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作者： 发布时间：2007-11-25 15:25:11 来源： 点击数：37
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John von Neumann (Neumann János)
(December 28, 1903 – February 8, 1957)
John von Neumann
Born: 28 Dec 1903 in Budapest, Hungary
Died: 8 Feb 1957 in Washington D.C., USA
John von Neumann was born János von Neumann. He was called Jancsi as a child, a diminutive form of János, then later he was called Johnny in the United States. His father, Max Neumann, was a top banker and he was brought up in a extended family, living in Budapest where as a child he learnt languages from the German and French governesses that were employed. Although the family were Jewish, Max Neumann did not observe the strict practices of that religion and the household seemed to mix Jewish and Christian traditions.
It is also worth explaining how Max Neumann's son acquired the "von" to become János von Neumann. In 1913 Max Neumann purchased a title but did not change his name. His son, however, used the German form von Neumann where the "von" indicated the title.
As a child von Neumann showed he had an incredible memory. Poundstone, in [8], writes:-
At the age of six, he was able to exchange jokes with his father in classical Greek. The Neumann family sometimes entertained guests with demonstrations of Johnny's ability to memorise phone books. A guest would select a page and column of the phone book at random. Young Johnny read the column over a few times, then handed the book back to the guest. He could answer any question put to him (who has number such and such?) or recite names, addresses, and numbers in order.
In 1911 von Neumann entered the Lutheran Gymnasium. The school had a strong academic tradition which seemed to count for more than the religious affiliation both in the Neumann's eyes and in those of the school. His mathematics teacher quickly recognised von Neumann's genius and special tuition was put on for him. The school had another outstanding mathematician one year ahead of von Neumann, namely Eugene Wigner.
World War I had relatively little effect on von Neumann's education but, after the war ended, Béla Kun controlled Hungary for five months in 1919 with a Communist government. The Neumann family fled to Austria as the affluent came under attack. However, after a month, they returned to face the problems of Budapest. When Kun's government failed, the fact that it had been largely composed of Jews meant that Jewish people were blamed. Such situations are devoid of logic and the fact that the Neumann's were opposed to Kun's government did not save them from persecution.
In 1921 von Neumann completed his education at the Lutheran Gymnasium. His first mathematics paper, written jointly with Fekete the assistant at the University of Budapest who had been tutoring him, was published in 1922. However Max Neumann did not want his son to take up a subject that would not bring him wealth. Max Neumann asked Theodore von Kármán to speak to his son and persuade him to follow a career in business. Perhaps von Kármán was the wrong person to ask to undertake such a task but in the end all agreed on the compromise subject of chemistry for von Neumann's university studies.
Hungary was not an easy country for those of Jewish descent for many reasons and there was a strict limit on the number of Jewish students who could enter the University of Budapest. Of course, even with a strict quota, von Neumann's record easily won him a place to study mathematics in 1921 but he did not attend lectures. Instead he also entered the University of Berlin in 1921 to study chemistry.
Von Neumann studied chemistry at the University of Berlin until 1923 when he went to Zurich. He achieved outstanding results in the mathematics examinations at the University of Budapest despite not attending any courses. Von Neumann received his diploma in chemical engineering from the Technische Hochschule in Zürich in 1926. While in Zurich he continued his interest in mathematics, despite studying chemistry, and interacted with Weyl and Pólya who were both at Zurich. He even took over one of Weyl's courses when he was absent from Zurich for a time. Pólya said [18]:-
Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me as soon as the lecture was over, with the complete solution in a few scribbles on a slip of paper.
Von Neumann received his doctorate in mathematics from the University of Budapest, also in 1926, with a thesis on set theory. He published a definition of ordinal numbers when he was 20, the definition is the one used today.
Von Neumann lectured at Berlin from 1926 to 1929 and at Hamburg from 1929 to 1930. However he also held a Rockefeller Fellowship to enable him to undertake postdoctoral studies at the University of Göttingen. He studied under Hilbert at Göttingen during 1926-27. By this time von Neumann had achieved celebrity status [8]:-
By his mid-twenties, von Neumann's fame had spread worldwide in the mathematical community. At academic conferences, he would find himself pointed out as a young genius.
Veblen invited von Neumann to Princeton to lecture on quantum theory in 1929. Replying to Veblen that he would come after attending to some personal matters, von Neumann went to Budapest where he married his fiancée Marietta Kovesi before setting out for the United States. In 1930 von Neumann became a visiting lecturer at Princeton University, being appointed professor there in 1931.
Between 1930 and 1933 von Neumann taught at Princeton but this was not one of his strong points [8]:-
His fluid line of thought was difficult for those less gifted to follow. He was notorious for dashing out equations on a small portion of the available blackboard and erasing expressions before students could copy them.
In contrast, however, he had an ability to explain complicated ideas in physics [3]:-
For a man to whom complicated mathematics presented no difficulty, he could explain his conclusions to the uninitiated with amazing lucidity. After a talk with him one always came away with a feeling that the problem was really simple and transparent.
He became one of the original six mathematics professors (J W Alexander, A Einstein, M Morse, O Veblen, J von Neumann and H Weyl) in 1933 at the newly founded Institute for Advanced Study in Princeton, a position he kept for the remainder of his life.
During the first years that he was in the United States, von Neumann continued to return to Europe during the summers. Until 1933 he still held academic posts in Germany but resigned these when the Nazis came to power. Unlike many others, von Neumann was not a political refugee but rather he went to the United States mainly because he thought that the prospect of academic positions there was better than in Germany.
In 1933 von Neumann became co-editor of the Annals of Mathematics and, two years later, he became co-editor of Compositio Mathematica. He held both these editorships until his death.
Von Neumann and Marietta had a daughter Marina in 1936 but their marriage ended in divorce in 1937. The following year he married Klára Dán, also from Budapest, whom he met on one of his European visits. After marrying, they sailed to the United States and made their home in Princeton. There von Neumann lived a rather unusual lifestyle for a top mathematician. He had always enjoyed parties [8]:-
Parties and nightlife held a special appeal for von Neumann. While teaching in Germany, von Neumann had been a denizen of the Cabaret-era Berlin nightlife circuit.
Now married to Klára the parties continued [18]:-
The parties at the von Neumann's house were frequent, and famous, and long.
Ulam summarises von Neumann's work in [35]. He writes:-
In his youthful work, he was concerned not only with mathematical logic and the axiomatics of set theory, but, simultaneously, with the substance of set theory itself, obtaining interesting results in measure theory and the theory of real variables. It was in this period also that he began his classical work on quantum theory, the mathematical foundation of the theory of measurement in quantum theory and the new statistical mechanics.
His text Mathematische Grundlagen der Quantenmechanik (1932) built a solid framework for the new quantum mechanics. Van Hove writes in [36]:-
Quantum mechanics was very fortunate indeed to attract, in the very first years after its discovery in 1925, the interest of a mathematical genius of von Neumann's stature. As a result, the mathematical framework of the theory was developed and the formal aspects of its entirely novel rules of interpretation were analysed by one single man in two years (1927-1929).
Self-adjoint algebras of bounded linear operators on a Hilbert space, closed in the weak operator topology, were introduced in 1929 by von Neumann in a paper in Mathematische Annalen . Kadison explains in [22]:-
His interest in ergodic theory, group representations and quantum mechanics contributed significantly to von Neumann's realisation that a theory of operator algebras was the next important stage in the development of this area of mathematics.
Such operator algebras were called "rings of operators" by von Neumann and later they were called W*-algebras by some other mathematicians. J Dixmier, in 1957, called them "von Neumann algebras" in his monograph Algebras of operators in Hilbert space (von Neumann algebras). In the second half of the 1930's and the early 1940s von Neumann, working with his collaborator F J Murray, laid the foundations for the study of von Neumann algebras in a fundamental series of papers.
However von Neumann is know for the wide variety of different scientific studies. Ulam explains [35] how he was led towards game theory:-
Von Neumann's awareness of results obtained by other mathematicians and the inherent possibilities which they offer is astonishing. Early in his work, a paper by Borel on the minimax property led him to develop ... ideas which culminated later in one of his most original creations, the theory of games.
In game theory von Neumann proved the minimax theorem. He gradually expanded his work in game theory, and with co-author Oskar Morgenstern, he wrote the classic text Theory of Games and Economic Behaviour (1944).
Ulam continues in [35]:-
An idea of Koopman on the possibilities of treating problems of classical mechanics by means of operators on a function space stimulated him to give the first mathematically rigorous proof of an ergodic theorem. Haar's construction of measure in groups provided the inspiration for his wonderful partial solution of Hilbert's fifth problem, in which he proved the possibility of introducing analytical parameters in compact groups.
In 1938 the American Mathematical Society awarded the Bôcher Prize to John von Neumann for his memoir Almost periodic functions and groups. This was published in two parts in the Transactions of the American Mathematical Society, the first part in 1934 and the second part in the following year. Around this time von Neumann turned to applied mathematics [35]:-
In the middle 30's, Johnny was fascinated by the problem of hydrodynamical turbulence. It was then that he became aware of the mysteries underlying the subject of non-linear partial differential equations. His work, from the beginnings of the Second World War, concerns a study of the equations of hydrodynamics and the theory of shocks. The phenomena described by these non-linear equations are baffling analytically and defy even qualitative insight by present methods. Numerical work seemed to him the most promising way to obtain a feeling for the behaviour of such systems. This impelled him to study new possibilities of computation on electronic machines ...
Von Neumann was one of the pioneers of computer science making significant contributions to the development of logical design. Shannon writes in [29]:-
Von Neumann spent a considerable part of the last few years of his life working in [automata theory]. It represented for him a synthesis of his early interest in logic and proof theory and his later work, during World War II and after, on large scale electronic computers. Involving a mixture of pure and applied mathematics as well as other sciences, automata theory was an ideal field for von Neumann's wide-ranging intellect. He brought to it many new insights and opened up at least two new directions of research.
He advanced the theory of cellular automata, advocated the adoption of the bit as a measurement of computer memory, and solved problems in obtaining reliable answers from unreliable computer components.
During and after World War II, von Neumann served as a consultant to the armed forces. His valuable contributions included a proposal of the implosion method for bringing nuclear fuel to explosion and his participation in the development of the hydrogen bomb. From 1940 he was a member of the Scientific Advisory Committee at the Ballistic Research Laboratories at the Aberdeen Proving Ground in Maryland. He was a member of the Navy Bureau of Ordnance from 1941 to 1955, and a consultant to the Los Alamos Scientific Laboratory from 1943 to 1955. From 1950 to 1955 he was a member of the Armed Forces Special Weapons Project in Washington, D.C. In 1955 President Eisenhower appointed him to the Atomic Energy Commission, and in 1956 he received its Enrico Fermi Award, knowing that he was incurably ill with cancer.
Eugene Wigner wrote of von Neumann's death [18]:-
When von Neumann realised he was incurably ill, his logic forced him to realise that he would cease to exist, and hence cease to have thoughts ... It was heartbreaking to watch the frustration of his mind, when all hope was gone, in its struggle with the fate which appeared to him unavoidable but unacceptable.
In [5] von Neumann's death is described in these terms:-
... his mind, the amulet on which he had always been able to rely, was becoming less dependable. Then came complete psychological breakdown; panic, screams of uncontrollable terror every night. His friend Edward Teller said, "I think that von Neumann suffered more when his mind would no longer function, than I have ever seen any human being suffer."
Von Neumann's sense of invulnerability, or simply the desire to live, was struggling with unalterable facts. He seemed to have a great fear of death until the last... No achievements and no amount of influence could save him now, as they always had in the past. Johnny von Neumann, who knew how to live so fully, did not know how to die.
It would be almost impossible to give even an idea of the range of honours which were given to von Neumann. He was Colloquium Lecturer of the American Mathematical Society in 1937 and received the its Bôcher Prize as mentioned above. He held the Gibbs Lectureship of the American Mathematical Society in 1947 and was President of the Society in 1951-53.
He was elected to many academies including the Academia Nacional de Ciencias Exactas (Lima, Peru), Academia Nazionale dei Lincei (Rome, Italy), American Academy of Arts and Sciences (USA), American Philosophical Society (USA), Instituto Lombardo di Scienze e Lettere (Milan, Italy), National Academy of Sciences (USA) and Royal Netherlands Academy of Sciences and Letters (Amsterdam, The Netherlands).
Von Neumann received two Presidential Awards, the Medal for Merit in 1947 and the Medal for Freedom in 1956. Also in 1956 he received the Albert Einstein Commemorative Award and the Enrico Fermi Award mentioned above.
Peierls writes [3]:-
He was the antithesis of the "long-haired" mathematics don. Always well groomed, he had as lively views on international politics and practical affairs as on mathematical problems.
Article by: J J O'Connor and E F Robertson
John von Neumann
原著：JJ O'Connor & EF Robertson 翻译：齐茹
John von Neumann出生时叫Janos von Neumann。小时侯他叫Jancsi,这是Janos的昵称，然后他去了美国改叫Johnny。他的父亲Max Neumann是个大银行家。Von Neumann在一个大家庭中成长，他的家位于布达佩斯。童年时，他的家庭教师教他德语和法语。尽管是犹太人，Max Neumann并不完全遵守严格的犹太教义，他的家似乎更像一个犹太教与基督教的混合体。
Max Neumann的儿子是如何得到“von”从而取名为Janos von Neumann的这件事也是很值得一提的。1913年Max Neumann买下了一个头衔，但却并不想改自己的名字。不过，他的儿子就用了德文的von，改姓氏为von Neumann,这里的“von”代表了他的头衔。
当von Neumann还是一个小孩的时候，他就表现出了惊人的记忆力。在Poundstone中有写道:von Neumann六岁时就能与他的父亲用古希腊语讲笑话。有时,Neumann一家招待客人，就让Johnny在客人面前表演背电话簿。一位客人随意地从簿中选一页上的一栏，小Johnny看上几遍然后就把簿还给客人。他可以回答客人提出的任何问题（例如谁谁的电话是多少？）或者就直接按顺序背出名字、地址、电话。
1911年von Neumann进入了Lutheran Gymnasium。这所学校有很强的学术传统。这点在von Neumann眼里和学校看来都似乎比宗教更重要。他的数学老师很快就发现了他的天分并给他减免了学费。学校里还有一位出色的数学家，比von Neumann高一年级，叫Eugene Wigner。
第一次世界大战几乎没有影响到von Neumann的学习。但是一战结束后，1919年匈牙利由共产党领导人Bela Kun掌管了5个月。Neumann一家作为富人逃往了奥地利。但是，一个月之后，他们又不得不回来面对布达佩斯所发生的一切。因为Bela Kun的政府中犹太人占了大部分，所以当他倒台后犹太人成为被攻击的对象。在当时那种情况下是毫无逻辑可言的。尽管Neumann一家是反对Kun政府的，可这一点并不能使他们免遭迫害。
1921年von Neumann完成了他在Lutheran Gymnasium的学业。1922年他的第一篇数学论文就发表了。他的合写人是Fekete，他是布达佩斯大学的助教，也是von Neumann的导师。不过，Max Neumann并不想让他的儿子学习一门不赚钱的学科。Max Neumann让Theodore von Karman去劝说von Neumann从商。也许von Karman并不适合去完成这样一个艰巨的任务。不过最后大家都同意了一个折衷的方案，就是让von Neumann在大学时修读化学。
从很多方面讲匈牙利对于犹太人来说不是个闲适的国家。对于想进入布达佩斯大学学习的犹太学生有严格的数量限制。当然，尽管名额有限，von Neumann的成绩也足以让他轻松地在1921年进入数学系，但他从不去听课，而是进入柏林大学学习化学。
Von Neumann在柏林大学学习化学，直到1923年去了苏黎世。尽管他没去听过一节课，von Neumann仍就在布达佩斯大学的数学考试中获得了优异的成绩。1926年他又获得了苏黎世的Technische Hochschule学院的化学工程的毕业证书。尽管在苏黎世学习化学，他仍对数学充满了兴趣，并且和当时也在苏黎世的Weyl和Polya俩人交流学术。甚至有一次，当Weyl不在苏黎世的时候，他还替Weyl代过课。Polya说过，Johnny是唯一让我感到有压力的学生。每当我在课堂上提出一个未解的问题，一下课他就过来找我，手里还拿着他在小纸片上了了数笔写出的完整的解题方法。
同在1926年，von Neumann还以一篇关于集合论的毕业论文获得了布达佩斯大学的数学博士学位。当他20岁时，他就发表了序数的定义，这个定义今天仍在使用。
1926至1929年von Neumann在柏林讲学，1929至1930年他又去了汉堡讲学。那时他还拥有一份洛克菲洛研究员薪金，这笔钱使得它可以在Guttingen大学继续他的数学博士后的学习。1926至1927年在Guttingen大学时，他就在Hilbert的门下学习。那时，von Neumann已经很有声望了。
在他25岁时，von Neumann的名声已经享誉全球的数学界。在学术大会上，它通常被看作是一位年轻的天才。
1929年Veblen邀请von Neumann到普林斯顿大学作关于量子论的演讲。von Neumann回复Veblen说，他办完一些个人事情就会去普林斯顿。von Neumann回到了布达佩斯，与他的未婚妻Marietta Kovesi结了婚，然后就出发去了美国。1930年von Neumann成为了普林斯顿的客座教授，1931年就被任命为教授。
1930到1933年，von Neumann一直在普林斯顿讲课。但这不是重点。我们要说的是，他那不定的思维方式让那些天份稍逊的人难以跟上。而且学生们对他总是只在一大块黑板的一小部分上写一大串方程式，然后不等学生们抄下来就擦掉的做法意见很大。 1933年，在刚成立的普林斯顿的高等数学研究所，他成为最初的六位数学教授之一。他一直拥有这个位置，直到去世。
在美国的头几年里，每到暑假von Neumann都回欧洲。直到1933年他在国内还任有一些学术上的职务，不过当纳粹上台后，他就把这些都辞掉了。与很多其他人不同，von Neumann到美国不是为了政治避难，而只是考虑到在美国的职位比在德国的更有学术发展上的前途。
同在1933年，von Neumann成为数学学会年刊的编辑。两年后，他又成为Compositio Mathematica的编辑。在这两个位置上他一直干到去世。
Von Neumann和妻子Marietta在1936年有了一个女儿叫Marina，但他们在1937年就离婚了。次年，他与同样来自布达佩斯的Klara Dan结婚了。他是在一次欧洲之行中认识Klara Dan的。结婚后，他们乘船来到美国并在普林斯顿安了家。在普林斯顿，von Neumann过上了一种对于顶尖数学家来说并不太常有的生活。他很喜欢各种聚会。
聚会和夜生活对von Neumann来说有一种特别的吸引力。还是在德国讲课时，他就是Cabaret时代的柏林夜生活圈子的常客。
与Klara结婚后，他的聚会又重新开始了。他家经常举办各种聚会，时间很长，也很有名。
Ulam在概括von Neumann的工作生活中写道：他青年时期的工作不单单只是关于数学逻辑和集合论的公理体系，而同时还是关于集合论自身实质内容的研究。在这过程中，他得到了一些有关测度论和真实变量的有趣结果。同样是在这一时期，他开始了自己关于量子论的经典研究，量子论的计量理论的数学基础和新的统计力学。
他在所写《Mathematische Grunlagen der Quantenmechanik》一书中建立了新的量子论的完整框架，Van Have写到：在1925年量子力学被发现的最初几年里，这一问题有幸引起了一个数学天才——von Neumann的兴趣。正因为如此，这一理论的数学框架得到了改进，理论的全新阐释规则的形式也由他一个人在两年之内分析研究了。Hilbert空间的有界线性算子的自伴代数，发展成为不太完善的拓扑学，这由von Neumann在1929年通过Mathematische Annalen(一本学术杂志）介绍给世人。
Kadison 解释道：正是由于von Neumann对遍历论，群表示和量子力学产生兴趣，他认识到算子代数理论将是数学发展的又一个重要阶段。
于是，算子代数被von Neumann称作“算子环”，之后又被人们命名为W-代数。J Dixmier在1957年写的专题著作《Hilbert空间的算子代数》中称这门学科为“冯.诺伊曼代数”，因为19世纪30年代至40年代里，von Neumann于他的合著者F J Murray合作，写出了一系列文章，为“冯.诺伊曼代数”建立了坚实的理论基础。
Ulam也曾写过von Neumann如何对博弈论产生兴趣的：von Neumann清楚地认识到由其他数学家取得的研究结果和这些结果的内在发展可能性。在他开始的工作中，一篇由Borel写出的关于极小极大性的文章给了他提示，使他将已有的想法发展成一个原创的观点，即“博弈论”。
在博弈论中，von Neumann证明了极小极大定理。他逐步扩大在这一领域内的研究，并和另一个合作者Oskar Morgenstern写出了经典的论文《博弈论与经济行为》(1944)。同时，koopman提出的用“函数空间算子”处理经典力学的可能性的想法激发了von Neumann，使他给出了第一个关于遍历定理的严格数学证明。并且，Haar的关于凭借数群方式计量的方法，又激发了他的灵感，使他出色地部分解决了“Hilbert第五猜想”，并证明了在紧群中引入分析参数的可能性。
1938年，美国数学委员会向von Neumann颁奖，以表彰他的杰出贡献，尤其是在周期函数和周期群方面的优异成绩。美国数学协会的公报分两次在1934年和1935年刊登了von Neumann研究成果。于此同时，他开始转向了应用数学领域。 在30年代中期，Johnny痴迷于有关液动体紊流的问题。正是在那时他发现了隐含于非线性偏微分方程式内的秘密。从二战开始时，他的工作就是集中研究流体动力学方程和振荡理论。由这些非线性方程所描述的现象用现有的方式分析起来会造成困惑，甚至还违反了原先的认识。在他看来关于数字的研究是了解这些体系的有效方法。这推动了他在电子机械上使用计算机的新的可能性方面的研究。
Von Neumann是计算机科学的先驱之一。他为逻辑设计做出了卓越的贡献。Shannon写道：von Neumann用他生命最后几年的大部分时间研究自动控制论。这项理论的研究综合了他早期对于逻辑和论证理论的兴趣还有后来二战和二战后对于大规模电子计算机的研究。既包含了纯属学和应用数学，又涉及了其他学科，自动控制论正是一个完美的领域，以使von Neumann的多方才能得以充分发挥。他提出了很多新的见解并且为该研究开创了至少两个新方向。
他发展了细胞自动控制论，还提出采用比特（bit）作为计算机记忆的度量单位，并且解决了如何从不稳定的计算机工作中得到可靠结果。
二战期间直到战后，von Neumann一直担任军方的顾问，他的重要贡献包括:提出以内爆方式引爆核燃料的建议，以及参与氢弹的研究。从1940年起，他就是马里兰州Aberdeen Proving Ground 的Ballistic研究实验室的科学顾问委员会的成员。1941至1955年，海军军械署吸收他为成员，在此期间，他还加入了Los Alamos科学实验室，1950到1955年，他参与了华盛顿特区军方特别武器研究计划。由于von Neumann的研究成果与奉献精神，1955年艾森豪威尔总统任命他为原子能委员会委员。1956年，von Neumann荣获Enrico Fermi奖，但那时，他已身患癌症。
Eugene Wigner这样写道：当von Neumann意识到自己患了不治之症而无法继续进行研究工作时，他强烈地感到绝望——这意味着他思想的终结。一个人被命运操纵，又陷入了深深的绝望，确实是一件痛苦的事。 Eugene Wigner又写道：他的思维严谨的头脑，那时已不再可靠了，接着他的精神上彻底崩溃了。他忍受着来自身体的痛苦与精神上的折磨，夜里他时常感到害怕，他的朋友Edward Teller说：“von Neumann遭受的痛苦是常人难以想象的”。任何权力，荣誉和成就都帮不了他，他曾经很坚强，但对死亡的恐惧彻底击垮了他。
Von Neumann一生大事记
1937年 美国数学委员会颁发B奖
1947年 加入美国数学委员会Gibbs所
1951年-1953年 担任Gibbs所主席
1947、1956年 两次获得总统奖（the Medal for Merit、the Medal for Freedom)
1956年 获爱因斯坦纪念奖， 同年获Enrico Fermi奖
von Neumann曾工作过的学术团体
Academia Nacional de Ciencias Exactas（秘鲁,利马）
Academia Nazionale dei Lincei （意大利,罗马）
American Academy of Arts and Sciences（美国）
American Philosophical Society（美国）
Instituto Lombardo di Scienze e Lettere（意大利，米兰）
National Academy of Sciences （美国）
Royal Netherlands Academy of Sciences and Letters（荷兰，阿姆斯特丹）
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