Informatics in the faces of John von Neumann. Game theory by J. von Neumann

John von Neumann short biography Hungarian-American mathematician who made contributions to functional analysis, quantum logic, quantum physics, set theory, economics, and computer science.

John von Neumann biography briefly

Life of John von Neumann 1903 – 1957

The future scientist was born in the capital of Hungary, Budapest. From a young age, the boy was interested in the nature of mathematical logic and numbers. In addition, Neumann loved history and read 40 volumes world history. At the age of 10, he was sent to the best Lutheran gymnasium in Budapest. And in 1922 he was already published in the journal of the German Mathematical Society.

At the insistence of his father, John von Neumann first mined higher education at the Peter Pazman Catholic University of Budapest, while completing a basic course in chemical engineering at the Technical School of Zurich in Switzerland. The young man graduated from the Catholic University with a doctorate in mathematics at the age of 22, just like the Zurich school.

Having received two scientific degrees, Neumann attended the German University of Göttingen in 1926, where he studied quantum mechanics and set out to improve and streamline its theories. The scientist was looking for common features of matrix and wave mechanics, studied the rules of Hilbert's abstract space.

Neumann's personal life

In the period 1927-1929, when he presented his theory of quantum mechanics, he began to attend colloquia and conferences. He already had 32 well-structured works to his credit. Neumann became a real star in academic circles, as his approaches to innovative theories were fresh and creative. In 1929 he was hired as a lecturer at Princeton University. Then he marries Marietta Keveshi, who in 1935 gave birth to his daughter Marina. But their marriage did not last long - they broke up in 1936. Neumann goes on a trip to Europe. Returning to America, the scientist meets a certain Clara Dan, who later became his wife in 1938.

But his most important contribution to science is that he took part in the creation of the computer, and he was also the first person to create the principles by which the computer works. The basic principles of John von Neumann are still relevant today: all modern electronic computers work on these principles:

• The principle of the binary system for computing commands and data.
• The principle of program control. The program is a set of instructions executed by the processor in a certain sequence.
• The principle of homogeneity of memory. All data is stored and encoded in one memory.
• The principle of memory addressability. Memory consists of numbered cells, and the processor has random access to any of them.
• The principle of sequential program control. The commands stored in memory are executed one by one after the previous command has completed.
• The principle of conditional transition. It was formulated by Charles Babbage and Ada Lovelace. Von Neumann added it to his overall architecture.

Cause of death of John von Neumann

Doctors made a disappointing diagnosis to the famous scientist - cancer. But, despite the fact that John was sitting in a gurney, the mathematician led an active life. The great scientist died on February 8, 1957.

Who is von Neumann? The broad masses of the population are familiar with his name, even those who are not fond of higher mathematics know the scientist.

The thing is that he developed an exhaustive logic of the functioning of a computer. To date, it has been implemented in millions of home and office computers.

Neumann's Greatest Achievements

He was called a man-mathematical machine, a man of impeccable logic. He sincerely rejoiced when he faced a difficult conceptual task that required not only a solution, but also the preliminary creation of this unique toolkit. The scientist himself, with his usual modesty, in recent years, extremely briefly - in three points - announced his contribution to mathematics:

Justification of quantum mechanics;

Creation of the theory of unbounded operators;

Ergodic theory.

He did not even mention his contribution to game theory, to the formation of electronic computers, to the theory of automata. And this is understandable, because he talked about academic mathematics, where his achievements look as impressive peaks of human intelligence as the works of Henri Poincaré, David Hilbert, Hermann Weyl.

Sociable sanguine type

With all this, his friends recalled that, along with inhuman ability to work, von Neumann had an amazing sense of humor, was a brilliant storyteller, and his house in Princeton (after moving to the USA) was reputed to be the most hospitable and cordial. Friends of the soul doted on him and even called him simply by his first name: Johnny.

He was in the highest degree atypical mathematician. The Hungarian was interested in people, he was unusually amused by gossip. However, he was more than tolerant of human weaknesses. The only thing he was uncompromising about was scientific dishonesty.

The scientist seemed to be collecting human weaknesses and quirks to collect statistics on system deviations. He loved history, literature, remembering facts and dates encyclopedically. Von Neumann, in addition to his native language, was fluent in English, German, and French. He also spoke, though not without flaws, in Spanish. Read in Latin and Greek.

What did this genius look like? Fat man of average height in a gray suit with a leisurely, but uneven, but somehow spontaneously accelerating and decelerating gait. Insightful look. A good conversationalist. He could talk for hours on topics of interest to him.

Childhood and youth

Von Neumann's biography begins on December 23, 1903. On that day in Budapest, Janos, the eldest of three sons, was born into the family of the banker Max von Neumann. It is he who will become John in the future across the Atlantic. How much means in a person's life the right upbringing, which develops natural abilities! Even before school, Jan was trained by teachers hired by his father. The boy received his secondary education in an elite Lutheran gymnasium. By the way, E. Wigner, the future Nobel Prize winner, studied with him at the same time.

Then the young man received his higher education at the University of Budapest. Fortunately for him, while still at university, Janos met a teacher of higher mathematics, Laszlo Ratz. It was this teacher with a capital letter who was given to discover in the young man the future mathematical genius. He introduced Janos to the circle of the Hungarian mathematical elite, in which Lipot Fejer played the first violin.

Thanks to the patronage of M. Fekete and I. Kurshak, von Neumann had already earned a reputation as a young talent in scientific circles by the time he received his matriculation certificate. His start was really early. my first scientific work"On the location of zeros of minimal polynomials" Janos wrote at the age of 17.

Romantic and classic rolled into one

Neumann stands out among venerable mathematicians for his versatility. With the possible exception of only number theory, all other branches of mathematics were influenced to one degree or another by the mathematical ideas of the Hungarian. Scientists (according to the classification of W. Oswald) are either romantics (generators of ideas) or classics (they are able to extract consequences from ideas and formulate a complete theory.) He could be attributed to both types. For clarity, we present the main works of von Neumann, while denoting the sections of mathematics to which they relate.

- "On the axiomatics of set theory" (1923).

- "On the theory of Hilbert's proofs" (1927).

2. Game theory:

- "On the theory of strategic games" (1928).

Fundamental work "Economic Behavior and Game Theory" (1944).

3. Quantum mechanics:

- "On the foundations of quantum mechanics" (1927).

Monograph "Mathematical Foundations of Quantum Mechanics" (1932).

4. Ergodic theory:

- "On the algebra of functional operators.." (1929).

A series of papers "On rings of operators" (1936 - 1938).

5. Applied tasks of creating a computer:

- "Numerical inversion of high-order matrices" (1938).

- "The logical and general theory of automata" (1948).

- "Synthesis of reliable systems from unreliable elements" (1952).

Originally, John von Neumann assessed a person's ability to engage in his favorite science. In his opinion, it is given to people to develop mathematical abilities up to 26 years. It is the early start, according to the scientist, that is fundamentally important. Then the adherents of the "queen of sciences" have a period of professional sophistication.

Growing through decades of practice, qualifications, according to Neumann, compensate for the decline in natural abilities. However, even after many years, the scientist himself was distinguished by both talent and amazing performance, which becomes limitless when solving important problems. For example, the mathematical justification of quantum theory took him only two years. And in terms of depth of study, it was equivalent to dozens of years of work by the entire scientific community.

On von Neumann's principles

How did the young Neumann usually begin his research, about whose work venerable professors said that “you recognize a lion by its claws”? He, starting to solve the problem, first formulated a system of axioms.

Let's take a special case. What are the principles of von Neumann that are relevant in his formulation of the mathematical philosophy of computer construction? In their primary rational axiomatics. Isn't it true that these messages are imbued with brilliant scientific intuition!

They are solid and objective, although they were written by a theoretician when there was no computer yet:

1. Computers must work with numbers represented in binary form. The latter correlates with the properties of semiconductors.

2. The computational process performed by the machine is controlled by a control program, which is a formalized sequence of executable commands.

3. Memory performs a dual function: storing both data and programs. Moreover, both those and others are encoded in binary form. Access to programs is similar to access to data. They are the same in terms of data type, but they differ in the ways of processing and accessing a memory cell.

4. Computer memory cells are addressable. At a certain address, you can access the data stored in the cell at any time. This is how variables work in programming.

5. Providing for a unique order of execution of commands by applying In this case, they will be executed not in the natural order of their recording, but following the transition addressing specified by the programmer.

Impressed physicists

Neumann's horizons made it possible to find mathematical ideas in the widest world physical phenomena. The principles of John von Neumann were formed in the creative joint work on the creation of the EDVAK computer with physicists.

One of them, named S. Ulam, recalled that John instantly grasped their thought, then translated it into the language of mathematics in his brain. Having resolved the expressions and schemes formulated by himself (the scientist almost instantly made rough calculations in his mind), he thus understood the very essence of the problem.

And at the final stage of the deductive work done, the Hungarian transformed his conclusions back into the “language of physics” and gave out this most up-to-date information to dumbfounded colleagues.

Such deductiveness made a strong impression on the colleagues involved in the development of the project.

Analytical substantiation of the computer operation

The principles of functioning of the von Neumann computer assumed separate machine and software parts. When changing programs, the unlimited functionality of the system is achieved. The scientist managed to extremely rationally analytically determine the main functional elements of the future system. As an element of control, he assumed feedback in it. The scientist also gave the name to the functional units of the device, which in the future became the key to the information revolution. So, von Neumann's imaginary computer consisted of:

Machine memory, or storage device (abbreviated as memory);

Logic Arithmetic Unit (ALU);

Control device (CU);

I/O devices.

Even staying in another century, we can perceive the brilliant logic he achieved as an insight, as a revelation. However, was it really so? After all, the entire aforementioned structure, in its essence, became the fruit of the work of a unique logical machine in human form, whose name is Neumann.

Mathematics became his main tool. Magnificently, unfortunately, the late classic Umberto Eco wrote about such a phenomenon. “Genius always plays on one element. But he plays so brilliantly that all other elements are included in this game!

Functional diagram of a computer

By the way, the scientist outlined his understanding of this science in the article "Mathematician". He considered the progress of any science in its ability to be in the sphere of action mathematical method. It was his mathematical modeling that became an essential part of the above invention. In general, the classic looked the way it is shown in the diagram.

This scheme works as follows: the initial data, as well as programs, enter the system through an input device. In the future, they are processed in it commands are executed. Each of them contains details: from which cells data should be taken, what transactions should be performed on them, where to save the result (the latter is implemented in a storage device - memory). Output data can also be output directly through an output device. In this case (as opposed to storage in memory), they are adapted to human perception.

The general administration and coordination of the above structural blocks of the circuit is performed by the control unit (CU). In it, the control function is entrusted to the command counter, which keeps a strict record of the order in which they are executed.

About the historical incident

To be fundamental, it is important to note that the work on the creation of computers was still collective. Von Neumann's computers were developed by order and at the expense of the US Armed Forces Ballistics Laboratory.

The historical incident, as a result of which all the work carried out by a group of scientists was attributed to John Neumann, was born by accident. The fact is that general description architecture (which was sent to the scientific community for review) on the first page contained a single caption. And it was Neumann's signature. Thus, due to the rules for reporting the results of the study, scientists had the impression that the famous Hungarian was the author of all this global work.

Instead of a conclusion

In fairness, it should be noted that even today the scale of the ideas of the great mathematician on the development of computers has exceeded the civilizational possibilities of our time. In particular, the work of von Neumann suggested giving information systems the ability to reproduce themselves. And his last, unfinished work was called super relevant even today: "The computer and the brain."

Biography

Janos Lajos Neumann was born the eldest of three sons in a wealthy Jewish family in Budapest, which at that time was the second capital of the Austro-Hungarian Empire. His father, Max Neumann(Hung. 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. Mother, Margaret Cann(Hung. Kann Margit, 1880-1956), was a housewife and eldest daughter(in the second marriage) a successful businessman Jacob Kann - a partner in the company Kann-Heller, specializing in the trade in millstones and other agricultural equipment.

Janos, or simply Janczy, was an extraordinarily gifted child. Already at the age of 6, he could divide in his mind two eight-digit numbers and talk with his father in ancient Greek. Janos has always been 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 calculus. In 1911 he entered the Lutheran Gymnasium. In 1913, his father received a title of nobility, and Janos, along with the Austrian and Hungarian symbols of nobility - the prefix background (von) to an Austrian surname and title Margittai (margittai) in Hungarian naming - became known as 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 English name was changed to John. It is curious that his brothers, after moving to the USA, received completely different surnames: Vonneumann and Newman. The first, as you can see, is an "alloy" of the surname and the prefix "background", 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 made the accumulation and development of nuclear weapons. He was confirmed by the United States Senate on March 15, 1955. In May, he and his wife moved to Washington, a suburb of Georgetown. During recent years von Neumann was the chief adviser on atomic energy, atomic weapons and intercontinental ballistic weapons. Possibly due to his background or early experience in Hungary, von Neumann was strongly on the right wing of his political views. In an article in the magazine "Life", published on February 25, 1957, shortly after his death, he is presented as an adherent of a 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 the surgeons diagnosed a form of bone cancer. It was thought that von Neumann's cancer could have been caused by radiation exposure during the test. atomic bomb in the Pacific, or perhaps in subsequent work at Los Alamos, New Mexico (his colleague, nuclear pioneer Enrico Fermi, died of stomach cancer at age 54). The disease progressed and attending three times a week meetings of the AEC (Commission on Atomic Energy) required great effort. A few months after the diagnosis, von Neumann died in great agony. Cancer had also taken its toll on his brain, virtually rendering him unable to think. As he lay dying in the Walter Reed Hospital, he shocked his friends and acquaintances by asking them to speak to a Catholic priest.

Cellular automata and the living cell

The concept of creating cellular automata was a product of the anti-vitalistic ideology (indoctrination), the possibility of creating life from dead matter. The argumentation of the vitalists in the 19th century did not take into account that it is possible to store information in dead matter - a program that can change the world (for example, Jaccard's machine tool - see Hans Driesch). This is not to say 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 limit of his intellectual abilities and felt that he could not perceive some of the highest mathematical and philosophical ideas.

Von Neumann was a brilliant, resourceful, efficient mathematician, with an astonishing 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 absolute self-confidence. Perhaps it seemed to him that he did not have the ability to intuitively foresee new truths at the highest levels, or the gift for a pseudo-rational understanding of the proofs and formulations of new theorems. It's hard for me to understand. Maybe this was due to 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 Godel's completeness theorems. He was more than capable of doing this, and alone with himself he admitted the possibility that Hilbert had chosen the wrong course of action. 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 to 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 wondrous ligature of its pattern. I remember the tall figure of my father, standing next to me, and his smile. I remember thinking: “He is smiling because he thinks that I am still just a child, but I know how amazing these patterns are!”. I do not claim that exactly these words occurred to me then, but I am sure that this thought occurred to me at that moment, and not later. I definitely felt, “I know something that my dad doesn't. Perhaps I know more than him."

- [Ulam, 13]

Compare with Grothendieck's "Harvests and Sowings".

Personal life

Von Neumann was married twice. The first time he married Marietta Kövesi ( Mariette Kovesi) in 1930. The marriage broke up in 1937, and already in he married Clara Dan ( Clara Dan). From his first wife, von Neumann had a daughter, Marina, later a well-known economist.

Bibliography

• Mathematical foundations of quantum mechanics. Moscow: Nauka, 1964.
• Game theory and economic behavior. Moscow: Nauka, 1970.

Literature

• Danilov Yu. A. John von Neumann. - M .: Knowledge, 1981.
• Monastyrsky M.I. John von Neumann is a mathematician and a man. // Historical and mathematical research. - M .: Janus-K, 2006. - No. 46 (11). - S. 240-266 ..
• Ulam S. M. Adventures of a mathematician. - Izhevsk: R&C Dynamics, 272 p. ISBN 5-93972-084-6.

Notes

see also

Links

• Perelman M., Amusya M. The fastest mind of the era (on the centenary of John von Neumann) // Network magazine "Notes on Jewish History".

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Neumann John (Janos) von (12/28/1903, Budapest, ‒ 2/8/1957, Washington), American mathematician, member of the National Academy of Sciences of the USA (1937). In 1926 he graduated from the University of Budapest. From 1927 he taught at the University of Berlin, in 1930‒33 - in ... ... Great Soviet Encyclopedia

Neumann, John von- Neumann (Neumann) John (Janosh) background (1903-57), American mathematician and physicist. Major works on functional analysis, game theory and automata theory. One of the founders computer science. … Illustrated encyclopedic Dictionary

- (Neumann, John von) (1903 1957), one of the most brilliant mathematicians of the first half of the 20th century. Born December 28, 1903 in Budapest. In 1926 he graduated from the University of Budapest with a Ph.D. He continued his mathematical research in ... ... Collier Encyclopedia

In the 1940s, John von Neumann (born John von Neumann or Johann von Neumann, German Johann von Neumann; at birth Janos Lajos Neumann (Hungarian Neumann János Lajos), December 28, 1903, Budapest February 8, 1957, Washington) Hungarian American mathematician , ... ... Wikipedia

John von Neumann in the 1940s John von Neumann (English John von Neumann or Johann von Neumann, German Johann von Neumann; at birth Janos Lajos Neumann (Hungarian Neumann János Lajos), December 28, 1903, Budapest February 8, 1957, Washington) Hungarian ... ... Wikipedia

John von Neumann in the 1940s John von Neumann (English John von Neumann or Johann von Neumann, German Johann von Neumann; at birth Janos Lajos Neumann (Hungarian Neumann János Lajos), December 28, 1903, Budapest February 8, 1957, Washington) Hungarian ... ... Wikipedia

John von Neumann in the 1940s John von Neumann (English John von Neumann or Johann von Neumann, German Johann von Neumann; at birth Janos Lajos Neumann (Hungarian Neumann János Lajos), December 28, 1903, Budapest February 8, 1957, Washington) Hungarian ... ... Wikipedia

(December 3, 1903, Budapest - February 8, 1957, Washington)- American mathematician and physicist. Works on functional analysis, quantum mechanics, logic, meteorology. He made a great contribution to the creation of the first computers and the development of methods for their application. His game theory played an important role in economics.

Biography

Janos von Neumann was the eldest of three sons of the successful Budapest banker Max von Neumann. Later, in Zurich, Hamburg and Berlin, Janos was called Johann, and after moving to the USA - John (friendly - Johnny). Von Neumann was a product of that intellectual milieu. from which came such prominent physicists as Edward Teller, Leo Szilard, Denis Gabor and Eugene Wigner. John stood out among them for his phenomenal abilities. At the age of 6, he exchanged witticisms with his father in ancient Greek, and at 8 he mastered the basics of higher mathematics. AT early years Janos studied at home with specially invited teachers, and at the age of 10 he entered one of the best educational institutions that time - a Lutheran gymnasium. While still at school, von Neumann became interested in mathematics. The genius in von Neumann was recognized by the mathematics teacher Laszlo Ratz. He helped him develop his talent. Ratz introduced von Neumann to the small but brilliant circle of Budapest mathematicians of that time, which was headed by the spiritual father of the Hungarian mathematicians, Lipot Fejer. Assisting von Neumon was entrusted to M. Fekete, an assistant at the University of Budapest, and an outstanding teacher, Professor Jozsef Kurshak, took over the overall leadership. The atmosphere of the university and the conversations with mathematicians and attention from Feuer helped to form von Neumann as a mathematician, as well as the study of university courses. By the time he received his Abitur, Janos von Neumann had a reputation among mathematicians as a young talent. His first published work was written jointly with M. Fekete "On the location of zeros of some minimal polynomials" (1921) was published when von Neumann was 18 years old. Soon von Neumann graduated from high school. Max von Neumann did not consider the profession of a mathematician reliable enough to ensure the future of his son. He insisted that Janos also acquire the profession of a chemical engineer. Therefore, Janos entered the Federal Higher Technical School in Zurich, where he studied chemistry, and at the same time at the Faculty of Mathematics at the University of Budapest. Thanks to this combination, he had free access to lectures, so he appeared in Budapest only at the end of the semester to take exams. Then he left for Zurich or Berlin, but not to study chemistry, but to prepare his papers for publication, talk with fellow mathematicians, attend seminars. Von Neumann believed that he learned a lot about this period from two mathematicians: Erhard Schmidt and Hermann Weyl. When Weyl needed to leave during the semester, von Neumann continued reading the course for him.

Achievements

Von Neumann's first work on axiomatic set theory was published in 1923. It was called "On the introduction of transfinite ordinal numbers". It was published in the Proceedings of the University of Szeged. Von Neumann developed his system of axioms and presented it in his doctoral dissertation and two papers. The dissertation was of great interest to A. Frenkel, who was instructed to review it. Despite the fact that he could not understand it completely, he invited von Neumann to his place. He Frenkel asked him to write popular article, in which a new approach to the problem and the consequences drawn from it would be stated. Von Neumann wrote such a work, calling it "On the question of the axiomatic construction of the theory of sets." It was published in 1925 as "Journal fuer Mathematik". Von Neumann built a wonderful system of set theory axioms, as simple as Hilbert's for Euclidean geometry. The von Neumann system of axioms occupies a little more than one printed page. In 1925, von Neumann received a degree in chemical engineering in Zurich and successfully defended his dissertation "Axiomatic Construction of Set Theory" for the title of Doctor of Philosophy at the University of Budapest. The young doctor goes to improve his knowledge at the University of Göttingen, where at that time people whose names became the pride of science gave lectures: K. Runge, F. Klein, E. Landau, D. Hilbert, E. Zermelo, G. Weyl, G. Minkowski, F. Frank, M. Born and others. Guest lecturers were G. Lorentz, N. Bohr, M. Plank, P. Ehrenfest, A. Poincaré, A. Sommerfeld...

On von Neumann very big influence had communication with David Hilbert. In Göttingen, von Neumann got acquainted with the ideas of then emerging quantum mechanics, its mathematical justification immediately captivated. Together with D. Hilbert and L. Nordheim, von Neumann wrote an article "On the Foundations of Quantum Mechanics". Then he publishes a series of works "Mathematical foundation of quantum mechanics", "Probability-theoretic construction of quantum mechanics" and "Thermodynamics of quantum mechanical systems". In the works of von Neumann, quantum mechanics found its natural language - the language of operators acting in the Hilbert space of states. In his works, a solid mathematical foundation was laid for the statistical interpretation of quantum mechanics, a new concept of the density matrix was introduced, and a quantum analogue of Boltzmann's H-theorem and the ergodic theorem was proved. On the basis of these works, von Neumann began another cycle - on the theory of operators, thanks to which he is considered the founder of modern functional analysis. Von Neumann showed that the "too free" justification of the theory (of Dirac) can be justified in terms of the axiomatic theory of the Hilbert space and the spectral theory of operators.

In 1927, von Neumann became Privatdozent at the University of Berlin, and since 1929 at the University of Hamburg.

Between 1927 and 1929, von Neumann carried out the fundamental work three big cycles: on set theory, game theory and the mathematical foundation of quantum mechanics.

In 1927, von Neumann wrote an article "On the Hilbert theory of proof". In it, he investigated the problem of the consistency of mathematics.

In 1928, von Neumann wrote the work "On the theory of strategic games", in which he proved the minimax theorem, which became the cornerstone of the game theory that arose later. In his theorem, von Neumann considers the situation when two people play a game, according to the rules of which the gain of one player is equal to the loss of the other. In addition, each player can choose from a finite number of strategies. In this case, the player believes that the opponent is acting in the best way for himself. Von Neumann's theorem states that in such a situation there exists a "stable" pair of strategies for which the minimum loss of one player coincides with the maximum gain of the other. The stability of strategies means that each of the players, deviating from the optimal strategy, only worsens his chances and, he has to return to the optimal strategy.

Von Neumann proved this theorem, drawing attention to its connection with the theory of fixed points. Later proofs were found using convex set theory. In the work "On the definition by transfinite induction and related questions of general set theory" (1928), von Neumann again returns to the problem of introducing ordinal numbers, and gives a rigorous axiomatic presentation of the theory.

In his work "On a Problem of Consistency in Axiomatic Set Theory" von Neumann showed that one of the "non-traditional" axioms in the system he proposed can be deduced from the axioms of other systems. Since backward derivability had been proven earlier, the result meant that his "unusual" axiom was equivalent to the usual ones in other systems.

In 1929, von Neumann wrote the work "The General Spectral Theory of Hermitian Operators".

In 1929, von Neumann received an invitation to read a series of lectures for one semester at Princeton University. Von Neumann first arrived in the United States in 1930. Shortly after the arrival of Johann von Neumann, for many colleagues, it becomes just Johnny. In 1931, von Neumann finally parted ways with the University of Hamburg to accept a professorship at Princeton.

In 1934, the article "On an algebraic generalization of quantum mechanical formalism" was published, co-authored with P. Jordan and E. Wigner.

Shortly before his first visit to Princeton, von Neumann married Marietta Kevushi, and in 1935 their daughter Marina was born.

In 1936, von Neumann, together with J. Birkhoff, wrote the article "The Logic of Quantum Mechanics".

In 1937, von Neumann's marriage broke up, and from another summer vacation trip to Budapest in 1938, von Neumann returned with his second wife, Clara Dan. Later, during World War II, Clara von Neumann became a programmer. She owns the first programs for electronic computers, in the development and creation of which her husband made a great contribution.

Oswald Veblen (in 1932) and Albert Einstein (1933) became the first professors at the Institute for Advanced Study at Princeton. In the same 1933, John von Neumann was awarded this high honor.

Neumann and computer

In 1938, von Neumann's On Infinite Direct Products was published. The first computer was built in 1943-1946 at the Moore School of Electrical Engineers at the University of Pennsylvania and was called ENIAC (according to the first letters of the English name - electronic digital integrator and calculator). Von Neumann suggested to its developers how ENIAC could be modified to make it easier to program.

But in the creation of the next machine - EDVAK (electronic automatic calculator with discrete variables), von Neumann took a more active part. He developed a detailed logical scheme of the machine, in which the structural units were not the physical elements of the circuits, but idealized computing elements. The use of idealized computing elements was an important step forward, as it made it possible to separate the creation of a conceptual logic circuit from its technical implementation. Von Neumann also proposed a number of engineering solutions. Von Neumann proposed using not delay lines as memory elements, but a cathode ray tube (electrostatic storage system), which should have greatly increased performance. In this case, it was possible to process all bits of the iashin word in parallel. This machine was named JONIAC ​​- in honor of von Neumann. With the help of JONIAK, important calculations were carried out when creating hydrogen bomb.

In 1944, the work of von Neumann and O. Morgenstern "The Theory of Games and Economic Behavior" was published. In the late forties, having accumulated practical experience in creating computers, von Neumann set about creating a general mathematical (logical) theory of automata. The differences between von Neumann's automata theory and Wiener's cybernetics are insignificant and are due to the personal taste of their creators, and not to fundamental considerations. Von Neumann's theory is devoted mainly to discrete mathematics, while Wiener's is continuous.

Von Neumann proposed a data correction system, to improve the reliability of systems - the use of duplicate devices with the choice of a binary result for the largest number.

Von Neumann worked hard on the self-reproduction of automata and was able to prove the possibility of self-reproduction. state machine, which had 29 internal states.

In the second half of the 1930s, together with F. J. Murray, Neumann published a number of papers on operator rings, initiating the so-called Neumann algebra, which later became one of the main tools for quantum research. Neumann became a US citizen in 1937. During World War II, he served as a consultant at the Los Alamos Atomic Center, where he calculated the explosive detonation method. nuclear bomb and participated in the development of the hydrogen bomb. In March 1955 he became a member of the American Atomic Energy Commission.

Of Neumann's 150 works, only 20 deal with problems in physics, while the rest are equally distributed between pure mathematics and its practical applications, including game theory and computer theory.

Neumann owns pioneering works on computer theory related to the logical organization of computers, the problems of the functioning of machine memory, the imitation of randomness, and the problems of self-reproducing systems. In 1944, Neumann joined the Mauchly and Eckert group working on the ENIAC machine as a mathematical consultant. Meanwhile, the group began developing a new model, the EDVAC, which, unlike the previous one, could store programs in its internal memory. In 1945, Neumann published a "Preliminary Report on the EDVAC Machine", which described the machine itself and its logical properties. The computer architecture described by Neumann was called "von Neumann's", and thus he was credited with the authorship of the entire project. This subsequently resulted in trial about the right to a patent and led to the fact that Eckert and Mauchly left the laboratory and founded their own company. Nevertheless, the "von Neumann architecture" was the basis for all subsequent computer models. In 1952, Neumann developed the first computer using programs stored on a flexible medium, the MANIAC I.

Neumann's "axiomatic method" is sometimes considered the secret of Neumann's success. He considered the subject, concentrating on its basic properties (axioms), from which everything else follows.

One of Neumann's utopian ideas, for the development of which he proposed using computer calculations, was the artificial warming of the climate on Earth, for which it was supposed to cover dark paint polar ice caps to reduce their reflection of solar energy. At one time this proposal was seriously discussed in many countries. In 1956, the Atomic Energy Commission awarded Neumann the Enrico Fermi Prize for outstanding contributions to computer theory and practice.

Many of von Neumann's ideas have not yet received due development, for example, the idea of ​​the relationship between the level of complexity and the system's ability to reproduce itself, the existence of a critical level of complexity, below which the system degenerates, and above it acquires the ability to reproduce itself. In 1949, the work "On the rings of operators. The theory of decomposition" was published.

John von Neumann was awarded the highest academic honors. He was elected a member of the Academy of Exact Sciences (Lima, Peru), the Accademia dei Lincei (Rome, Italy), the American Academy of Arts and Sciences, the American Philosophical Society, the Lombard Institute of Sciences and Letters, the Royal Netherlands Academy of Sciences and Arts, National Academy USA, honorary doctorate from many universities in the USA and other countries.

John von Neumann was born in Budapest, the capital of Hungary, on December 28, 1903. He was the eldest son of his parents, Max Neumann and Margaret Kann. From the early age Neumann was interested in the nature of numbers and mathematical logic.

Mathematics was not the only subject in which young Neumann was interested. He also liked history, so much so that at the age of eight he read 40 volumes of world history. This testified to the fact that Neumann felt equally well in both the logical and social branches of science. Neumann was also lucky with his parents, who supported him in all his endeavors.

In 1914, at the age of ten, Neumann entered the Lutheran gymnasium, which was one of the top three at that time in Budapest. He published his first paper in the journal of the German Mathematical Society in 1922, which dealt with the zeros of certain minimal polynomials.

Berlin, Zurich, Budapest

Although Neumann had little interest in either chemistry or engineering, his father convinced him to pursue engineering as it was considered prestigious at the time. Neumann studied at the Catholic University of Peter Pazman in Budapest, where he received a doctorate in mathematics, and in parallel completed a basic university course in chemical engineering at the Swiss Technical School of Zurich.

In his doctoral work, Neumann postulated Cantor's set theory. Of course, it was an unusual achievement that a seventeen-year-old boy was simultaneously studying at one university and writing his doctoral work at the second. He received good grades in both the basic chemical engineering course and his doctoral work in mathematics. He was only twenty-two years old.

Quantum mechanics

After receiving two degrees at once, in 1926 Neumann began to attend the University of Göttingen in Germany, where he studied quantum mechanics. He was creative and original in his thinking, offering complete and logical concepts. In the same 1926, he was engaged in the theories of quantum mechanics with the aim of streamlining and improving them.

Neumann tried to find similar features in the wave and matrix mechanics. He also worked on the abstract Hilbert space rules and developed a mathematical structure in terms of quantum theory.

Personal life

During 1927-1929, after presenting the theory of quantum mechanics, Neumann attended numerous conferences and colloquia. By 1929 he had written about 32 works on English language. These papers were well structured so that other mathematicians could incorporate Neumann's work into their theories. By this time, he had become a celebrity in academia for his creative and innovative theories. By the end of 1929, Neumann was offered a teaching position at Princeton University. At the same time, he married Mariette Kövesi, a childhood friend. In 1935 they had a daughter, who was named Marina. The marriage of John and Marietta ended in 1936. Marietta returned to Budapest, while Neumann traveled around Europe for a while and then returned to the United States. During a trip to Budapest, he met Clara Dan, whom he married in 1938.

Death

John von Neumann was diagnosed with cancer, but despite this, he took part in the award ceremonies organized in his honor, while in a seated gurney. He maintained close ties with family and friends during his illness. John von Neumann died on February 8, 1957.

Significant contribution

Neumann took part in one of the government projects at Los Alamos ("Manhattan Project"), in which he worked on the creation of a circuit and a working prototype of an explosive lens. The mathematical modeling he used during these works contributed to the development of modern computers. In addition to working with these models, he also funded a project that was involved in the creation of a computer. He was also involved in designing the architecture of the computer, and his efforts eventually convinced other scientists that the computer was more than just a "big calculator".

Quantum logic, business game theory, linear programming and mathematical statistics are just some of what he "gave" to science.

Awards and achievements

• Speaker at the Colloquium of the American Mathematical Society (AMS), 1937
• Winner of the Bocher Prize from the AMO, 1938
• Speaker at the Gibbs Lectures from AMO, 1944
• Enrico Fermi Prize, 1956
• Speaker at international congress, 1950
• Honorary Member of the London Mathematical Society, 1952
• President of the American Mathematical Society, 1951-1952
• Speaker at the International Congress, 1954