（亚历山大·格罗滕迪克与塞尔之间的通信）（2001），（与S Garibaldi和A Merkurjev合著）Cohomological Invariants in Galois Cohomology（2003），以及Lectures on $N_{X}(p)$（2011）。

你可以在THIS LINK看到这些书的一些评论摘录。

这些著作非常出色，使塞尔获得了荣誉。1995年，他因数学阐述而获得凯瑟琳·斯蒂尔奖，该奖项的颁奖词写道[2]：-

要决定像塞尔这样地位的数学家的哪一部作品最值得获得斯蒂尔奖是很困难的。塞尔众多其他著作中的任何一部都可能成为该奖项的依据。他的每一本书都写得优美，包含大量作者原创材料，且一切都打磨得光滑流畅。很难对他的阐述做出任何重大改进；其中许多已成为各自领域的日常标准参考，无论对在职数学家还是研究生而言。塞尔将他整个数学个性倾注于这些书的材料之中；它们因真正数学的广度而生动，为所有人树立了如何为效果、清晰和影响力而写作的榜样。

参考文献[8]和[9]提供了塞尔关于其职业生涯某些方面直到1985年的观点的迷人视角：-

目前，最让我感兴趣的主题是有限域上代数曲线上的点计数。这是一种应用数学：你尝试使用代数几何和数论中你知道的任何工具，……而你并不完全成功！

[8]和[9]中的访谈也提供了一个考察塞尔数学观点的机会。不过，我们在此选择引用[16]中关于塞尔对数学应用的看法：-

至于数学与其他科学的关系，数学可以被看作一个装满架子的大仓库。数学家把东西放在架子上，并保证它们是真的。他们还解释如何使用它们以及如何重建它们。其他科学来从架子上自助取用，数学家不关心他们用取走的东西做什么。这个比喻相当粗糙，但它足够好地反映了情况。（当然，人们选择做数学并不是为了把东西放在架子上；人们做数学是为了其中的乐趣。）这里有一个个人例子。我的妻子Josiane是一位量子化学专家。她需要某些对称群的线性表示。她正在使用的书并不令人满意；它们是正确的，但它们使用了非常笨拙的记号。我写了一篇适合她需要的文本，然后以书的形式出版，名为《有限群的线性表示》。我因此履行了我作为数学家（以及作为丈夫）的职责：把东西放在架子上。

在访谈[18]中，塞尔谈到了他的爱好。他喜欢攀岩、滑雪和乒乓球。我[EFR]当然可以从个人经验中说塞尔是一位多么优秀的乒乓球运动员，因为我曾在我们都参加的许多会议上看到他打球。我总是有（非常愚蠢的）想法：一个在数学上如此出色的人怎么能在乒乓球上也如此出色！塞尔喜欢的其他事情是下棋、读书和看电影。他说他喜欢[9]的书：-

……各种各样的，从Giono到Böll到川端康成，包括童话和哈利·波特系列。

塞尔获得了众多奖项。除了1954年的约翰·查尔斯·菲尔兹奖章外，他于1973年当选为伦敦数学会荣誉会员，并于1974年成为伦敦皇家学会会士。他还被授予荣誉军团军官和国家功绩勋章指挥官。除了皇家学会外，他还被选入许多国家科学院，特别是法国（1977年）、荷兰（1978年）、美国（1979年）、瑞典（1981年）、俄罗斯（2003年）、挪威（2009年）、都灵（2010年）和台湾（2010年）的科学院。他获得了法兰西公学院的Prix Peccot-Vimont奖（1955年）、Académie des Sciences的Prix Francoeur奖（1957年）、Prix 茹利亚奖（1970年）、Académie des Sciences的Médaille 埃米尔·皮卡奖（1971年）、巴尔赞奖（1985年）、C.N.R.S.金奖（1987年）、上文所述的美国数学会的斯蒂尔奖（1995年）以及2000年的沃尔夫奖。他获得了剑桥大学（1978年）、斯德哥尔摩大学（1980年）、格拉斯哥大学（1983年）、雅典大学（1996年）、哈佛大学（1998年）、达勒姆大学（2000年）、伦敦大学（2001年）、奥斯陆大学（2002年）、牛津大学（2003年）、布加勒斯特大学（2004年）、巴塞罗那大学（2004年）、马德里大学（2006年）和麦吉尔大学（2008年）的荣誉学位。2003年6月，他被挪威科学与文学院授予首届尼尔斯·阿贝尔奖[6]：-

……因为在赋予若干数学主题现代形式方面发挥了主要作用，特别是拓扑学、代数几何和数论。

围绕这一仪式的活动在几篇文章中有所描述。以下内容摘自[18]：-

活动于2003年6月1日星期日在奥斯陆明媚的阳光下开始，在Slottsparken的尼尔斯·阿贝尔纪念碑前举行了简单的仪式。在尼尔斯·阿贝尔董事会主席（奖项活动组织者）Jens Erik Fenstad简短致辞后，尼尔斯·阿贝尔奖得主塞尔在纪念碑前献了花圈。6月2日，科学活动在Georg Sverdrup's house开始，这是位于Blindern的奥斯陆大学美妙的新图书馆。……塞尔的讲座题为“素数、方程和模形式”。他完全不负其大师级阐述者的声誉，以老式方式用粉笔在黑板上讲课，并以无笔记的非常清晰的陈述给所有人留下深刻印象。……下午晚些时候，塞尔接待了几批记者进行采访。星期二上午，塞尔以及阿贝尔委员会和阿贝尔董事会的代表会见了世界媒体：来自挪威、英国、法国和德国的十名记者。星期二下午，颁奖仪式在奥斯陆大学隆重举行。哈拉尔国王和索尼娅王后出席，在几场演讲后，国王将奖项颁发给塞尔。

Jean-Pierre Serre's parents, Jean Serre and Adèle Diet, were both pharmacists. His mother Adèle had been a pharmacy student at the University of Montpellier and she took a calculus course (just for fun, she said, since she liked mathematics). In 1932 Jean-Pierre began his primary school education at the École de Vauvert. It was at the age of seven or eight that he began to enjoy doing mathematics. In 1937 he moved from the École de Vauvert to study at the Lycée Alphonse-Daudet in Nîmes. His mother had kept the calculus books that she had bought when she took the mathematics course at the University of Montpellier and Jean-Pierre began to learn mathematics from these books [9]:-

When I was 14 or 15, I used to look at these books, and study them. This is how I learned about derivatives, integrals, series and such (I did that in a purely formal manner - Euler's style so to speak: I did not like, and did not understand, epsilons and deltas.)

At this time mathematics wasn't the only subject he enjoyed. Although he never took much interest in physics, he enjoyed chemistry which was a topic that his parents, being pharmacists, knew a lot about. In particular his father had a lot of chemistry books which Jean-Pierre read when he was fifteen or sixteen years old. In fact he enjoyed one of these books so much that he kept a copy of it - this was the book "Les colloïdes", Gauthier-Villars, 1922 by Jacques Duclaux (1877-1978). However, as he went deeper into chemistry he became less enthusiastic about the subject and became more convinced that mathematics was the topic for him.

He spoke about his time at the Lycée Alphonse-Daudet in Nîmes in [9]:-

In high school I used to do problems for more advanced classes. I was then in a boarding house in Nimes, staying with children older than I was, and they used to bully me. So to pacify them, I used to do their mathematics homework. It was as good a training as any.

At the Lycée in Nîmes in the year 1943-44 he had a good mathematics teacher who was nicknamed "Le Barbu" since he had a beard. He was [9]:-

... very clear, and strict; he demanded that every formula and proof be written neatly.

He coached Serre for the Concours General in mathematics which he sat in 1944 and was placed first. Also in 1944 he sat the Concours General in physics but since he spent the whole six-hour examination using an incorrect formula, he scored poorly. Serre was awarded his Bachelier ès sciences et ès lettres in 1944 but remained at the Lycée until 1945 preparing to take the entrance examination to enter the École Normale Supérieure in Paris. While at the Lycée [9]:-

I had no idea one could make a living by being a mathematician. It was only later I discovered one could get paid for doing mathematics! What I thought at first was that I would become a high school teacher: this looked natural to me. Then, when I was 19, I took the competition to enter the École Normale Superieure, and I succeeded. Once I was at "l'École", it became clear that it was not a high school teacher I wanted to be, but a research mathematician.

From 1945 to 1948 Serre studied at the École Normale Supérieure and was awarded his Agrégé des sciences mathematique in 1948. At this time he became the youngest member of the Bourbaki group of mathematicians. This group included those who had been involved since the mid 1930s such as Henri Cartan, Claude Chevalley, Jean Delsarte, Jean Dieudonné and André Weil. Around the time that Serre joined the Bourbaki group, others such as Roger Godement, Pierre Samuel and Jacques Dixmier also joined.

Serre married Josiane Heulot (1922-2004) on 10 August 1948; they had one child, a daughter Claudine born on 29 November 1949. Josiane was an organic chemist working at the École Normale Supérieure de jeunes filles at Sèvres.

From 1948 to 1954 Serre held positions at the Centre National de la Recherche Scientifique in Paris, first as attaché and then as chargé de recherches. In 1948-49 he attended Henri Cartan's seminar which was on algebraic topology and sheaf theory. Also attending Henri Cartan's seminar in that year were Claude Chevalley, Jean Delsarte, Jean Dieudonné, Roger Godement, Laurent Schwartz, and André Weil. One of Serre's fellow students was Alexander Grothendieck and he also attended the seminar. Grothendieck and Serre became friends at this time. Serre was advised by Henri Cartan but [18]:-

... Cartan did not suggest research topics to his students: they had to find one themselves; after that he would help them. This is what happened to me. I found that Leray's theory (about fibre spaces and their spectral sequence) could be applied to many more situations than was thought possible and that such an extension could be used to compute homotopy groups.

He was awarded his doctorate from the Sorbonne in 1951 for his thesis Homologie singulière des espaces fibrés. Applications Ⓣ. In 1952 he went to Princeton where he lectured on the results in his thesis and also on $C$-theory which was the continuation of this work. While in Princeton he attended the Artin-Tate seminar on class field theory. Returning to Paris, he again attended the Henri Cartan seminar which, in that year, was discussing functions of several complex variables and Stein manifolds. The ideas he met in this seminar motivated the direction of his research. In 1953-54 he was maître de recherches at the Centre National de la Recherche Scientifique.

In 1954 Serre went to the University of Nancy where he worked until 1956. From 1956 he held the chair of Algebra and Geometry in the Collège de France until he retired in 1994 when he became an honorary professor. He describes in [16] his inaugural lecture at the Collège de France:-

I was a young man, about 30, when I arrived at the Collège. The inaugural lecture was almost like an oral examination in front of professors, family, mathematician colleagues, journalists etc. I tried to prepare it, but after a month I only managed to write half a page. When the day of the lecture came, it was quite a tense moment. I started by reading the half page I had prepared and then I improvised.

A few months later he was informed that inaugural lectures were published and he was asked to supply a transcript. As the lecture had been improvised he had no transcript but tried to recreate it by giving an impromptu lecture into a tape recorder and then giving the tape to a secretary to type up. However, the secretary said that the recording was inaudible. Serre then gave up and his inaugural lecture was never published. This makes it unique as every other inaugural lecture at the Collège de France that has been published.

He has also spoken about his teaching career at the Collège de France (see for example [16]):-

Teaching at the Collège is both a marvellous and a challenging privilege. Marvellous because of the freedom of choice of subjects and the high level of the audience: Centre National de la Recherche Scientifique researchers, visiting foreign academics, colleagues from Paris and Orsay - many regulars who have been coming for 5, 10 or even 20 years. It is challenging too: new lectures have to be given each year, either on one's own research (which I prefer), or on the research of others. Since a series of lectures for a year's course is about 20 hours, that's quite a lot.

His permanent position in the Collège de France allowed Serre to spend quite a lot of time making research visits. In particular he spent time at the Institute for Advanced Study at Princeton (in 1955, 1957, 1959, 1961, 1963, 1967, 1970, 1972, 1978, 1983, 1999) and at Harvard University (in 1957, 1964, 1974, 1976, 1979, 1981, 1985, 1988, 1990, 1992, 1994, 1995, 1996). Here is a list of the universities where Serre delivered courses (in alphabetical order): Algiers (1965, 1966), Bonn (1976), CalTech (1997), Eugene (1998), Geneva (1999), Göttingen (1970), McGill (1967), Mexico (1956), Moscow (1961, 1984), Princeton (1952, 1999), Singapore (1985), U.C.L.A. (2001), Utrect (1974).

Serre's early work was on spectral sequences. A spectral sequence is an algebraic construction like an exact sequence, but more difficult to describe. Serre did not invent spectral sequences, these were invented by the French mathematician Jean Leray. However, in 1951, Serre applied spectral sequences to the study of the relations between the homology groups of fibre, total space and base space in a fibration. This enabled him to discover fundamental connections between the homology groups and homotopy groups of a space and to prove important results on the homotopy groups of spheres.

Serre's work led to topologists realising the importance of spectral sequences. The Serre spectral sequence provided a tool to work effectively with the homology of fiberings. For this work on spectral sequences and his work developing complex variable theory in terms of sheaves, Serre was awarded a Fields Medal at the International Congress of Mathematicians in 1954. Serre's theorem led to rapid progress not only in homotopy theory but in algebraic topology and homological algebra in general. As an example of Serre's approach to attacking a problem, we quote from the interview [9]. Here Serre was answering a question about the importance of inspiration:-

I don't know what "inspiration" really means. Theorems, and theories, come up in funny ways. Sometimes, you are just not satisfied with existing proofs, and you look for better ones, which can be applied in different situations. A typical example for me was when I worked on the Riemann-Roch theorem (circa 1953), which I viewed as an "Euler-Poincaré" formula (I did not know then that Kodaira-Spencer had had the same idea.) My first objective was to prove it for algebraic curves - a case which was known for about a century! But I wanted a proof in a special style; and when I managed to find it, I remember it did not take me more than a minute or two to go from there to the 2-dimensional case (which had just been done by Kodaira). Six months later, the full result was established by Hirzebruch, and published in his well-known Habilitation thesis. Quite often, you don't really try to solve a specific question by a head-on attack. Rather you have some ideas in mind, which you feel should be useful, but you don't know exactly for what they are useful. So, you look around, and try to apply them. It's like having a bunch of keys, and trying them on several doors.

Over many years Serre has published many highly influential texts covering a wide range of mathematics. These texts, which show the topics Serre has worked on, are Homologie singulière des espaces fibrés Ⓣ (1951), Faisceaux algébriques cohérents Ⓣ (1955), Groupes d'algébriques et corps de classes Ⓣ (1959), Corps locaux Ⓣ (1962), Cohomologie galoisienne Ⓣ (1964), Algèbre Locale. Multiplicités Ⓣ (1965), Lie Algebras and Lie Groups (1965), Algèbres de Lie semi-simples complexes Ⓣ (1966), Abelian l-adic representations and elliptic curves (1968), Représentations linéaires des groupes finis Ⓣ (1968), Cours d'arithmétique Ⓣ (1970), Représentations linéaires des groupes finis Ⓣ (1971), Arbres, amalgames Ⓣ, $SL_{2}$ (1977), Lectures on the Mordell-Weil theorem (1989), Topics in Galois theory (1992), Exposés de Séminaires Ⓣ 1950-1999 (2001), Correspondance Grothendieck-Serre Ⓣ (2001), (with S Garibaldi and A Merkurjev) Cohomological Invariants in Galois Cohomology (2003), and Lectures on $N_{X}(p)$ (2011).

You can see some extracts from reviews of these books at THIS LINK.

These books are outstanding and led to Serre being honoured. In 1995 he was awarded the Steele Prize for mathematical exposition and the citation for the award reads [2]:-

It is difficult to decide on a single work by a mathematician of Jean-Pierre Serre's stature which is most deserving of the Steele Prize. Any one of Serre's numerous other books might have served as the basis of this award. Each of his books is beautifully written, with a great deal of original material by the author, and everything smoothly polished. It would be hard to make any significant improvement on his expositions; many are the everyday standard references in their areas, both for working mathematicians and graduate students. Serre brings his whole mathematical personality to bear on the material of these books; they are alive with the breadth of real mathematics and are an example to all of how to write for effect, clarity, and impact.

The references [8] and [9] provide a fascinating view of Serre's views on some aspects of his career up to 1985:-

Presently, the topic which amuses me most is counting points on algebraic curves over finite fields. It is a kind of applied mathematics: you try to use any tool in algebraic geometry and number theory that you know of, ... and you don't quite succeed!

The interview in [8] and [9] also provides a chance to examine Serre's views on mathematics. However, we choose here to quote from [16] on Serre's view on applications of mathematics:-

As for the place of mathematics in relation to other sciences, mathematics can be seen as a big warehouse full of shelves. Mathematicians put things on the shelves and guarantee that they are true. They also explain how to use them and how to reconstruct them. Other sciences come and help themselves from the shelves, mathematicians are not concerned with what they do with what they have taken. this metaphor is rather coarse, but it reflects the situation well enough. (Of course one does not choose to do mathematics just for putting things on shelves; one does mathematics for the fun of it.) Here is a personal example. My wife, Josiane, was a specialist in quantum chemistry. She needed linear representations of certain symmetry groups. The books she was working with were not satisfactory; they were correct, but they used very clumsy notation. I wrote a text that suited her needs, and then published it in book form, as 'Linear Representations of Finite Groups'. I thus did my duty as a mathematician (and as a husband): putting things on shelves.

In the interview [18] Serre speaks about his hobbies. He loved rock climbing, skiing and table tennis. I [EFR] can certainly say from personal experience what an excellent table tennis player Serre was, for I've seen him playing at many conferences that we both attended. I always had the (very silly) thought: How can someone who is so good at mathematics be so good at table tennis! Other things that Serre enjoys are chess, reading books and the movies. He said he liked books [9]:-

... of all kinds, from Giono to Böll to Kawabata, including fairy tales and the Harry Potter series.

Serre has received numerous awards. In addition to the Fields Medal in 1954 he was elected an honorary member of the London Mathematical Society in 1973, and a Fellow of the Royal Society of London in 1974. He has also been made an Officer Légion d'Honneur and Commander Ordre National du Mérite. He has been elected to many national academies in addition to the Royal Society, in particular the academies of France (1977), the Netherlands (1978), the United States (1979), Sweden (1981), Russia (2003), Norway (2009), Turin (2010) and Taiwan (2010). He was awarded the Prix Peccot-Vimont by the Collège de France (1955), the Prix Francoeur by the Académie des Sciences (1957), the Prix Gaston Julia (1970), the Médaille Émile Picard by the Académie des Sciences (1971), the Prix Balzan (1985), the Gold Medal from the C.N.R.S. (1987), the Steele Prize, described above, from the American Mathematical Society (1995) and the Wolf Prize in 2000. He has been awarded honorary degrees from the University of Cambridge in 1978, the University of Stockholm in 1980, the University of Glasgow in 1983, the University of Athens in 1996, Harvard University in 1998, the University of Durham in 2000, the University of London in 2001, the University of Oslo in 2002, the University of Oxford in 2003, the University of Bucharest in 2004, the University of Barcelona in 2004, the University of Madrid in 2006 and the University of McGill in 2008. In June 2003 he was awarded the first Abel Prize by the Norwegian Academy of Science and Letters [6]:-

... for playing a major role in giving a number of mathematical topics their modern form, notably topology, algebraic geometry and the theory of numbers.

The events surrounding this ceremony are described in several articles. The following is extracted from [18]:-

The events started in bright sunshine in Oslo on Sunday, 1 June 2003, with a simple ceremony at the Abel Monument in Slottsparken. After Jens Erik Fenstad, chair of the Abel Board (organizer of the prize events), had given a short speech, the Abel laureate, Jean-Pierre Serre, laid a wreath at the monument. On 2 June the scientific program started in Georg Sverdrup's house, the wonderful new library at the University of Oslo in Blindern. ... Serre's lecture was entitled "Prime numbers, equations and modular forms". He fully lived up to his reputation as a master expositor, lecturing in the old-fashioned way with chalk on the blackboard, and impressed everybody with a very clear presentation without notes. ... Later in the afternoon, Jean-Pierre Serre received several parties of journalists for interviews. On Tuesday morning Serre and representatives of the Abel Committee and the Abel Board met the world press: ten journalists from Norway, England, France, and Germany. On Tuesday afternoon the prize was presented at a ceremony, with due pomp and circumstance, at the University of Oslo. King Harald and Queen Sonja attended, and after some speeches the king presented the prize to Serre.