弗里曼·戴森Freeman Dyson

弗里曼·戴森的父母是Mildred Lucy Atkey和George Dyson。George非常有才华，无论是作为音乐教师还是音乐作家。在戴森出生时，George在伯克郡的惠灵顿学院教授音乐。他早些时候曾在马尔伯勒学院任教，在那里他是Mildred的兄弟戴森 Atkey的同事和密友。在戴森 Atkey去世后，他在第一次世界大战期间阵亡，George和Mildred都深受打击。这使他们更加亲近，他们于1916年结婚。他们的第一个孩子Alice出生于1919年，然后他们的第二个孩子是戴森，以戴森 Atkey命名。

戴森出生后不久，他的父亲接受了温彻斯特学院音乐硕士的职位，因此戴森在温彻斯特度过了他的早年。他与母亲比与父亲更亲近，因为母亲是两人中更严肃的，极其有才华且博览群书。家庭富裕，雇用了厨师、园丁、女佣和保姆。戴森从五岁起就上了由Scott小姐办的走读学校。他已经显示出在阅读、写作和计算方面的非凡才能。从九岁起，他成为Twyford学院的寄宿生，该学院离他家只有三英里。尽管学校离家如此之近，戴森只在学校假期回家，他的父母从未在学校看望过他。

1936年，戴森在温切斯特公学的奖学金考试中夺得第一名；他当时十二岁。这个第一名显示出巨大的潜力，他一生中第一次开始意识到自己有多么才华横溢。他在各科都是出类拔萃的学生，但在数学上表现得尤为杰出。在此之前，他一直显得是个非常不寻常的学生，与同学们截然不同。然而现在他赢得了同学们的尊重，他的父母也为儿子的成功感到十分震惊。温切斯特公学对弗里曼很重要，因为它给了他出色的数学教育。他不仅师从全国最优秀的数学教师之一，即C V Durell，而且还与詹姆斯·莱特希尔同班，两人一起学习高等数学，例如卡米耶·若尔当的Cours d'Analyse。外语对戴森来说轻而易举，当他在1938年对数论产生兴趣时，他决定阅读伊万·维诺格拉多夫所著的An introduction to the theory of numbers。当时这本书只有俄文版，这显然不成问题，他自学了这门语言并将书译成了英文。第二年，他读了亚瑟·爱丁顿的The mathematical theory of relativity。

戴森于1941年获得剑桥大学三一学院的奖学金。第一年，他跟随保罗·狄拉克学习物理学，跟随戈弗雷·哈罗德·哈代和阿布拉姆·萨莫伊洛维奇·贝西科维奇学习纯数学。在那里期间，他写了几篇直到1944年才发表的论文。第一篇写于1941年（1944年发表）的是A proof that every equation has a root。戴森写道：-

……关于每个方程都有一个根这一定理，已有如此多的证明，以至于再给出一个几乎像是犯罪。不过，我可以为自己说两点：第一，我将给出的证明很可能不是新的；第二，如果我的证明是新的，它相较于其他证明有一个优势，即只使用了最初步的论证。

戴森在1943年发表了三篇论文，Three identities in combinatory analysis和On the order of magnitude of the partial quotients of a continued fraction是Journal of the London Mathematical Society中连续的两篇论文，而A note on kurtosis则发表在Journal of the Royal Statistical Society上。当然，戴森在剑桥度过的这些年正值第二次世界大战中期，因此许多学者都已离开去从事战争工作。尽管对戴森来说这不是一段特别愉快的时光，但他确实有几个好朋友。作为工作之余的消遣，他和朋友们会在晚上去“夜攀”剑桥的各种建筑。

1943年，尽管戴森早先抱有和平主义信念，他还是开始作为科学家为轰炸机司令部工作，致力于提高任务效率。他在这项工作上花费了很长时间，但也设法继续自己的数学研究，并阅读了一些物理学著作。战争结束时，戴森在帝国理工学院获得了一份演示员的工作。在此期间，他写了一篇关于连分数的有影响力的论文On simultaneous Diophantine approximations。1946年，他作为会士回到三一学院，此前他写了一篇学位论文，并从中发表了三篇论文：A theorem on the densities of sets of integers（1945年）、A theorem in algebraic topology（1948年）和On the product of four non-homogeneous linear forms（1948年）。然而回到剑桥后，他开始研究理论物理，这后来成为他的主要研究课题，尽管如下文所述，他继续发表纯数学论文。在此期间，有人建议他考虑移居美国。根据鲁道夫·佩尔斯（伯明翰）等人的建议，他决定申请去康奈尔与汉斯·贝特一起工作。杰弗里·泰勒给贝特写了一封推荐信（例如见[4]）：——

您应该已经收到戴森先生申请作为研究生来您这里工作的申请。我希望您能接受他。尽管他只有23岁，但在我看来他是英格兰最好的数学家。

戴森与贝特密切合作，并对他产生了深深的敬佩（正如所有贝特的学生一样）。1948年，戴森在Physical Review上发表了一篇关于兰姆位移的论文，题为The Electromagnetic Shift of Energy Levels。这是他发表的第一篇物理学论文，它显示了他在计算方面的卓越能力以及深刻的物理理解。显然，此时戴森被认为是一位极具天赋和能力的学生。贝特说服奥本海默接收戴森到普林斯顿高等爱德华·斯图迪。他在推荐信中写道：——

戴森的能力和成就绝对非同寻常。我可以毫无保留地说，他是我曾经拥有或见过的最好的。

正是从这时起，戴森的工作聚焦于量子电动力学。此时发生了一件让戴森非常高兴的事：日本的朝永振一郎在相对论量子场论方面做出了重要工作。这不仅因为这项工作如此重要，还因为它来自一个意想不到的地方，表明美国并不是这一领域唯一产生重要研究的地方。朝永振一郎的工作与朱利安·施温格的不同之处在于其清晰和简洁。大约在1948年春天，戴森和理查德·费曼成为朋友，戴森熟悉了理查德·费曼的方法。两人的特点是他们在计算方面具有惊人的能力。在乘坐长途巴士前往普林斯顿之后，戴森著名地解决了一个困扰他整整一年的非常重要的问题。他现在明白了如何证明朱利安·施温格和理查德·费曼理论的等价性。这些想法最终构成了他令人印象深刻的工作The radiation theories of Tomonaga, Schwinger, and Feynman的基础，该工作于1949年发表在Physical Review上。Corben在一篇评论中写道：-

讨论了朝永-朱利安·施温格量子电动力学，适当强调了其中涉及的物理思想，并建立了与理查德·费曼一个主要未发表理论的等价性。

戴森于1948年秋抵达普林斯顿。他与奥本海默相处从未完全自在。他觉得奥本海默肤浅——与贝特相比，在给予学生指导和支持方面很差。贝特继续是戴森的真正支持者，并在一次有影响力的研讨会上帮助戴森说服听众（包括奥本海默），使他们相信理查德·费曼的方法是最有希望的前进方式。戴森1949年关于$S$-矩阵The S matrix in quantum electrodynamics重正化的著名论文成为量子电动力学中备受推崇和极具影响力的工作。这篇重要论文的内容和方法由W H Furry总结如下：-

从S矩阵计算的角度讨论了量子电动力学在散射问题中的应用，S矩阵是一种将初态的入射波转换为末态的出射波的算符。……S矩阵的计算由一组图表示，其中有向线代表电子，无向虚线代表光子或与给定电磁场的相互作用。图的内部线代表粒子的虚态，或者用于提供被观测粒子之间的相互作用，或者代表场的涨落，产生诸如自能之类的效应；延伸到图的边缘的线代表被观测粒子或与给定场的相互作用。当然，对于任何给定过程都有许多图，并且对应于每一个图都有对S矩阵的一项贡献，可以根据理查德·费曼设计的规则通过检查图写出，这些规则已在[戴森的]前一篇论文中给出。

戴森开始在科学界成为名人。他意识到这种名声的风险，并意味深长地说：-

我相信我有足够的智慧享受这种成功而不被它所迷惑；如果我没有，我有理查德·费曼的例子来教导我。

1949年初，他计划返回英国，并征求奥本海默关于加入哪个机构的建议。奥本海默说：-

嗯，伯明翰有最优秀的理论物理学家可以合作，佩尔斯；布里斯托尔有最优秀的实验物理学家，鲍威尔；剑桥有一些出色的建筑……

在贝特为戴森申请加入佩尔斯所写的推荐信中，他将戴森描述为：-

……自保罗·狄拉克以来最优秀的英国理论家。

1949年夏天，戴森在高等斯图迪研究所遇到了Verena Esther Haefeli-Huber。她是一位瑞士数学家，前一年发表了她的博士论文Ein Dualismus als Klassifikationsprinzip in der abstrakten Gruppentheorie。该论文推广了菲利浦·霍尔的两篇论文。戴森于1950年夏天与Verena订婚，并于同年8月11日结婚。他们有两个孩子：Esther 戴森于1951年7月14日出生在瑞士苏黎世，George Dyson于1953年出生在纽约伊萨卡。Esther 16岁进入哈佛大学，主修经济学。作为一名作家和记者，她是计算领域的杰出人物。George Dyson16岁离家，搬到不列颠哥伦比亚省，在那里建造独木舟，探索西北海岸，并在树屋中安家。戴森和妻子于1958年离婚，同年11月21日，他与Imme Jung结婚；他们有四个女儿，Dorothy、Emily、Mia和Rebecca。

完成$S$矩阵论文后，戴森转向介子理论，在那里他设计了一种分离高频率和低频率相互作用计算的方法。在更多重要出版物和对国际会议的贡献之后，1950年5月，戴森接替了理查德·费曼在康奈尔的教授职位。贝特对戴森的钦佩此时已变得非常强烈。贝特表示，戴森是“世界上唯一”能在康奈尔接替理查德·费曼的人。

有趣的是，在戴森令人印象深刻的职业生涯中，他似乎从未获得博士学位。这根本不在他的计划之中。也许不那么有趣的是，他很可能有资格获得“从未获得诺贝尔奖的最佳物理学家”奖。这似乎从未困扰过他，但许多人认为他本应与理查德·费曼、朱利安·施温格和朝永一起获得诺贝尔奖。

1953年，戴森接受了普林斯顿高等斯图迪研究所物理学教授的职位。我们上面提到，尽管戴森现在是一名物理学家，但他继续发表纯数学研究论文。例如，他于1951年在Annals of Mathematics上发表了巧妙论文Continuous functions defined on spheres，1961年发表A new symmetry of partitions，1989年发表Mappings and symmetries of partitions，1994年与Pavel Bleher合作发表Mean square value of exponential sums related to representation of integers as sum of two squares，2001年发表The sixth Fermat number and palindromic continued fractions。

我们应特别提及戴森于1988年发表的论文A walk through Ramanujan's garden。Christian Radoux在评论中写道：-

本文是作者所作的一次演讲的文本。它讲述了一个漫长而优美的故事：48年来，作者一直在研究拉马努金的工作，最初是通过戈弗雷·哈罗德·哈代和爱德华·梅特兰·赖特的书，接着是在《文集》、《遗失的笔记》以及其他几位数学家的著作中。这使我们有机会追随他自己关于分拆的同余性质、特殊级数与无穷乘积、生成函数以及模函数的研究……

戴森还出版了几本关于科学/哲学的著作，包括Disturbing the Universe（1979）、Weapons and Hope（1984）、Origins of Life（1986）、Infinite in all Directions（1988）、From Erod to Gaia（1992）、Imagined Worlds（1997）和The Sun, the Genome and the Internet（1999）。他撰写了许多阐述性文章，如Scientific American上的Mathematics in the physical sciences（1964），论述数学，特别是群论，在物理科学中的作用。American Mathematical Monthly上的Missed opportunities（1972）是以下内容的文本：-

……[戴森]于1972年1月所作的约西亚·威拉德·吉布斯演讲。这场演讲精彩、大胆且富有争议。它引发了大量讨论和一些批评，但确实激发了听众……关于数学家与物理学家之间交流中断以及人们对詹姆斯·克拉克·麦克斯韦的方程缺乏兴趣的历史叙述，构成了对数学界的一种控诉。

在Unfashionable pursuits（1983）中，戴森：-

……向那些为研究机构（如斯图迪高等研究院和洪堡基金会）分配研究经费的“权威”委员会发出强烈呼吁，希望他们更多地关注那些想要在“冷门”领域工作的科学家。他强调，最初提出时“冷门”的想法在许多年后被证明非常重要，并以赫尔曼·格拉斯曼和索菲斯·李的工作为例……

戴森因其杰出贡献获得了许多荣誉，包括1952年当选为伦敦皇家学会会士。他还当选为国家科学院（美国）（1964）和巴黎科学院（1989）的成员。他获得了荷兰皇家科学院颁发的洛伦兹奖章（1966）、Royal Society颁发的休斯奖章（1968）、德国物理学会颁发的马克斯·普朗克奖章（1969）、美国能源部颁发的恩里科·费米奖（1995），以及宗教进步坦普尔顿奖（2000）。

1994年，戴森从普林斯顿高等斯图迪研究所的教授职位上退休，并被任命为荣休教授。1996年，Selected papers of Freeman Dyson with commentary由美国数学会出版。Aernout C D van Enter对这本书的评论很好地总结了戴森的贡献：-

对这本书发表意见几乎像是一种冒昧。它的主题广泛，包含许多深刻、往往是经典的结果，并且文笔无可挑剔。对所有读者来说，这本书中既有贴近他们兴趣的内容，也有超出他们理解范围的内容。它拥有丰富的主题和开创性贡献：著名的QED[量子电动力学]论文、物质稳定性、层级Ising模型的发明、无序线性链、随机矩阵、自旋波理论等；戴森在所有这些不同的主题中都留下了自己的印记。这还没有包括纯数学中的主题，我觉得自己更没资格评判。戴森的多才多艺、数学实力和深度是众所周知的，他的评论以及有时颇具挑衅性的观点发人深省，读来令人愉快。我最好的推荐方式莫过于重复那句老话：研究大师！

Freeman Dyson's parents were Mildred Lucy Atkey and George Dyson. George was very talented, both as a teacher of music and as a writer on music. At the time of Freeman's birth George was teaching music at Wellington College in Berkshire. He had earlier taught at Marlborough College where he was a colleague and close friend of Mildred's brother Freeman Atkey. After the death of Freeman Atkey, who was killed in action during World War I, both George and Mildred were shattered. It brought them close together and they married in 1916. Their first child Alice was born in 1919, then their second child was Freeman who was named after Freeman Atkey.

Shortly after Freeman was born, his father accepted the post of Master of Music at Winchester College, and so Freeman spent his early years in Winchester. He was closer to his mother than to his father, for she was the more serious of the two being extremely talented and well read. The family were well off and employed a cook, gardener, housemaid and nursemaid. Freeman attended a day school run by Miss Scott from the time he was five years old. Already he was showing exceptional talents for reading, writing and calculating. From the age of nine he was a boarder at Twyford College which was only three miles from his home. Despite the fact that the school was so close to his home, Freeman only went home in the school holidays and his parents never visited him in the school.

In 1936 Dyson won first place in a scholarship examination to Winchester College; he was twelve. That first place indicated significant promise and for the first time in his life he began to realise how talented he was. He was an outstanding student across the curriculum, but proved to be brilliant at mathematics. Up until that time he had appeared as a very unusual pupil, very different from his fellow pupils. However he now gained respect from his fellow pupils and his parents were quite bowled over by their son's success. Winchester College was important for freeman for it gave him an outstanding mathematical education. Not only did he have one of the finest mathematics teachers in the country, namely C V Durell, but he was in the same class as James Lighthill and the two studied advanced mathematics together such as Jordan's Cours d'Analyse. Foreign languages came easily to Dyson and when he became interested in number theory in 1938 he decided to read An introduction to the theory of numbers by Vinogradov. The fact that the book was only available in Russian at that time was apparently no problem and he taught himself the language and translated the book into English. In the following year he read Eddington's The mathematical theory of relativity.

Dyson gained a scholarship to Trinity College, Cambridge in 1941. In his first year he studied physics under Dirac and pure mathematics under Hardy and Besicovitch. During his time there he wrote several papers that were not published until 1944. The first, written in 1941 (published in 1944) is A proof that every equation has a root. Dyson writes:-

... there are so many proofs of the theorem that every equation has a root that it seems almost criminal to produce another. I can however say two things in my defence; first, the proof I shall give is probably not a new one; second, if my proof is new it has a certain advantage over other proofs in using only the most elementary arguments.

Dyson had three papers published in 1943, Three identities in combinatory analysis and On the order of magnitude of the partial quotients of a continued fraction are consecutive papers in the Journal of the London Mathematical Society while A note on kurtosis appeared in the Journal of the Royal Statistical Society. Of course these years that Dyson spent at Cambridge were in the middle of World War II and as a result many of the academics had left to undertake war work. Although not a particularly happy time for Dyson he did have a couple of good friends. As a diversion from his work, he and his friends would occupy evenings "night climbing" various architectural features of Cambridge.

In 1943 Dyson, despite earlier pacifist beliefs, started work as a scientist with Bomber Command where he worked on increasing mission efficiency. He worked long hours at this work but also managed to continue with his mathematics research and to read some physics texts. At the end of the war, Dyson took a job as a demonstrator at Imperial College. During this time he wrote an influential paper On simultaneous Diophantine approximations on continued fractions. He returned to Trinity College in 1946 as a fellow having written a dissertation from which he published three papers; A theorem on the densities of sets of integers (1945), A theorem in algebraic topology (1948), and On the product of four non-homogeneous linear forms (1948). Back at Cambridge, however, he began working on theoretical physics which was to become his main topic of research although, as we note below, he continued to publish papers on pure mathematics. During this time he was advised to consider moving to the USA. On advice from Peierls (Birmingham) and others, he decided to apply to work with Bethe in Cornell. Geoffrey Taylor wrote a letter of reference to Bethe (see for example [4]):-

You'll have received an application from Mr Freeman Dyson to come to work with you as a graduate student. I hope that you will accept him. Although he is only 23 he is in my view the best mathematician in England.

Dyson worked closely with Bethe and became deeply impressed by him (as all Bethe's students were.) In 1948 Dyson published a paper on Lamb shift in Physical Review called The Electromagnetic Shift of Energy Levels. This was the first paper he had published on physics, and it showed his remarkable ability at calculation as well as a deep physical understanding. It is clear that at this time Dyson was considered to be an extraordinarily gifted and able student. Bethe persuaded Oppenheimer to take Dyson on at the Institute for Advanced Study at Princeton. He wrote in his letter of recommendation:-

Mr Dyson is absolutely unusual in his ability and accomplishments. I can say without reservation that he is the best I have ever had or observed.

It was from this time that Dyson's work focused on quantum electrodynamics. Something happened at this time that greatly pleased Dyson; Tomanaga in Japan had developed significant work in relativistic quantum field theory. It was not just that the work was so significant, it was that it came from an unexpected source and indicated that the USA was not the only place producing significant research in this field. Tomonaga's work differed from Schwinger's by virtue of its clarity and simplicity. Around spring in 1948, Dyson and Feynman became friends and Dyson became familiar with Feynman's methods. What characterised the two was their prodigious ability at calculation. After a long bus ride to Princeton Dyson famously figured out a very significant problem that had bothered him during the year. He now saw how to demonstrate the equivalence of Schwinger's and Feynman's theories. These ideas eventually formed the basis for his impressive work The radiation theories of Tomonaga, Schwinger, and Feynman which was published in the Physical Review in 1949. Corben wrote in a review:-

The Tomonaga-Schwinger quantum electrodynamics is discussed with due emphasis on the physical ideas involved and the equivalence with a mainly unpublished theory by Feynman is established.

Dyson arrived at Princeton in the Autumn of 1948. He was never quite at ease with Oppenheimer. He felt that Oppenheimer was superficial - and compared with Bethe was poor at giving guidance and support to his students. Bethe continued to be a real support to Dyson and at an influential seminar helped Dyson persuade the audience (which including Oppenheimer) that Feynman's methods were the most promising way to proceed. Dyson's famous paper on renormalisation of the $S$-matrix The S matrix in quantum electrodynamics in 1949 became a very highly regarded and influential work in quantum electrodynamics. The contents and methods of this important paper are summarised by W H Furry:-

The application of quantum electrodynamics to scattering problems is discussed in terms of the calculation of the S matrix, an operator which converts the ingoing waves of the initial state into the outgoing waves of the final state. ... The calculation of the S matrix is represented by a set of graphs, in which directed lines represent electrons and undirected dotted lines represent photons or interactions with a given electromagnetic field. Internal lines of a graph represent virtual states of particles, either serving to provide interactions between observed particles or else representing fluctuations of the fields, giving rise to effects such as self-energy; lines extending to the edge of a graph represent observed particles or interactions with the given field. There are, of course, many graphs for any given process, and corresponding to each of these there is a contribution to the S matrix, which can be written down from inspection of the graph, according to rules devised by Feynman and presented in [Dyson's] previous paper.

Dyson started to become a celebrity in scientific circles. He was aware of the risks of such fame and tellingly said:-

I believe I am wise enough to enjoy this sort of success without having been taken in by it; if I were not, I have the example of Feynman to instruct me.

In early 1949 he planned to return to Britain and asked Oppenheimer's advice on which institution to join. Oppenheimer said:-

Well, Birmingham has much the best theoretical physicist to work with, Peierls; Bristol has much the best experimental physicist, Powell; Cambridge has some excellent architecture ...

In Bethe's reference for Dyson's application to join Peierls, he described Dyson as the:-

... best English theorist since Dirac.

In the summer of 1949 Dyson met Verena Esther Haefeli-Huber at the Institute for Advanced Study. She was a Swiss mathematician who had published her doctoral thesis Ein Dualismus als Klassifikationsprinzip in der abstrakten Gruppentheorie in the previous year. It generalised two papers by P Hall. Dyson became engaged to Verena in the summer of 1950 and they were married later that year on 11 August. They had two children: Esther Dyson was born on 14 July 1951 in Zürich, Switzerland, and George Dyson born in Ithaca, New York in 1953. Esther went to Harvard at the age 16, where she majored in economics. An author and journalist, she is a major figure in the world of computing. George Dyson left home at age 16, moved to British Columbia where he built canoes, explored the Northwest Coast, and made his home in a tree-house. Dyson and his wife were divorced in 1958 and in the same year, on 21 November, he married Imme Jung; they had four daughters, Dorothy, Emily, Mia and Rebecca.

After finishing the $S$-matrix paper, Dyson turned to meson theory where he devised a method of separating the calculation of high and low frequency interactions. After further important publications and contributions to international conferences, in May 1950 Dyson took over Feynman's professorship at Cornell. Bethe's admiration for Dyson had by now become great. Bethe stated that Dyson was "the only man in the world " who could replace Feynman at Cornell.

It is amusing to note that at no point during Dyson's impressive career did he appear to obtain a Ph.D. It just did not figure in the scheme of things. Less amusing perhaps is that he may well qualify for the "best physicist never to receive a Nobel Prize" award. This never seemed to trouble him, but many people believe he should have received one along with Feynman, Schwinger and Tomonaga.

In 1953 Dyson accepted a post as professor of physics at Institute for Advanced Study, Princeton. We remarked above that Dyson continued to publish research papers on pure mathematics despite now being a physicist. For example he published the ingenious paper Continuous functions defined on spheres in the Annals of Mathematics in 1951, A new symmetry of partitions in 1961, Mappings and symmetries of partitions in 1989, Mean square value of exponential sums related to representation of integers as sum of two squares (jointly with Pavel Bleher) in 1994, and The sixth Fermat number and palindromic continued fractions in 2001.

We should give special mention to the paper A walk through Ramanujan's garden which Dyson published in 1988. Christian Radoux writes in a review:-

This paper is the text of a lecture given by the author. It tells a long and beautiful story: for 48 years, the author has studied Ramanujan's work, first through the book of Hardy and Wright, next in the "Collected papers", in the "Lost notebook" and in the work of several other mathematicians. It gives us the opportunity to follow his own research about congruence properties of partitions, special series and infinite products, generating functions, and modular functions, ...

Dyson has also published several books on science/philosophy, including Disturbing the Universe (1979), Weapons and Hope (1984), Origins of Life (1986), Infinite in all Directions (1988), From Erod to Gaia (1992), Imagined Worlds (1997) and The Sun, the Genome and the Internet (1999). He has written a number of expository articles such as Mathematics in the physical sciences (1964) in Scientific American, on the role of mathematics, in particular group theory, in the physical sciences. Missed opportunities (1972) in the American Mathematical Monthly is the text of:-

... the Josiah Willard Gibbs lecture given by [Dyson] in January of 1972. The lecture was brilliant, bold and controversial. It generated much discussion and some criticism, but it did stimulate the audience .... The historical account of the breakdown in communications between mathematicians and physicists and of the lack of interest in Maxwell's equations constitutes an indictment of the mathematical community.

In Unfashionable pursuits (1983) Dyson:-

... puts in a strong plea to the committees of "mandarins" granting funds for research from institutions, such as the Institute for Advanced Study and the Humboldt Foundation, that they pay more attention to scientists wanting to work in "unfashionable" areas. He stresses the fact that ideas which were "unfashionable" when first put forward turned out to be very important many years later, and gives as examples the work of Grassmann and Lie ...

Dyson has received many honours for his outstanding contributions including election to a fellowship of the Royal Society of London in 1952. He has also been elected to the National Academy of Sciences (United States) (1964) and the Paris Academy of Sciences (1989). He has been awarded the Lorentz Medal by the Royal Netherlands Academy of Sciences (1966), the Hughes Medal by the Royal Society (1968), the Max Planck Medal by the German Physical Society (1969), the Enrico Fermi Award by the U.S. Department of Energy (1995), and the Templeton Prize for Progress in Religion (2000).

In 1994 Dyson retired from his professorship at the Institute for Advanced Study at Princeton and was appointed professor emeritus. In 1996 Selected papers of Freeman Dyson with commentary was published by the American Mathematical Society. The review of this book by Aernout C D van Enter provides a good summary of Dyson's contributions:-

To express an opinion about this book almost feels like a presumption. It is wide in subject matter, contains many deep, often classic, results, and is written in an impeccable style. For all readers there are things close to their interests, as well as things beyond their grasp in this book. It has a wealth of topics and of seminal contributions: the famous QED [quantum electrodynamics] papers, the stability of matter, the invention of the hierarchical Ising models, the disordered linear chain, random matrices, spin wave theory, etc.; Dyson has made his mark in all these varied subjects. This still leaves out the topics in pure mathematics, which I feel even less qualified to judge. Dyson's versatility, mathematical strength and depth are well known and his comments and sometimes provocative opinions are thought-inspiring and a pleasure to read. I cannot do better than recommending this volume by repeating the old saying: study the masters!