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John von Neumann
Born: 28 Dec 1903 in Budapest, Hungary
Died: 8 Feb 1957 in Washington D.C., USA
Article by: J J O'Connor and E F Robertson
October 2003
Edited by XiaJingbo, mailto: xjb@mail.hzau.edu.cn
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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.
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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.
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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.
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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
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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),
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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.
References for John von Neumann
1. J Dieudonne, Biography in Dictionary of Scientific Biography (New York 1970-1990).
2. Biography in Encyclopaedia Britannica. [Available on the Web]
3. Obituary in The Times [available on the Web]
Books:
4. W Aspray, John von Neumann and the origins of modern computing (Cambridge, M.,
1990).
5. S J Heims, John von Neumann and Norbert Wiener: From mathematics to the
technologies of life and death (Cambridge, MA, 1980).
6. T Legendi and T Szentivanyi (eds.), Leben und Werk von John von Neumann (Mannheim,
1983).
7. N Macrae, John von Neumann (New York, 1992).
8. W Poundstone, Prisoner's dilemma (Oxford, 1993).
9. N A Vonneuman, John von Neumann: as seen by his brother (Meadowbrook, PA, 1987).
Articles:
10. A Adám, John von Neumann, Life and work of John von Neumann (Mannheim, 1983),
11-43.
11. H Araki, Some of the legacy of John von Neumann in physics: theory of measurement,
quantum logic, and von Neumann algebras in physics, The legacy of John von Neumann
(Providence, R.I., 1990), 119-136.
12. W Aspray, The mathematical reception of the modern computer: John von Neumann and
the Institute for Advanced Study computer, Studies in the history of mathematics
(Washington, DC, 1987), 166-194.
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13. W Aspray, John von Neumann's contributions to computing and computer science, Ann.
Hist. Comput. 11 (3) (1989), 189-195.
14. W Aspray, The transformation of numerical analysis by the computer: an example from
the work of John von Neumann, The history of modern mathematics II (Boston, MA,
1989).
15. W Aspray, The origins of John von Neumann's theory of automata, The legacy of John
von Neumann (Providence, R.I., 1990), 289-309.
16. H Baumgärtel, John von Neumann, aus Leben und Werk, Mitt. Math. Ges. DDR 3-4
(1982), 87-98.
17. G Birkhoff, Von Neumann and lattice theory, Bull. Amer. Math. Soc. 64 (1958), 50-56.
18. P R Halmos, The legend of John von Neumann, Amer. Math. Monthly 80 (1973), 382-394.
19. P R Halmos, Von Neumann on measure and ergodic theory, Bull. Amer. Math. Soc. 64
(1958), 86-94.
20. I Halperin, The extraordinary inspiration of John von Neumann, The legacy of John von
Neumann (Providence, R.I., 1990), 15-17.
21. T A Heppenheimer, How Von Neumann showed the way, American heritage of invention
and technology 6 (2) (1990), 8-16.
22. R V Kadison, Theory of operators, Part I. Operator algebras, Bull. Amer. Math. Soc. 64
(1958), 61-85.
23. H W Kuhn and A W Tucker, John von Neumann's work in the theory of games and
mathematical economics, Bull. Amer. Math. Soc. 64 (1958), 100-122.
24. P D Lax, Remembering John von Neumann, John von Neumann: a personal view, The
legacy of John von Neumann (Providence, R.I., 1990), 5-7.
25. F J Murray, Theory of operators, Part I. Single operators, Bull. Amer. Math. Soc. 64
(1958), 57-60.
26. L Rédei, John von Neumann's work in algebra and number theory (Hungarian), Mat.
Lapok 10 (1959), 226-230.
27. U Rellstab, New insights into the collaboration between John von Neumann and Oskar
Morgenstern on the Theory of games and economic behavior, Toward a history of game
theory (Durham, NC, 1992), 77-93.
28. G Révész, John von Neumann und der Rechner, Life and work of John von Neumann
(Mannheim, 1983), 99-113.
29. C E Shannon, Von Neumann's contributions to automata theory, Bull. Amer. Math. Soc. 64
(1958), 123-129.
30. F Smithies, John von Neumann, J. London Math. Soc. 34 (1959), 373-384.
31. N Stern, John von Neumann's influence on electronic digital computing, 1944-1946, Ann.
Hist. Comput. 2 (4) (1980), 349-362.
32. J Szelezsán, John von Neumann, 'der Rechentechniker' (sein Werk auf dem Gebiet der
numerischen Methoden), Life and work of John von Neumann (Mannheim, 1983),
115-151.
33. J Todd, John von Neumann and the national accounting machine, SIAM Rev. 16 (1974),
526-530.
34. C B Tompkins, John von Neumann, 1903-1957, Math. Tables Aids Comput. 11 (1957),
127-128.
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35. S Ulam, John von Neumann, 1903-1957, Bull. Amer. Math. Soc. 64 (1958), 1-49.
36. L van Hove, Von Neumann's contributions to quantum theory, Bull. Amer. Math. Soc. 64
(1958), 95-99.
37. N Vonneuman, The philosophical legacy of John von Neumann, in the light of its
inception and evolution in his formative years, The legacy of John von Neumann
(Providence, R.I., 1990), 19-24.
38. M v N Whitman, John von Neumann: a personal view, The legacy of John von Neumann
(Providence, R.I., 1990), 1-4.
39. O P Yee, On the life and work of John von Neumann, Menemui Mat. 4 (3) (1982),
114-127.
JOC/EFR October 2003
