Neumann John

John von Neumann

John von Neumann (on December 3, 1903, Budapest - on February 8, 1957, Washington) — the American mathematician and the physicist. Works according to the functional analysis, a quantum mechanics, logic, meteorology. Made a big contribution to creation of the first computers and development of methods of their application. Its games theory played an important role in economy.

Biography

Janos von Neumann was a senior from three sons of the successful Budapest banker Max von Neumann. Later, in Zurich, Hamburg and Berlin, Janos was named by Johann, and after moving to the USA - John (friendly - Johnny). Von Neumann was a product of that intellectual environment. which left such outstanding physicists as Edward Teller, Leo Stsillard, Denis Gabor and Eugene Vigner. John was selected among them with the fenemenalny capabilities. In 6 years he was transferred with the father jokes on Ancient Greek, and in 8 mastered fundamentals of the higher mathematics. In young years Janos was engaged with specially invited to teachers at home, and at the age of 10 years came to one of the best educational institutions of that time - a Lutheran gymnasium. Still a background Neumann became interested in school in mathematics. The genius in a background Neumann was distinguished by the teacher of mathematics László Ratts. It also helped it to develop his talent. Ratts entered Neumann's background into a small, but brilliant circle of the Budapest mathematicians of that time which was headed by the confessor of the Hungarian mathematicians Lipot Fejer. To Pomogat von Nejmona it was entrusted to the assistant to the Budapest university M. Feketa: and the general management was undertaken by the outstanding teacher: professor Yozhef Kyurshak. The atmosphere of the universiyet and a conversation with mathematicians and attention from Fejer it helped to be created a background to Neumann as the mathematician, also as studying of university rates. By the time of receiving the school-leaving certificate Janos von Neumann had reputation of young talent at mathematicians. Its first printing work was written together with M. Fekete "About arrangement of zero some minimum polynoms" (1921) was published when a background Neumann was 18 years old. Vskore von Neumann ended a gymnasium. Max von Neumann did not consider a profession of the mathematician rather reliable, capable to provide the future of the son. He insisted on that Janos purchased also the chemical engineer's profession. Therefore Janos was admitted to the Federal higher technical school in Zurich where he studied chemistry, and at the same time on mathematical faculty of the Budapest university. Thanks to such combination, it had a garden leave of lectures therefore it appeared in Budapest only at the end of a semester, for examination. Then he went to Zurich or Berlin, but not to study chemistry, and for preparation for printing of the works, conversations with colleagues mathematicians, visit of seminars. Von Neumann considered that about this period he learned from two mathematicians much: Erhard Schmidt and Herman Veyl. When to Veyl podnadobitsya to leave during a semester, reading a rate for it Neumann continued a background.

Achievements

The first work Neumann's background according to the axiomatic set theory was published in 1923. It was called "To introduction of transfinite ordinal numbers". It was published in works of the Szeged university. Von Neumann developed the system of axioms and stated it in the doctoral dissertation and two articles. The thesis strongly interested A. Frenkel to whom charged to review it. In spite of the fact that he could not understand it completely, he invited to himself Neumann's background. He Frenkel asked it to write popular article in which new approach to a problem and the investigations taken from it would be stated. Von Neumann wrote such work, having called it "To a question of axiomatic creation of the theory of sets". It was published in 1925 and "Journal fuer Mathematik". Von Neumann constructed the remarkable system of axioms of the theory of sets, same simple as gilbertovy for Euclidian geometry. The system of axioms Neumann's background occupies a little more than one page of the printing text. In 1925 a background Neumann gains the diploma of the chemical engineer in Zurich and successfully "Axiomatic creation of the theory of sets" on a rank of the doctor of philosophy at the Budapest university defends the dissertation. The young doctor goes to improve the knowledge in the University of Göttingen where people whose names became pride of science at that time gave lectures: K. Runge, F. Klein, E. Landau, D. Gilbert, E. Zermelo, G. Veyl, G. Minkowski, F. Frank, M. Bourne and others. G. Lorentz, N. Bohr, M. Planck, P. Erenfest, A. Poincare, A. Sommerfeld were the invited lecturers...

Communication with David Gilbert had Na von Neumann very great influence. In Gettingene von Neumann got acquainted with the ideas of the quantum mechanics arising then, its mathematical justification took at once. Together with D. Gilbert and L. Nordgejmom von Neumann wrote article "About the Bases of a Quantum Mechanics". Then "Mathematical justification of a quantum mechanics", "Probability-theoretic creation of a quantum mechanics" and "Thermodynamics of the quantum mechanical systems" releases a series of works. In works Neumann's background the quantum mechanics found the natural language - language of the operators acting in the Hilbert state space. In its works the strong mathematical basis under statistical interpretation of a quantum mechanics was brought, the new concept of a density matrix is entered, the quantum analog of the H-theorem of Boltzmann and the ergodic theorem is proved. On the basis of these works a background Neumann began other cycle - according to the theory of operators thanks to which he is considered the founder of the modern functional analysis. Von Neumann showed that "too free" justification of the theory {Dirac} can be proved in terms of the axiomatic theory of Hilbert space and the spectral theory of operators.

In 1927 a background Neumann becomes privatdozent Berlin, and since 1929 - the Hamburg university.

During 1927 for 1929 a background Neumann performed fundamental works of three big cycles: according to the theory of sets, games theory and mathematical justification of a quantum mechanics.

In 1927 a background Neumann wrote article "To the Hilbert Theory of the Proof". In it he investigated a problem of consistency of mathematics.

In 1928 a background Neumann wrote work "To the theory of strategic games", in which proved the theorem of a minimax, become a cornerstone, to the games theory which arose later. In the theorem a background Neumann considers a situation when two play a game by which rules vigrysh one player it is equal to loss of another. At the same time each player can select from a finite number of strategy. At the same time the player considers that the opponent acts with the best for himself in the way. Teorema von Neumann claims that in such situation there is a "steady" couple of strategy for which the minimum loss of one player matches the maximum prize of another. Stability of strategy means that each of players, deviating from optimal strategy only worsens the chances and, he should return to optimal strategy.

Von Neumann proved this theorem, having paid attention to its communication with the theory of motionless points. Later the proofs using the theory of convex sets were found. In work "About determination through transfinite induction and related questions of the general theory of sets" (1928), a background Neumann returns to a problem of introduction of ordinal numbers again, and gives strict axiomatic statement of the theory.

In work "About one problem of consistency of the axiomatic set theory" a background Neumann showed that one of "nonconventional" axioms in the system offered them is brought out of axioms of other systems. As the return deductibility was proved earlier, the result meant that its "unusual" axiom is equivalent normal in other systems.

In 1929 a background Neumann writes work "The general spectral theory of Hermite operators".

In 1929 a background Neumann receives the invitation to read during one semester series of lectures in Princeton University. In the USA a background Neumann for the first time appeared in 1930. Soon after arrival Johann von Neumann for many colleagues becomes just Johnny. In 1931 a background Neumann finally leaves the Hamburg university to accept professorate in Princeton.

In 1934 article "About Algebraic Generalization of a Quantum Mechanical Formalism" written in collaboration with P. Iordan and E. Vigner is published.

Shortly before the first visit to Prinston von Neumann married Marietta Chevuscii, and in 1935 they gave birth to the daughter Marina.

In 1936 a background Neumann together with J. Birkgof writes article "Logic of a Quantum Mechanics".

In 1937 defects the background Neumann broke up, and from another trip to summer vacation to Budapest in 1938 Neumann's background returned with the second wife - Klara Dan. Later, during World War II, Klara von Neumann became a programmer. It possesses the first programs for elektronynkh computers to which development and creation her husband entered a big deposit.

The first professors of Institute of the highest researches in Princeton became Oswald Veblen (in 1932) and Albert Einstein (1933). In the same 1933 this great honor also John von Neumann was awarded.

Neumann and computer

John von Neumann and computer

In 1938 there was a work Neumann's background "About infinite direct products". The first computer was constructed in 1943-1946 at school of electrical engineers of Moore of the Pennsylvanian university and received the name ENIAK (on the first letters of the English name - electronic digital integrator and the calculator). Von Neumann prompted it to razrabotika as it is possible to modify ENIAK to simplify its programming.

And here - EDVAK (the electronic automatic calculator with discrete variables) a background Neumann took more active part in creation of the following machine. He developed the detailed logical network of the machine in which not physical elements of chains, but idealized computing elements were structural units. Use of idealized computing elements became an important step forward as allowed to separate creation of the schematic logical network from its technical embodiment. Takzhe von Neumann proposed a number of engineering solutions. Von Neumann suggested to use as memory cells not of a delay circuit, and the cathode ray tube (the electrostatic memorable system) that had to is strong to increase high-speed performance. At the same time it was possible to process all discharges of an iashinny word in parallel. This machine was called by DZHONIAK - in honor of Neumann's background. Using DZHONIAKA important calculations during creation of a hydrogen bomb were performed.

In 1944 work Neumann and O. Morgenstern's background "Games theory and economic behavior" was issued. In the late forties, having accumulated practical experience of creation of computers, a background Neumann started creation of the general mathematical (logical) automata theory. Differences between the automata theory Neumann's background and Winer's cybernetics are insignificant and caused by personal taste of their creators, but not basic reasons. Teoriya von Neumann is devoted, generally to discrete mathematics while at Winer - continuous.

Von Neumann offered the system of adjustment of data, for reliability augmentation of systems - use of the duplicated devices with the choice of binary result on the greatest number.

Von Neumann worked hard over self-reproduction of automatic machines and could prove a possibility of a samovosproizvdeniye of the finite state machine which had 29 internal states.

In the second half of the 1930th years together with F.J. Murray Neumann published a number of works on rings of operators, having laid the foundation for so-called algebra of Neumann which became afterwards one of the main tools for quantum researches. In 1937 Neumann was naturalized the USA. During World War II served as the consultant in Atomic Center in Los Alamos where calculated an explosive method of a detonation of a nuclear bomb and participated in development of a hydrogen bomb. In March, 1955 became the member of the American commission on atomic energy.

From 150 works of Neumann only 20 concern physics problems, the others are similarly distributed between a pure mathematics and its practical applications, including games theory and the computer theory.

Neumann possesses the innovative works on the computer theory connected with the logical organization of computers, problems of functioning of machine memory, randomness simulation, problems of the self-replicating systems. In 1944 Neumann joined group Became wet also Eckert, the machine ENIAC occupied with creation, as the consultant for mathematical questions. Meanwhile in group development of new model, EDVAC which, unlike previous, could store programs in the internal memory began. In 1945 Neumann published "The preliminary report on the machine EDVAC" in which the machine and its logical properties was described. The computer architecture described by Neumann received the name "von Neumann", and thus authorship of all project was attributed to it. It developed afterwards into judicial proceedings about a right to patent and led to the fact that Eckert both Became wet left laboratory and founded own firm. Nevertheless "von Neumann architecture" was the basis for all subsequent models of computers. In 1952 Neumann developed the first computer using the programs written on the floppy medium, MANIAC I.

Secret of success of Neumann sometimes consider his "postulational method". He considered a subject, having concentrated on its main properties (axioms) from which all the rest follows.

Artificial warming of climate on Earth for what prepolagatsya to cover with dark paint polar ices to reduce reflection of solar energy by them was one of the utopian ideas of Neumann for which development he suggested to use computer calculations. At one time this offer was seriously discussed in many countries. In 1956 the Commission on atomic energy awarded Neumann with Enrico Fermi's prize for an outstanding contribution to the computer theory and practice.

Many ideas Neumann's background did not gain due development, for example, the idea about interrelation of level of complexity and capability of a system to self-reproduction yet, about existence of critical level of complexity below which a system degenerates, and finds capability to self-reproduction above. In 1949 there is a work "About rings of operators. Theory of decomposition".

John von Neumann was awarded the highest academic honors. He was elected the member of Academy of the exact sciences (Lima, Peru), Academies of a dea of Linchei (Rome, Italy), the American academy of arts and sciences, the American philosophical society, Lombardsky institute of sciences and literature, the Netherlands royal akdayemiya of sciences and arts, National academy of the USA, the honourable doctor of many universities of the USA and other countries.