Who is the father of computers?

John von neumann (1903- 1957), the "father of modern electronic computers", is a Hungarian-born American physicist, mathematician and inventor, and the "father of modern electronic computers" is the inventor of computers (that is, the world's first modern general-purpose computer EDVAC). 1903 12.28 was born in john von neumann.

In Budapest, my father is a banker and his family is well-off. He attaches great importance to children's education. Von Neumann was brilliant since he was a child, with a wide range of interests, and he was obsessed with reading. It is said that he was able to chat with his father in ancient Greek at the age of 6 and mastered seven languages in his life. He is good at German, but when he thinks about ideas in German, he can translate them into English at the speed of reading. He can read books and papers word for word quickly. And after a few years, it can still be like this. 1911-1921year, when von Neumann was studying in Lu Se Lun Middle School in Budapest, he made his mark and was highly valued by teachers. Under the individual guidance of Mr Fichte, he jointly published his first mathematical paper. At this time, von Neumann was less than 18 years old. 192 1- 1923, studied at the Federal Institute of Technology in Zurich, Switzerland. Soon after, he got his Ph.D. in Mathematics from Budapest University with 1926, when von Neumann was only 22 years old .5438+0927. 1930 accepted the position of visiting professor at Princeton University and went to the United States. 193 1 became the first batch of tenured professors at Princeton university in the United States. At that time, he was less than 30 years old. 1933 transferred to the Institute of Advanced Studies, became one of the first six professors, and worked there all his life. Von Neumann is an honorary doctor of Princeton University, University of Pennsylvania, Harvard University, Istanbul University, University of Maryland, Columbia University and Munich Institute of Advanced Technology. He is a member of the National Academy of Sciences of the United States, the National Academy of Natural Sciences of Peru and the National Forestry Institute of Italy, etc.1030.6666 President of the American Mathematical Society 195 1 to 1953. 1954 In the summer, von Neumann was diagnosed with cancer and died in Washington on February 8, 1957 at the age of 54.

The outstanding contribution of editing this paragraph

Main contribution

Von Neumann is one of the most important mathematicians in the 20th century. He has made outstanding contributions to both pure mathematics and applied mathematics. His work can be roughly divided into two periods: before 1940, he mainly studied pure mathematics: he put forward a simple and clear ordinal number theory in mathematical logic, and made a new axiomatization of set theory, in which set and class were clearly distinguished; Later, he studied the spectral theory of linear self-adjoint operators on Hilbert space, thus laying the mathematical foundation of quantum mechanics; From 65438 to 0930, he proved that the average ergodic theorem opened up a new field of ergodic theory; In 1933, he solved Hilbert's fifth problem by using compact groups. In addition, he also made pioneering contributions in the fields of measure theory, lattice theory and continuous geometry. From 1936 to 1943, he cooperated with Murray to establish the operator ring theory, which is now called von Neumann algebra. After 1940, von Neumann turned to applied mathematics. If his pure mathematical achievements belong to mathematics, then his work in mechanics, economics, numerical analysis and electronic computers belongs to all mankind. At the beginning of World War II, von Neumann studied the motion of compressible gas, established shock wave theory and theory of turbulence, and developed fluid mechanics. Starting from 1942, he co-authored the book Game Theory and Economic Behavior with Morgenstein, which is a classic work in game theory, making him one of the founders of mathematical economics. Von Neumann suggested designing the world's first electronic computer ENIAC (Electronic Digital Integral Computer). 1March, 945, on the basis of discussion, he drafted the first draft of the design report of EDVAC (electronic discrete variable automatic computer), which had a decisive influence on the later computer design, especially the determination of computer structure, the use of stored programs and binary codes, which are still followed by electronic computer designers. From 65438 to 0946, von Neumann began to learn programming. He is one of the founders of modern numerical analysis and computational mathematics. He first studied the numerical calculation of linear algebra and arithmetic, then focused on the discretization and stability of nonlinear differential equations, and gave the error estimation. He helped develop some algorithms, especially the Monte Carlo method. In the late 1940s, he began to study automata theory, general logic theory and self-replication system. At the last moment of his life, he made a profound comparison between natural automata and artificial automata. After his death, his unfinished manuscript was published in the name of computer and human brain in 1958. Von Neumann's major works are included in The Complete Works of Von Neumann (6 volumes, 196 1). Whether in pure mathematics or applied mathematics research, von Neumann has shown outstanding talents and made many far-reaching and significant achievements. It is his characteristic to constantly change the research theme and succeed repeatedly in the cross-infiltration of several disciplines. To put it simply, his essential contributions are two points: binary thought and program memory thought. Looking back on the brilliant development of science and technology in the 20th century, one of the most outstanding mathematicians in the 20th century, von Neumann, cannot be ignored. As we all know, the electronic computer invented by 1946 has greatly promoted the progress of science and technology and social life. In view of von Neumann's key role in the invention of electronic computers, he is praised by westerners as "the father of computers". In economics, he also. In the field of physics, the Mathematical Basis of Quantum Mechanics written by von Neumann in 1930s has proved to be of great value to the development of atomic physics. He also has considerable attainments in chemistry and obtained a university degree from the Chemistry Department of Zurich Institute of Technology. Like Hayek, a Jew, he is undoubtedly one of the greatest generalists of the last century. John Von Neumann

Von Neumann has done pioneering work and made great contributions in many fields of mathematics. Before World War II, he mainly engaged in the research of operator theory and set theory. 1923' s paper on the over-limit ordinal number in set theory shows von Neumann's unique way and style of dealing with the problem of set theory. He axiomatized set theory, and his axiomatic system laid the foundation of axiomatic set theory. Many important concepts, basic operations and important theorems in set theory are derived by algebraic methods. Especially in a paper in 1925, von Neumann pointed out that there are undecidable propositions in any axiomatic system. 1933, von Neumann solved Hilbert's fifth problem. It is proved that local Euclidean compact groups are Lie groups. 1934, he unified the compact group theory and Bohr's almost periodic function theory. He also has a deep understanding of the structure of general topological groups, and clearly points out that its algebraic structure and topological structure are consistent with real numbers. He made pioneering work in operator algebra and laid its theoretical foundation. Thus, a new branch of mathematics, operator algebra, is established. This branch is called von Neumann algebra in contemporary mathematical literature. This is a natural extension of matrix algebra in finite dimensional space. Von Neumann also founded another important branch of modern mathematics-game theory. 1944, he published a basic and important paper, Game Theory and Economic Behavior. This paper expounds the pure mathematical form of game theory and its application in actual game. This paper also contains teaching ideas such as statistical theory. Von Neumann has done important work in lattice theory, continuous geometry, theoretical physics, dynamics, continuum mechanics, meteorological calculation, atomic energy and economics. Von Neumann's greatest contribution to mankind is the pioneering work of computer science, computer technology and game theory in numerical analysis and economics. Now it is generally believed that ENIAC computer is the first electronic computer in the world. It was developed by American scientists and started running in Philadelphia on February 1946. In fact, the "Crosas" computer developed by British scientists Tommy and Fei Rawls was more than two years earlier than the Eniac computer. On1944 65438+1October 10, it was put into operation in Blackley Park. ENIAC machine proves that electronic vacuum technology can greatly improve computing technology. But the ENIAC machine itself has two major shortcomings: (1) has no memory; (2) Controlled by the wiring board, even if it has to overlap for several days, the calculation speed will be offset by this work. Moakley and eckert. The ENIAC machine development team obviously felt this, and they also wanted to start developing another computer as soon as possible in order to improve it. From 65438 to 0944, Neumann participated in the development of atomic bombs, which involved extremely difficult calculations. When studying the nuclear reaction process, we should give a "yes" or "no" answer to the propagation of a reaction. Solving this problem usually requires billions of mathematical operations and logical instructions. Although the final data is not required to be very accurate, all intermediate operations are essential and should be as accurate as possible. For this reason, his Los Alamos laboratory employs more than 100 female calculators, and it is still far from meeting the needs by using desktop computers to calculate from morning till night. Endless numbers and logical instructions suck up human wisdom and energy like a desert. Neumann, who was troubled by computers, learned about the development plan of ENIAC computer by a very accidental opportunity. Since then, he devoted himself to the great cause of computer development and established the greatest achievement in his life. 1one day in the summer of 944, Neumann happened to meet Goldstein while waiting for the bus at the train station and had a short talk with him. At that time, Goldstein was the military director of American Ballistic Laboratory, and he participated in the development of ENIAC computer. During the conversation, Goldstein told Neumann about the development of ENIAC. The visionary Neumann was attracted by this development plan, and he realized the far-reaching significance of this work. Von Neumann was introduced to Eniac Machine Development Group by Captain Golds Ding, and then he led this group of innovative young scientific and technological personnel to a higher goal. 1948+0945, on the basis of discussion, a brand-new "stored program general electronic computer scheme"-edvac (abbreviation of electronic discrete variable automatic computer) was published. In this process, von Neumann showed his strong basic knowledge of mathematics and physics, and gave full play to his advisory role and his ability to explore problems and analyze comprehensively. Neumann drafted a 10 1 page summary report entitled "Draft Report on EDVAC". The report introduces the new ideas of making electronic computers and programming extensively and concretely. This report is an epoch-making document in the history of computer development. It announced to the world the beginning of the era of electronic computers. The EDVAC scheme clearly establishes that the new machine consists of five parts, including arithmetic unit, logic control device, memory and input/output device, and describes the functions and relationships of these five parts. In the report, Neumann further demonstrated two major design ideas in EDVAC, which set a milestone for computer design. One of the design ideas is binary. According to the characteristics of bistable operation of electronic components, he suggested using binary in electronic computers. The report mentions the advantages of binary system and predicts that adopting binary system will greatly simplify the logic circuit of the machine. The basic working principle of the computer used now is stored program and program control, which was put forward by the world famous mathematician von Neumann. Von Neumann, a Hungarian-born American mathematician, is called "the father of computers". Practice has proved the correctness of Neumann's prediction. Nowadays, the application of logic algebra has become an important means to design electronic computers. The main logic circuits used in EDVAC have been used all the time, but the engineering method to realize logic circuits and the analysis method of logic circuits have been improved.

Program memory

Program memory is another masterpiece of Neumann. Through the investigation of ENIAC, Neumann keenly grasped its biggest weakness-no real memory. ENIAC has only 20 registers, its program is extrapolated, and its instructions are stored in other circuits of the computer. In this way, before solving the problem, you need to get all the necessary instructions and manually connect the corresponding circuits. This preparation takes hours or even days, while the calculation itself takes only a few minutes. There is a great contradiction between the high speed of calculation and the manual operation of the program In order to solve this problem, Neumann put forward the idea of program memory: the operation program is stored in the memory of the machine, and the programmer only needs to look for the operation instructions in the memory, and the machine will calculate by itself, so that it is not necessary to reprogram every problem, which greatly speeds up the operation process. This idea marks the realization of automatic operation and the maturity of electronic computer, and has become the basic principle of electronic computer design. 1In July and August, 1946, when von Neumann, Goldstein and Boxer were developing IAS computers for the Institute of Advanced Studies of Princeton University, they also put forward a more perfect design report, Preliminary Research on Logic Design of Electronic Computers. These two documents with both theory and concrete design have set off a "computer craze" all over the world for the first time. Their comprehensive design of EDVAC is the famous "von Neumann machine", and its center is the principle of storing programs-instructions and data are stored together. This concept is called "a milestone in the history of computer development". It marks the real beginning of the electronic computer era and guides the future computer design. Everything in nature is constantly developing. With the progress of science and technology, today people realize the shortcomings of "von Neumann Machine", which hinders its development. And put forward the viewpoint of "non-von Neumann machine". Von Neumann also actively participated in the popularization and application of computers, and made outstanding contributions in how to write programs and engage in numerical calculation. Von Neumann won the Potsdam Prize of the American Mathematical Society in 1937. 1947 won the US Presidential Medal of Meritorious Service and the US Navy Outstanding Citizen Service Award; 1956 was awarded the Medal of Freedom, Einstein Memorial Award and Fermi Award by the President of the United States.

Related books

After von Neumann's death, this unfinished manuscript was published in the name of computer and human brain in 1958. The main works are included in the Complete Works of von Neumann, published in 196 1. In addition, the book Game Theory and Economic Behavior published by von Neumann in the 1940s made him erect a monument in the fields of economics and decision science. He is recognized by economists as the father of game theory. At that time, young johnf nash began to research and develop this field when he was studying at Princeton University, and won the 1994 Nobel Prize in Economics for his outstanding contribution to game theory.

Edit this life experience

Neumann, a famous Hungarian-American mathematician in the first half of his life. 1903 12.3 was born in a Jewish family in Budapest, Hungary. Max, von Neumann's father, is young and handsome. With diligence, wit and good management, he was one of the bankers in Budapest when he was young. Von Neumann's mother is a kind woman, virtuous and docile, with a good education. Von Neumann showed a mathematical genius since he was a child, and there are many legends about his childhood. Most legends are talking about von Neumann's amazing speed of absorbing knowledge and solving problems since childhood. At the age of six, I can mentally calculate the multiplication and division of eight figures, master calculus at the age of eight, and understand the essence of Bohr's masterpiece Function Theory at the age of twelve. The essence of calculus is the mathematical analysis of infinitesimal. For a long time, human beings have been exploring finite and infinite and their relationship. /kloc-Calculus discovered by Newton Leibniz in the 0/7th century is a great and exciting achievement of human exploration. It has been the teaching content of colleges and universities for 300 years. With the development of the times, calculus is constantly changing its form, its concept has become accurate, its basic theory has been solid, and there are even many concise and appropriate expressions. But in any case, it is rare for an eight-year-old child to understand calculus. Although the above rumors are not credible, von Neumann's intelligence is extraordinary, which is the unanimous view of those who know him. 19 14 summer, John entered the college preparatory class. On July 28th, 2008, Austria-Hungary declared war on Serbia, which started the First World War. Due to years of war and turmoil, the von Neumann family left Hungary and then returned to Budapest. Of course, his studies will also be affected. However, in the graduation exam, von Neumann's performance is still among the best. 192 1 year, von Neumann was already a mathematician when he passed the "mature" exam. His first paper was written with Fichte, when he was less than 18 years old. Max asked someone to dissuade von Neumann of Kloc-0/7 from specializing in mathematics for economic reasons. Later, the father and son reached an agreement that von Neumann would study chemistry. In the next four years, Von Neumann registered as a student of mathematics at Budapest University, but he didn't attend classes, but just took the exam on time every year. At the same time, von Neumann entered the University of Berlin (192 1 year) and 1923 went to study chemistry at the Federal Institute of Technology in Zurich, Switzerland. From 65438 to 0926, he obtained a university degree in chemistry in Zurich. 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. Von Neumann's learning style of taking exams instead of attending classes was very special at that time, which was completely irregular in Europe. But this irregular learning method is very suitable for von Neumann. During his study in Berlin University, von Neumann was carefully cultivated by chemist hubbell. Haber is a famous German chemist who won the Nobel Prize for synthesizing ammonia. 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 smart wisdom and unique cultivation, von Neumann is growing sturdily. By the time he finished his student days, he had explored some frontier fields 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 articles on set theory, algebra and quantum theory. 1927, von Neumann went to Lviv, Poland to attend the congress of mathematicians. At that time, his work on the basis of mathematics and set theory was already very famous. 1929, von Neumann became a part-time lecturer at the University of Hamburg. 1930 went to America for the first time and became a visiting lecturer at Princeton University. The United States, which is good at pooling talents, soon hired von Neumann as a visiting professor. Von Neumann once calculated that German universities have few vacancies to look forward to. According to his typical reasoning, there are three professors appointed in three years, and there are as many as 40 competing lecturers. In Princeton, von Neumann returned to Europe every summer until 1933 when he became a professor at the Institute for Advanced Studies in Princeton. At that time, the Institute for Advanced Studies hired six professors, including Einstein, and von Neumann, who was only 30 years old, was the youngest among them. In the early days of the Institute of Advanced Studies, European tourists will find an excellent informal and strong research atmosphere here. The professor's office is located in the "beautiful building" of the university, with stable life, active thoughts and high-quality research results emerging one after another. It can be said that there are the most talents with mathematical minds in history. 1930, von Neumann married Marida Kvasz. Their daughter Marina was born in Princeton on 1935. As we all know, von Neumann's family often holds lasting social gatherings. Von Neumann divorced his wife in l937, married Clara Dan in 1938 and returned to Princeton together. Dan studied mathematics with von Neumann and later became an excellent programmer. After he married Clara, von Neumann's home is still a place where scientists meet, and it is still so hospitable, where everyone will feel an atmosphere of wisdom. 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. Since 1943, he has been a consultant in the manufacture of atomic bombs, and he still served in many government departments and committees after the war. 1954, he became a member of the American atomic energy commission. Strauss, Von Neumann's long-time friend and chairman of the Atomic Energy Commission, once commented on him: From his appointment to the late autumn of 1955, Von Neumann did a beautiful job. He has an ability that people can't catch up with, and the most difficult problem is in his hands. Will be broken down into seemingly simple things ... in this way, he greatly promoted the work of the atomic energy commission. In his later years, Von Neumann was in good health, but he began to feel very tired in 1954 due to his busy work. 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.

Set theory, mathematical basis

Von Neumann's first paper, co-authored with Fichte, is a generalization of the Fehn's theorem of Chebyshev polynomial root method, and the date is 1922. At that time, Von Neumann was less than 18 years old. Another article discusses uniformly dense series written in Hungarian. The choice of topic and the simplicity of proof technology reveal the intuitive combination of von Neumann's algebraic skills and set theory. 1923, when von Neumann was a university student in Zurich, he published a paper exceeding the ordinal number. The first sentence of the article bluntly said, "The purpose of this article is to make Cantor's concept of ordinal number concrete and precise. His definition of ordinal number has been widely adopted now. It is von Neumann's wish to explore axiomatization vigorously. From about l925 to l929, most of his articles tried to carry out this axiomatic spirit, even in theoretical physics research. At that time, his expression of set theory was particularly informal. At the beginning of his doctoral thesis on axiomatic system of set theory in 1925, he said, "The purpose of this thesis is to give an axiomatic exposition of set theory logically and irreproachable." Interestingly, von Neumann foresaw the limitations of any form of axiomatic system in his paper, which vaguely reminded people of the incompleteness theorem proved by Godel later. Professor frankl, a famous logician and one of the founders of axiomatic set theory, once commented on this article: "I can't insist that I have understood everything, but I can safely say that this is an outstanding work, and I can see a giant through him". 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. It seems that this is not far from the final answer Hilbert wants. It was at this time that Godel proved the incompleteness theorem in 1930. 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.

The Three Most Important Math Tasks

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. 1927 von Neumann has been engaged in the research work in the field of quantum mechanics. He co-published a paper "Fundamentals of Quantum Mechanics" with Silvito and Nordam. This paper is based on Hilbert's lecture on the new development of quantum mechanics in the winter of 1926. Nordem helped prepare the lecture, and von Neumann devoted himself to the mathematical formalization of the subject. The purpose of this paper is to replace the exact function relation in classical mechanics with probability relation. Hilbert's metamathematics and axiomatic scheme have been put into use in this dynamic field, and the isomorphic relationship between theoretical physics and corresponding mathematical system has been obtained. We can't overestimate the historical importance and influence of this article. In his article, Von Neumann also discussed the operational outline of observable operators in physics and the properties of self-adjoint operator. There is no doubt that these contents constitute the prelude to the book Mathematical Basis of Quantum Mechanics. 1932 The world-famous springer Publishing House published his Mathematical Basis of Quantum Mechanics, which is one of von Neumann's main works. The first edition is in German, the French edition is published in 1943, the Spanish edition is published in 1949, and the English translation is published in 1955. It is still a classic in this field. Of course, he has also done a lot of important work in quantum statistics, quantum thermodynamics, gravitational field and so on. Objectively speaking, in the history of the development of quantum mechanics, von Neumann made at least two important contributions: Dirac's mathematical treatment of quantum theory was not strict enough in a sense, and von Neumann developed Hilbert operator theory through the study of unbounded operators, which made up for this deficiency; In addition, von Neumann clearly pointed out that the statistical characteristics of quantum theory are not caused by the unknown state of the observer engaged in measurement. With the help of Hilbert space operator theory, he proved that all the assumptions of quantum theory, including the correlation of general physical quantities, must lead to this result. For von Neumann's contribution, Wegner, the winner of the Nobel Prize in Physics, once commented: "His contribution to quantum mechanics ensures his special position in the field of contemporary physics." In von Neumann's works, operator spectrum theory and operator ring theory in Hilbert space occupy an important position, and the articles in this field account for about one-third of his published papers. They include a very detailed analysis of the properties of linear operators and an algebraic study of operator rings in infinite dimensional space. 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. During the period of 1936 ~ 1940, von Neumann published six papers on noncommutative operator rings, which can be described as the analysis masterpieces of the 20th century, and its influence continues to this day. Von Neumann once said in "Mathematical Basis of Quantum Mechanics" that the ideas first put forward by Hilbert can provide an appropriate foundation for the quantum theory of physics without introducing new mathematical ideas into these physical theories. His research achievements in operator rings have achieved this goal. Von Neumann's interest in this subject runs through his whole career. An amazing growth point of operator ring theory is continuous geometry named by von Neumann. The dimensions of general geometry are integers 1, 2, 3, etc. As von Neumann saw in his works, it was actually rotation group who decided the dimensional structure of a space. So the dimension can no longer be an integer. Finally, the geometry of continuous series space is proposed. 1932, von Neumann published a paper on ergodic theory, which solved the proof of ergodic theorem and expressed it with operator theory. This is the first accurate mathematical result obtained in the whole research field of ergodic hypothesis of statistical mechanics. Von Neumann's achievements may once again be attributed to his mastery of mathematical analysis methods influenced by set theory and the methods he created in the study of Hilbert operators. It is one of the most influential achievements in the field of mathematical analysis in the 20th century, and it also marks that a field of mathematical physics has begun to approach the general research of accurate modern analysis. In addition, von Neumann has also made many achievements in mathematical fields such as real variable function theory, measure theory, topology, continuous group and lattice theory. In the famous speech 1900, Hilbert raised 23 questions for mathematical research in the 20th century, and von Neumann also contributed to solving Hilbert's fifth question.

Edit this paragraph of general applied mathematics.

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.