Von Neumann showed talent in mathematics and memory from an early age. Since childhood, von Neumann has a gift of never forgetting anything. At the age of six, he was able to play jokes on his father in Greek. At the age of six, he could divide eight digits in his mind, and at the age of eight, he could master calculus. 10 years old, he spent several months reading 48 volumes of world history, and was able to compare the current events with an event in history and discuss their military theories and political strategies. At the age of twelve, he understood the essence of Bohr's masterpiece "On Function".
Near the college entrance examination, Neumann's father began to worry about his son's career planning. He consulted many friends, including some famous scientists, and finally decided that the 20th century was the century of chemical engineering. Neumann is only interested in mathematics, but he also knows that the future of Hungarian mathematicians is not good. In order to reach a win-win understanding, after discussion, the two decided to take two subjects at the same time.
In the following four years, Von Neumann registered as a student of mathematics at Budapest University, but he didn't attend classes. He just takes the exam on time every year and gets an A in the exam. At the same time, von Neumann entered the University of Berlin (192 1 year) and studied chemistry at the Federal Institute of Technology in Zurich, Switzerland in 1923. From 65438 to 0926, he obtained a degree in university chemistry from the Federal Institute of Technology in Zurich, Switzerland. He also returned to Budapest University at the end of each semester and passed the course examination, and obtained a doctorate in mathematics from Budapest University.
During his stay in Zurich, von Neumann often used his spare time to study mathematics, write articles and correspond with mathematicians. During this period, influenced by Hilbert and his students Schmidt and Weil, von Neumann began to study mathematical logic. At that time, Weil and Boya were also in Zurich, and he was in contact with them. Once Val left Zurich for a short time, and von Neumann took classes for him. With wisdom and unique cultivation, Von Neumann is thriving. By the time he finished his student days, he had been at the forefront of mathematics, physics and chemistry.
1926 In the spring, von Neumann went to the University of G? ttingen as Hilbert's assistant. From 1927 to 1929, von Neumann was a part-time lecturer at the University of Berlin, during which he published the set theory Algebraic Sum.
After the outbreak of World War II in Europe, von Neumann surpassed Princeton and participated in many scientific research projects related to the anti-fascist war. From 1943, he became a consultant to make atomic bombs, and still served in many government departments and committees after the war. 1954, he became a member of the American atomic energy commission.
1955 In the summer, he was diagnosed with cancer by X-ray, but he persisted in his work and his condition expanded. Later, he was placed in a wheelchair and continued to think, speak and attend meetings. Long-term heartless illness tortured him and slowly stopped him from all activities. /kloc-0 entered Walter Reed Hospital in Washington in April, 1956, and/kloc-0 died in the hospital on February 8, 1957 at the age of 53.
The main points of von Neumann's theory are: the number system of digital computer adopts binary; Computers should be executed in program order. People call this von Neumann theory the von Neumann framework. From ENIAC(ENIAC is not von Neumann architecture) to the most advanced computers at present, von Neumann architecture is adopted. So von Neumann is the father of digital computers.
1928, von Neumann published the article "Axiomatization of Set Theory", which is an axiomatic treatment of the above set theory. The system is very concise. It uses the first type object and the second type object to represent the set and the properties of the set in naive set theory. It takes a little more than one page to write the axioms of the system, which is enough to establish all the contents of naive set theory, thus establishing the whole modern mathematics. Von Neumann's system may give the first foundation of set theory, and the finite axiom used has a logical structure as simple as elementary geometry. Starting from axioms, Von Neumann's ability to skillfully use algebraic methods to deduce many important concepts in set theory is simply amazing, which has prepared conditions for his interest in computers and "mechanization" proof in the future.
In the late 1920s, von Neumann participated in Hilbert's meta-mathematics project and published several papers to prove that some arithmetic axioms were not contradictory. 1927 The article "On Hilbert's Proof" has attracted the most attention, and its theme is to discuss how to get rid of contradictions in mathematics. The article emphasizes that the question put forward and developed by Hilbert and others is very complicated and has not been answered satisfactorily at that time. It is pointed out that Ackerman's proof of eliminating contradictions is impossible in classical analysis. Therefore, von Neumann gave a strict finiteness proof of the subsystem. This seems to be not far from the final answer Hilbert is looking for. Just then, 1930 Godel proved the incompleteness theorem. Theorem assertion: In an incongruous formal system containing elementary arithmetic (or set theory), the incongruity of the system is unprovable in the system. At this point, von Neumann can only stop this research. Von Neumann also got a special result about set theory itself. His interest in mathematical basics and set theory continued until the end of his life.
During the period of 1930 ~ 1940, von Neumann's achievements in pure mathematics were more concentrated, his creation was more mature and his reputation was higher. Later, in a question-and-answer table for the National Academy of Sciences, von Neumann chose the mathematical basis of quantum theory, operator ring theory and ergodic theorem of states as his most important mathematical work. Operator ring theory began in the second half of 1930. Von Neumann was very familiar with the noncommutative algebra of Nott and Adin, and soon applied it to the algebra of bounded linear operators on Hilbert space, which was later called von Neumann operator algebra.
1940 is a turning point in von Neumann's scientific career. Before that, he was a pure mathematician who was familiar with physics. From then on, he became a superb applied mathematician who firmly grasped pure mathematics. He began to pay attention to the most important tool for applying mathematics to physics at that time-partial differential equations. At the same time, he constantly innovated and applied non-classical mathematics to two new fields: game theory and electronic computer.
Von Neumann studies meteorology. For quite some time, he has been attracted by the extremely difficult problems raised by the hydrodynamic equations of the earth's atmospheric movement. With the appearance of electronic computer, it is possible to study and analyze this problem numerically. The first high-scale calculation by von Neumann involved a two-dimensional model, which was related to the geostrophic approximation. He believes that people can finally understand, calculate and control climate change.
Von Neumann also put forward the proposal of detonating nuclear fuel by fusion and supported the development of hydrogen bombs. 1947, the army issued a commendation order praising him as a physicist, engineer, weapon designer and patriot.
Von Neumann not only played his talents in weapons research, but also in social research. 1928, von Neumann proved the basic principles of game theory, thus announcing the formal birth of game theory. The game theory he created is undoubtedly his most enviable outstanding achievement in the field of applied mathematics. The current game theory mainly refers to the study of social phenomena with specific mathematical methods. Its basic idea is to analyze the interests of multiple subjects. 1944, Game Theory and Economic Behavior, co-authored by von Neumann and Morgan Stern, is a basic work in this field. The two-person game is extended to the n-person game structure, and the game theory system is applied to the economic field, thus laying the foundation and theoretical system of this discipline. The paper includes the explanation of pure mathematical form of game theory and the detailed explanation of practical application. This paper and the discussion of some basic problems of economic theory have triggered various studies on economic behavior and some sociological problems. Today, this is a widely used and increasingly rich mathematical discipline. Some scientists enthusiastically praised it as "one of the greatest scientific contributions in the first half of the 20th century".
The last subject that contributed to von Neumann's popularity was electronic computer and automation theory.
The development of computer engineering should also be largely attributed to von Neumann. The logic schema, storage, speed, the choice of basic instructions and the design of interaction between circuits in modern computers are deeply influenced by von Neumann's thought. He not only participated in the development of electronic tube component ENIAC computer, but also personally supervised the construction of computer in Princeton Institute of Advanced Studies.
In the last few years of von Neumann's life, his thoughts were still very active. He integrated the results of logic research and his early work on computers, and extended his vision to the general automata theory. With his unique courage, he overcame the most complicated problem: how to design a reliable automaton with unreliable components and build an automaton that he can replicate. From this, he realized some similarities between computer and human brain mechanism, which was reflected in Hillemann's speech; It was not until after his death that someone published a pamphlet under the name of Computer and Human Brain. Although this is an unfinished work, some quantitative results obtained by his accurate analysis and comparison of human brain and computer system still have important academic value.