John von Neumann biography briefly. Game theory by J. von Neumann

John von Neumann is a renowned scientist and polymath who specialized in mathematics, physics, economics, statistics and computer science. The author of 150 papers became a pioneer in the application of operator theory to quantum mechanics and a central figure in the development of the concepts of cellular automata, universal constructor and digital computer. As a participant in the Manhattan Project, von Neumann created mathematical models, used in nuclear weapons, and later became a consultant to the government's weapons system assessment team.

Childhood and youth

A man known to the scientific world under the name John von Neumann was born on December 28, 1903 in the capital of Hungary, Budapest, into a prosperous Jewish family. Father Max Neumann, a doctor of jurisprudence, worked in a bank, and mother Margaret Kann ran a household and raised three children. The future scientist showed incredible abilities from childhood: at the age of 6, he could freely divide and multiply long numbers in his head and spoke ancient Greek.

Having received his first lessons from governesses, the boy became acquainted with differential and integral calculus and studied several volumes of history written by Wilhelm Oncken. When von Neumann was 10 years old, his parents sent him to the best school Budapest, which raised more than one generation of great minds, and hired private tutors to develop and strengthen their son’s knowledge.

By the age of 19, the young man published a publication in which he gave modern definition ordinal numbers, which replaced Georg Cantor's formulation, and won the national Eötvös prize. His father admired the mind of young von Neumann, but did not see a productive use for his knowledge. Having made a compromise, the young man agreed to become a chemical engineer and studied for 2 years necessary items at the University of Berlin. In 1923 he entered the ETH Zurich, at the same time becoming a candidate of mathematical sciences at ELTE.

Having graduated from both educational institutions, the young man continued to improve and passed entrance exams at the Georg-August University of Göttingen, received a Rockefeller Foundation scholarship and joined the chair of David Hilbert, famous for the axiomatics of Euclidean geometry and the creation of functional analysis.

In 1926, von Neumann received his doctorate in mathematics and became a lecturer at the University of Berlin. Judging by the photo, the novice teacher organically fit into the college environment and taught classes, constantly being at the blackboard covered with formulas and calculations. By the end of 1929, the young privatdozent published 32 scientific articles and moved to the staff of a higher educational institution in the city of Princeton, USA, where he worked until the end of his life.

Scientific activity

Von Neumann's first major work was a dissertation describing a new approach to the formalization of set theory. The scientist formulated 2 ways to get rid of Russell’s paradox by introducing the terms “axiom of foundation” and “class”.

The axiom of foundation implied the construction of sets from the bottom up and the organization of a sequence, where each set preceded or followed another. To demonstrate the absence of contradictions, John used the concept of the internal model method, which became a fundamental tool in work on set theory.

To describe the 2nd method of eliminating the mathematical paradox, von Neumann identified a set with the concept of a class and demonstrated the probability of constructing a group of sets that do not belong to themselves.

In papers published in the late 1920s, von Neumann distinguished himself for his contributions to ergodic theory and then moved on to questions of quantum mechanics and its mathematical foundations. He wrote a series scientific essays in this area and proved that quantum systems are nothing more than points in a Hilbert space over which linear operators consisting of ordinary physical quantities are located.

Von Neumann's proof set in motion the research that led to the claim that quantum physics either needed a concept of reality or had to include nonlocality in clear violation of special relativity.

John von Neumann with colleagues Richard Feynman and Stanislaw Ulam

Reflecting on the mathematics of quantum mechanics, John von Neumann analyzed the so-called measurement theory and concluded that the physical universe could be governed by a universal wave function.

This prompted the researcher to discover the fundamental principles of functional analysis, create the theory of bounded operators, and introduce the concept of the “direct integral,” which earned John the Bocher Memorial Prize in 1938.

One of numerous merits The Hungarian mathematician proved the “minimax theorem,” a necessary element of the emerging game theory. The scientist realized that in zero-sum games there are a couple of strategies that allow each participant to minimize their own maximum losses. The player is obliged to take into account all existing reactions of the enemy and play the optimal strategy, which will guarantee minimization of his maximum loss.

John von Neumann with university graduates

Between 1937 and 1939, von Neumann studied lattice theory, where the object of study was partially ordered sets in which every 2 elements had a greatest lower bound and a smallest upper bound, and in the process proved the following fundamental representation theorem.

In addition, von Neumann invested in the development of economics, publishing works on the intellectual and mathematical level of this discipline. Based on the results, John invented the theory of duality in linear programming and became the author of the first internal point method, based on the Gordan system.

Another merit of John von Neumann is considered to be his work in the field of computer science, dedicated to the creation and description of computer architecture, which was based on binary coding, homogeneity and addressability of memory, conditional jump and sequential control programming. Using first-generation computers, John, in collaboration with others, explored the problems of the philosophy of artificial intelligence, but did not advance very far in this matter.

In hydrodynamics, the main invention of von Neumann is the algorithm for determining artificial viscosity, which helped in understanding the phenomenon shock waves. The scientist discovered the classical flow solution and used computer simulations for ballistic research in this area.

Beginning in the late 1930s, John became the leading expert on the mathematics of shaped charges, advising the United States military. Being one of the creators atomic bomb, the scientist developed the concept and design of the explosive lenses used to compress the plutonium core of the weapon, which was soon dropped on Hiroshima and Nagasaki.

As a member of the Manhattan Project, von Neumann served on the committee that selected atomic bomb targets and the calculations involved in predicting the size of the explosions and the number of people killed. The mathematician, who did not regard this page of his biography as shameful, became an eyewitness to the first explosive tests at a test site near the Alamogordo army airfield, codenamed Trinity.

In the mid-1940s, John supported the idea of ​​a hydrogen bomb design and, together with theorist Klaus Fuchs, filed a secret patent to improve the methods and means of using nuclear energy.

In the postwar era, von Neumann was made a consultant to a weapons system evaluation team working for the government, military, and CIA. In 1955, the scientist became Commissioner of the AEC and participated in the production of compact hydrogen bombs suitable for transportation on intercontinental ballistic missiles.

Personal life

In 1930, John converted to Catholicism and married a girl named Marietta Kövesi, who was studying economics at the University of Budapest. In 1935, the couple had a daughter, Marina, who became a professor of business administration and public policy in Michigan. During his visits to his homeland, von Neumann became interested in Clara Dahn, who soon took a central place in the mathematician’s personal life and in 1938 became his second wife.

The new family moved to Princeton and settled in a luxurious estate located near primary school Community Park, becoming the center of the campus academic community.

The scientist lived in grand style, paying close attention appearance and home environment, loved delicious food and expensive drinks. An interesting fact is that while working at home, von Neumann turned on the TV at full volume and disturbed those around him. A roommate regularly complained about the noisy German music coming from John's office.

In addition, the mathematician acquired a reputation as a bad driver, allowing himself to read a book while driving a car. This provoked several accidents and endless proceedings with the traffic police.

Death

Von Neumann's health problems began in 1954, when doctors discovered bone cancer. The real causes of the disease are unknown, but biographers suggest that the tumor could have been caused by radiation received during work on nuclear project during the Second World War.

The last years and months of the Hungarian mathematician’s life were spent in torment associated with relapses of the disease. Winter 1957 physical state von Neumann required urgent hospitalization, but the treatment did not help, and on February 8 the scientist died in the ward medical center named after Walter Reed. The cause of death was malignant tumor bone tissue.

(53 years old) Alma mater

• Swiss ETH Zurich ( )
• University of Budapest ( )
• University of Göttingen

Awards and prizes

Encyclopedic YouTube

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Biography

Janos Lajos Neumann was born the eldest of three sons into a wealthy Jewish family in Budapest, which at that time was the second capital of the Austro-Hungarian Empire. His father, Max Neumann(Hungarian Neumann Miksa, 1870-1929), moved to Budapest from the provincial town of Pécs in the late 1880s, received a doctorate in law and worked as a lawyer in a bank; his entire family came from Serenc. Mother, Margaret Kann(Hungarian Kann Margit, 1880-1956), was a housewife and eldest daughter(in his second marriage) successful businessman Jacob Kann - a partner in the Kann-Heller company, specializing in the trade of millstones and other agricultural equipment. Her mother, Catalina Meisels (the scientist's grandmother), came from Munkács.

Janos, or simply Janczy, was extraordinary gifted child. Already at the age of 6, he could divide two eight-digit numbers in his mind and talk with his father in ancient Greek. Janos was always interested in mathematics, the nature of numbers and the logic of the world around him. At the age of eight, he was already well versed in mathematical analysis. In 1911, he entered the Lutheran gymnasium. In 1913, his father received noble title, and Janos together with the Austrian and Hungarian symbols of nobility - the prefix background (von) to an Austrian surname and title Margittai (Margittai) in Hungarian naming - began to be called Janos von Neumann or Neumann Margittai Janos Lajos. While teaching in Berlin and Hamburg he was called Johann von Neumann. Later, after migrating to the USA in the 1930s, his name on English manner changed to John. It is curious that after moving to the USA, his brothers received completely different surnames: Vonneumann And Newman. The first, as you can see, is a “fusion” of the surname and the prefix “von”, while the second is a literal translation of the surname from German into English.

In October 1954, von Neumann was appointed to the Atomic Energy Commission, which had as its main concern the accumulation and development of nuclear weapons. It was confirmed by the United States Senate on March 15, 1955. In May, he and his wife moved to the Washington, D.C., suburb of Georgetown. During recent years von Neumann was the chief adviser on atomic energy, atomic weapons and intercontinental ballistic weapons. Perhaps as a result of his origins or early experiences in Hungary, von Neumann was strongly right-wing political views. An article in Life magazine published on February 25, 1957, shortly after his death, portrayed him as an advocate of preventive war with the Soviet Union.

In the summer of 1954, von Neumann bruised his left shoulder in a fall. The pain did not go away, and surgeons diagnosed: bone cancer. It has been suggested that von Neumann's cancer may have been caused by radiation exposure from atomic bomb testing in the Pacific, or perhaps from subsequent work at Los Alamos, New Mexico (his colleague, nuclear research pioneer Enrico Fermi, died of stomach cancer at 54 years old). The disease progressed, and attending AEC (Atomic Energy Commission) meetings three times a week required enormous effort. A few months after the diagnosis, von Neumann died in great agony. As he lay dying in Walter Reed Hospital, he asked to see a Catholic priest. A number of the scientist's acquaintances believe that since he was an agnostic for most of his adult life, this desire did not reflect his real views, but was caused by suffering from illness and fear of death.

Foundations of Mathematics

At the end of the nineteenth century, the axiomatization of mathematics followed the example of Began Euclid reached new levels of precision and breadth. This was especially noticeable in arithmetic (thanks to the axiomatics of Richard Dedekind and Charles Sanders Peirce), as well as in geometry (thanks to David Hilbert). By the beginning of the twentieth century, several attempts had been made to formalize set theory, but in 1901 Bertrand Russell showed the inconsistency of the naive approach used earlier (Russell's paradox). This paradox again left the question of formalizing set theory in the air. The problem was solved twenty years later by Ernst Zermelo and Abraham Fraenkel. The Zermelo-Frenkel axiomatics made it possible to construct sets commonly used in mathematics, but they could not explicitly exclude Russell's paradox from consideration.

In his doctoral dissertation in 1925, von Neumann demonstrated two ways to eliminate sets from Russell's paradox: the axiom of ground and the concept class. The axiom of foundation required that each set could be constructed from bottom to top in order of increasing steps according to the principle of Zermelo and Frenkel in such a way that if one set belongs to another, then it is necessary that the first should come before the second, thereby eliminating the possibility of the set belonging to itself. In order to show that the new axiom does not contradict other axioms, von Neumann proposed a method of demonstration (later called the internal model method), which became an important tool in set theory.

The second approach to the problem was to take as a basis the concept of a class and define a set as a class that belongs to some other class, and at the same time introduce the concept of its own class (a class that does not belong to other classes). In the Zermelo-Fraenkel assumptions, the axioms prevent the construction of the set of all sets that do not belong to themselves. Under von Neumann's assumptions, the class of all sets that do not belong to themselves can be constructed, but it is a class of its own, that is, it is not a set.

With the help of this von Neumann construction, the Zermelo–Fraenkel axiomatic system was able to eliminate Russell's paradox as impossible. The next problem was whether these structures could be identified, or whether this object could not be improved. A strictly negative answer was received in September 1930 at the mathematical congress in Köningsberg, at which Kurt Gödel presented his incompleteness theorem.

Mathematical foundations of quantum mechanics

Von Neumann was one of the creators of the mathematically rigorous apparatus of quantum mechanics. He outlined his approach to the axiomatization of quantum mechanics in his work “ Mathematical Basics quantum mechanics" (German) Mathematische Grundlagen der Quantenmechanik) in 1932.

After completing the axiomatization of set theory, von Neumann began the axiomatization of quantum mechanics. He immediately realized that the states of quantum systems can be considered as points in Hilbert space, just as in classical mechanics states are associated with points in a 6N-dimensional phase space. In this case, quantities common in physics (such as position and momenta) can be represented as linear operators over Hilbert space. Thus, the study of quantum mechanics was reduced to the study of algebras of linear Hermitian operators over Hilbert space.

It should be noted that in this approach the principle of uncertainty, according to which precise definition location and momentum of a particle are simultaneously impossible, is expressed in the noncommutativity of the operators corresponding to these quantities. This new mathematical formulation included the formulations of Heisenberg and Schrödinger as special cases.

Operator theory

Von Neumann's main works on the theory of operator rings were those related to von Neumann algebras. A von Neumann algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator.

Von Neumann's bicommutant theorem proves that the analytic definition of a von Neumann algebra is equivalent to the algebraic definition as a *-algebra of bounded operators on a Hilbert space coinciding with its second commutant.

In 1949, John von Neumann introduced the concept of a direct integral. One of von Neumann's merits is considered to be the reduction of the classification of von Neumann algebras on separable Hilbert spaces to the classification of factors.

Cellular automata and living cell

The concept of creating cellular automata was a product of anti-vitalistic ideology (indoctrination), the possibility of creating life from dead matter. The vitalist argumentation in the 19th century did not take into account that in dead matter it is possible to store information - a program that can change the world (for example, Jacquard's machine - see Hans Driesch). It cannot be said that the idea of ​​cellular automata turned the world upside down, but it has found application in almost all areas of modern science.

Neumann clearly saw the limits of his intellectual capabilities and felt that he could not perceive some higher mathematical and philosophical ideas.

Von Neumann was a brilliant, inventive, efficient mathematician with a stunning range of scientific interests that extended beyond mathematics. He knew about his technical talent. His virtuosity in understanding the most complex reasoning and intuition were developed to the highest degree; and yet he was far from being completely self-confident. Perhaps he felt that he did not have the ability to intuitively predict new truths at the most higher levels or the gift of a pseudo-rational understanding of proofs and formulations of new theorems. It's hard for me to understand. Perhaps this was explained by the fact that a couple of times he was ahead of or even surpassed by someone else. For example, he was disappointed that he was not the first to solve Gödel's completeness theorems. He was more than capable of this, and alone with himself he admitted the possibility that Hilbert had chosen the wrong decision. Another example is J. D. Birkhoff's proof of the ergodic theorem. His proof was more convincing, more interesting, and more independent than Johnny's.

- [Ulam, 70]

This issue of personal attitude towards mathematics was very close to Ulam, see, for example:

I remember how, at the age of four, I frolicked on an oriental carpet, looking at the marvelous script of its pattern. I remember the tall figure of my father standing next to me and his smile. I remember thinking: “He’s smiling because he thinks I’m still just a child, but I know how amazing these patterns are!” I do not claim that these exact words came to my mind then, but I am sure that this thought arose in me at that moment, and not later. I definitely felt like, “I know something that my dad doesn’t know. Perhaps I know more than him."

- [Ulam, 13]

Compare with Grothendieck's Harvests and Sowings. implosion.

Calculations for this problem required large calculations, which were initially carried out in Los Alamos hand calculators, then on IBM 601 mechanical tabulators, which used punched cards. Von Neumann, traveling freely around the country, collected information from different sources about current projects to create electronic-mechanical (Bell Telephone Relay-Computer, Howard Aiken's Mark I computer at Harvard University was used by the Manhattan Project for calculations in the spring of 1944) and all-electronic computers (ENIAC was used in December 1945 for calculations on the problem of thermal nuclear bomb).

Von Neumann helped develop the ENIAC and EDVAC computers, and contributed to the development of computer science in his work “The First Draft of the EDVAC Report,” where he introduced the idea of ​​a computer with a program stored in memory to the scientific world. This architecture still bears the name, and already in,

Bibliography

• Neumann J. Mathematical foundations of quantum mechanics - M.: Nauka, 1964.
• Neumann J.,

John von Neumann(born Janos Lajos Neumann) was born on December 3, 1903 in Budapest.

He was a gifted child and already at the age of 8 mastered the basics of higher mathematics. In 1911, Neumann entered the Lutheran Gymnasium, where he further developed his mathematical abilities. Soon his father received a noble title, and together with the prefixes “von” to the surname, the boy began to be called Janos von Neumann. Later, already in the USA, his name changed to John in the English manner.

Neumann's first published work, “On the location of the zeros of certain minimal polynomials,” was published in 1921. He soon graduated from high school and entered the Technical High School in Zurich, where he studied chemistry, and at the same time at the Faculty of Mathematics of the University of Budapest, from which he graduated in 1926, receiving a PhD and a diploma in chemical engineering in Zurich. Neumann continued his mathematical research at the universities of Göttingen, Berlin and Hamburg; they were related to quantum physics and operator theory. During the same period, the young scientist carried out fundamental work on set theory, game theory and the mathematical foundation of quantum mechanics and wrote a number of articles in these areas. In 1931, Neumann was invited to Princeton University in the USA, where he first worked as a lecturer and then as a professor of mathematical physics. Two years later he moved to the newly created Institute for Advanced Study at Princeton and remained a professor at this institute for the rest of his life. Neumann is responsible for the rigorous mathematical formulation of the principles of quantum mechanics and the proof of the ergodic hypothesis in mathematical statistics. His work “Mathematical Foundations of Quantum Mechanics” (1932) is considered a classic teaching aid. In the 1930s, he published a number of papers on operator rings, laying the foundation for the so-called Neumann algebra, which later became one of the main tools for quantum research. In 1937, von Neumann became a US citizen, and in subsequent years his activities were closely associated with military organizations. During World War II, he was involved in various defense projects, including being instrumental in the creation of the first nuclear bomb and participating in the development of the hydrogen bomb. Since 1954 he has been a member of the Atomic Energy Commission. Neumann made significant contributions to the development of many areas of mathematics; his works also influenced economic science. The scientist became one of the creators of game theory, which formed the basis of a mathematical approach to the phenomena of competitive economics, the theory of computers and the axiomatic theory of automata. He made a great contribution to the creation of the first computers and the development of methods for their use. In 1952, the scientist developed the first computer using programs recorded on flexible media. Basic scientific works Neumann's works are devoted to functional analysis and its applications to problems of classical and quantum mechanics. More than 150 works of the scientist are devoted to problems of physics, mathematics and its practical applications, game theory and computer theory, the theory of topological groups and meteorology. John von Neumann was a member of the US National Academy of Sciences, the American Philosophical Society, and an honorary member of various foreign academies, scientific institutions and societies. His outstanding achievements marked by numerous prestigious awards. The scientist was married twice. In his first marriage, he had a daughter, Marina, who would become a famous economist.

"The Mathematician" (probably originally a lecture or report) gives the reader a rare opportunity to become acquainted with the concept of mathematics developed by the man whose work largely defined it. modern look. Responding to a questionnaire from the US National Academy in 1954, von Neumann (by the way, he had been a member of this academy since 1937) named his three highest scientific achievements: mathematical foundation of quantum mechanics, theory of unbounded operators and ergodic theory. This assessment is not only a manifestation of von Neumann's personal tastes, but also the generosity of a genius: much of what von Neumann did not include in the list of his best achievements entered the golden fund of mathematical science and rightfully immortalized the name of its creator. Suffice it to say that among the “rejected” works were a partial solution (for locally compact groups) of Hilbert’s famous fifth problem, and fundamental works on game theory and automata theory.

Von Neumann's article is also interesting because its author belongs to a rare type of universal mathematician these days, who despises artificial partitions between the individual areas of his ancient but eternally young science, perceives it as a single living organism and freely moves from one section to another. another, at first glance very far from the previous one, but in reality connected with it by indissoluble bonds of internal unity.

Not only historians of science, but also many actively working mathematicians tried to find an explanation for this unique phenomenon. Here is what, for example, the famous mathematician S. Ulam, who personally knew von Neumann and worked with him for many years, says about this: “Von Neumann’s wanderings through numerous branches of mathematical science were not a consequence of the inner restlessness that consumed him. They were driven neither by a desire for novelty nor by a desire to apply a small set of general methods to many different special cases. Mathematics, unlike theoretical physics, is not limited to solving several central problems. The desire for unity, if it is based on a purely formal basis, von Neumann considered doomed to failure. The reason for his insatiable curiosity lay in certain mathematical motives and was largely conditioned by the world physical phenomena, which, as far as one can judge, will not be formalized for a long time...

With its tireless search for new areas of application and a general mathematical instinct that operates equally unerringly in all exact sciences, von Neumann is reminiscent of Euler, Poincaré or, in a more recent era, Hermann Weyl. It should not be overlooked, however, that the diversity and complexity modern problems many times greater than what Euler and Poincaré encountered."

The world of physical phenomena was for von Neumann the compass by which he calibrated his course in the vast ocean of modern mathematics; his subtle intuition allowed him to predict in which direction he should look for unknown lands, and his high scientific potential and masterly mastery of technology allowed him to overcome the difficulties that are encountered in abundance on the path of every discoverer of something new.

But having an excellent understanding of the problems of contemporary physics, von Neumann always remained primarily a mathematician. In their work, mathematicians deal with abstractions of a higher order than theoretical physicists, the subject of their consideration is even greater “distance” from reality, and it might seem that mathematicians, to a greater extent than theoretical physicists, are inclined to consider the reality of creation of your mind. But, turning to the works of von Neumann, we see a different picture:

Having experienced the strong influence of Hilbert's axiomatic school in his youth, von Neumann, as a rule, began his work, no matter what field it belonged to, by compiling a list of axioms. Visual representations of the object were replaced by a schematic description of its most essential properties, and only these properties were used in subsequent reasoning and evidence.

Von Neumann floated freely in a rarefied atmosphere of abstractions, without resorting to visual images, unlike many other mathematicians. Abstraction was his element. Noting this feature of von Neumann’s creative style, S. Ulam wrote: “It is not without interest to note that in many mathematical conversations on topics related to set theory and related areas of mathematics, von Neumann’s formal thinking was clearly felt. Most mathematicians, when discussing such problems, proceed from intuitive ideas based on geometric or almost tangible pictures of abstract sets, transformations, etc. Listening to von Neumann, you vividly felt how consistently he operated with purely formal conclusions. By this I mean that the basis of his intuition, which allowed him to formulate new theorems and find proofs (as, indeed, the basis of his “naive” intuition), belonged to a type that is much less common. If we, following Poincaré, divided mathematicians into two types - those with visual and auditory intuition, then Johnny, most likely, would belong to the second type. However, his “inner hearing” was very abstract. It was more about a certain complementarity between formal sets of symbols and playing with them, on the one hand, and interpretation of their meaning, on the other. The difference between the one and the other is to some extent reminiscent of the mental representation of a real chessboard and the mental representation of the sequence of moves on it, written in chess notation."

Subtle interaction between abstraction and empirical in origin foundations of modern mathematics, inextricable ties connecting the “queen and maid of all sciences” with the inexhaustible supplier of purely mathematical problems - the natural sciences, traditionally deductive presentation mathematical theories, supplemented by inductive, as in all natural science, searches for truth, this is not a complete list of topics touched upon in a small but significant work “Mathematics” by von Neumann.

The specifics of mathematical thinking is an interesting topic in itself. Von Neumann was also interested in it because he was thinking about a wide range of problems associated with the creation of artificial intelligence and self-replicating automata. At the end of the 40s, having accumulated enormous practical experience in the creation of mathematical software, the development of logical circuits and the design of high-speed computers, von Neumann began to develop a general (or, as he himself preferred to call it, logical) theory of automata. It was then (in 1947) that the article “Mathematician” was first published in a collection published by the University of Chicago under the expressive title “The Work of the Mind.”

Alien to any rhetoric, simple and clear speech von Neumann still captivates with the beauty of his thoughts, the power of conviction, and the evidence of his judgments. And this is genuine evidence of the authenticity of “Mathematics”, its adequacy to the essence and spirit of mathematics. We hope that mathematicians, opening the first of the six volumes of von Neumann's Collected Scientific Works, will for a long time begin their acquaintance with the legacy of the outstanding mathematician of our time with concise presentation philosophy of mathematics article “Mathematician”, now published in Russian translation.

Notes

1.	Von Neumann's name was transcribed differently at different periods of his life. In children's and teenage years spent in Budapest, his name was Janos. In Zurich, where von Neumann studied at the chemistry department of the Higher Polytechnic School, in Hamburg and Göttingen von Neumann was called Johann. After moving to the United States in 1932 (from 1933 he was a professor at the Princeton Institute for Advanced Study, from 1940 a consultant to various army and naval institutions, from 1954 a member of the Atomic Energy Commission), von Neumann elected English version named John.
2.	John von Neumann. Bull. Amer. Math. Soc., 1958, v. 64, No. 3 (part 2), p. 8.
3.

Janos Lajos Neumann was born in Budapest, which at that time was a city of the Austro-Hungarian Empire. He was the eldest of three sons in the family of successful Budapest banker Max Neumann (Hungarian: Neumann Miksa) and Margaret Kann (Hungarian: Kann Margit). Janos, or simply "Yancy", was an unusually gifted child. Already at the age of 6, he could divide two eight-digit numbers in his mind and talk with his father in ancient Greek. Janos was always interested in mathematics, the nature of numbers and the logic of the world around him. At the age of eight he was already well versed in mathematical analysis. In 1911 he entered the Lutheran Gymnasium. In 1913, his father received the title of nobility, and Janos, together with the Austrian and Hungarian symbols of nobility - the prefixes von (von) to the Austrian surname and the title Margittai (Margittai) in the Hungarian naming - began to be called Janos von Neumann or Neumann Margittai Janos Lajos. While teaching in Berlin and Hamburg he was called Johann von Neumann. Later, after moving to the United States in the 1930s, his name was changed to John in English. It is curious that von Neumann's brothers received completely different surnames after moving to the USA: Vonneumann and Newman.

Von Neumann received his PhD in mathematics (with elements experimental physics and chemistry) at the University of Budapest at age 23. At the same time, he studied chemical engineering in Zurich, Switzerland (Max von Neumann considered the profession of a mathematician insufficient to ensure a reliable future for his son). From 1926 to 1930, John von Neumann was a privatdozent in Berlin.

In 1930, von Neumann was invited to a teaching position at the American Princeton University. He was one of the first invited to work at the Institute for Advanced Study, founded in 1930, also located in Princeton, where he held a professorship from 1933 until his death.

In 1936-1938, Alan Turing defended his doctoral dissertation at the institute under the direction of Alonzo Church. This happened shortly after the publication of Turing's 1936 paper "On Computable Numbers with an Application to the Entscheidungs ​​problem", which included the concepts of logical design and universal machine. Von Neumann was undoubtedly familiar with Turing's ideas, but it is unknown whether he applied them to the design of the IAS machine ten years later.

In 1937, von Neumann became a full US citizen. In 1938 he was awarded the M. Bocher Prize for his work in the field of analysis.

Von Neumann was married twice. He first married Mariette Kövesi in 1930. When making an offer, he did not find the best way express your feelings rather than with a romantic phrase: “It would be nice for us to be together, judging by how much we both like to drink.” Von Neumann even agreed to convert to Catholicism to please her family. The marriage broke up in 1937, and already in 1938 he married Klara Dan. From his first wife, von Neumann had a daughter, Marina, a future famous economist.

In 1957, von Neumann developed bone cancer, possibly caused by radiation exposure while researching the atomic bomb in Pacific Ocean or perhaps during subsequent work at Los Alamos, New Mexico (his colleague, nuclear research pioneer Enrico Fermi, died of bone cancer in 1954). A few months after the diagnosis, von Neumann died in great agony. The cancer also attacked his brain, leaving him virtually unable to think. As he lay dying in Walter Reed Hospital, he shocked his friends and acquaintances by asking him to speak with Catholic priest.