The 20th century is coming, and 2 1 century is coming. When we stand on the threshold of the turn of the century and review the brilliant development of science and technology in the 20th century, we cannot but mention von Neumann, one of the most outstanding mathematicians in the 20th century. As we all know, the electronic computer invented by 1946 has greatly promoted the progress of science and technology and social life. In von Neumann's view,
John von Numa (1903- 1957), a Hungarian American, was born in Budapest, Hungary on February 28th, 1903. His father is a banker, his family is very rich, and he attaches great importance to children's education. Von Neumann is talented and has many interests. Reading never forgets anything. It is said that he was able to chat with his father in ancient Greek when he was six years old, and he mastered seven languages in his life. He is best at German, but when he thinks about ideas in German, he can translate them into English at the speed of reading. He can quickly repeat the contents of books and papers he has read word for word, and still do so a few years later. 1911-1921von Neumann made his mark when he was studying in Lu Se Lun Middle School in Budapest, and was highly valued by teachers. Under the individual guidance of Mr Fichte, he co-published his first mathematical paper. At this time, von Neumann was less than 18 years old. 192 1- 1923, he studied at the University of Zurich. Soon after, he got a doctorate in mathematics from Budapest University with 1926. Von Neumann was only 22 years old at this time .30438+0927. 1930, he accepted the position of visiting professor at Princeton University and went to the United States. 193 1 became a tenured professor of the school. 1933 transferred to the Institute of Advanced Studies of our school and became one of the first six professors. He has 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. From 1938 to 0954, he was a member of the American Atomic Energy Commission. 195 1 to 1953, President of the American Mathematical Society.
1954 In the summer, von Neumann was diagnosed with cancer. 1957 died in Washington on February 8, at the age of 54.
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, nose 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. His axiomatic system laid the foundation of axiomatic set theory. Starting from axioms, he deduced many important concepts, basic operations and important theorems in set theory 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, that is, he proved that a locally Euclidean compact group is a Lie group. 1934, he unified the compact group theory with 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 has done pioneering work on his subalgebra, but this is uncertain. 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. 1948+0944 published a fundamental and important paper Game Theory and Economic Behavior. This paper includes the explanation and practice of pure mathematical form of game 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 his pioneering work in computer science, computer technology and numerical analysis.
Now it is generally believed that ENIAC is the first electronic computer in the world. Developed by American scientists, February 1946 began to run in Philadelphia. In fact, the "Crosas" computer developed by British scientists such as Tommy and Rauls came out more than two years before ENIAC. 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) It is controlled by the wiring board, and even needs to be connected to the sky, so the calculation speed is 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.
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.
The EDVAC scheme clearly establishes that the new machine consists of five parts: arithmetic unit, logic control device, memory and input/output device, and describes the functions and relationships of these five parts. EDVAC machine has two remarkable improvements, namely: (1) it uses binary, not only data, but also instructions; (2) After the stored program is established, instructions and data can be put in the memory together and processed in the same way, which simplifies the structure of the computer and greatly improves the speed of the computer. During July and August of 2008+0946, when von Neumann, Goldstein and Boxer developed IAS computer for the Institute of Advanced Studies of Princeton University on the basis of the EDVAC scheme, they put forward a more perfect design report, Preliminary Study on Logic Design of Electronic Computer. 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 idea is the famous "von Neumann machine", and its center is the stored program.
Principle-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 that the deficiency of "von Neumann Machine" hinders the further improvement of computer speed. 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.
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 19 1.
Math Wizards-Top of Galois Page
1832 On the morning of May 30, a young man was unconscious near Lake Glazer in Paris. Passing farmers judged that he was seriously shot after a duel, so they sent the unknown young man to the hospital. He died at ten o'clock the next morning. The youngest and most creative mind in the history of mathematics stopped thinking. People say that his death has delayed the development of mathematics for decades. This young man is Galois, who died before 2 1 year old.
Galois was born in a town not far from Paris. His father is the headmaster of the school and has served as mayor for many years. The influence of family makes Galois always brave and fearless. 1823, 12-year-old galois left his parents to study in Paris. Not content with boring classroom indoctrination, he went to find the most difficult mathematics original research by himself. Some teachers also helped him a lot. Teachers' evaluation of him is "only suitable for working in the frontier field of mathematics".
1828, 17-year-old Galois began to study the theory of equations, and founded the concept and method of "permutation group", which solved the problem of solving equations that had been a headache for hundreds of years. Galois's most important achievement is that he put forward the concept of "group" and changed the whole face of mathematics with group theory. 1829 In May, Galois wrote down his own achievements and submitted them to the French Academy of Sciences, but this masterpiece was accompanied by a series of blows and misfortunes. First, my father committed suicide because he couldn't bear the priest's slander, and then he failed to enter the famous Paris Polytechnic because his defense was simple and abstruse, which made the examiner dissatisfied. As for his paper, he thinks that there are too many new concepts, which are too brief and need to be rewritten; The second draft with detailed derivation was missing because the reviewer died of illness; The third paper 183 1 submitted in June was rejected because the reviewers could not fully understand it.
On the one hand, young Galois pursues the true knowledge of mathematics, on the other hand, he devotes himself to the cause of social justice. 183 1 In the "July Revolution" in France, Galois, as a freshman in a normal university, led the masses to protest against the autocratic rule of the king and was unfortunately arrested. In prison, he contracted cholera. Even under such harsh conditions, Galois continued his mathematical research after he was released from prison and wrote a paper for publication. Shortly after he was released from prison, he died in a duel because he was involved in a boring "love" entanglement.
After Galois died in 16, his 60-page manuscript was published and his name spread all over the scientific community.
"God of Mathematics" —— Archimedes' Home Page
Archimedes was born in Syracuse, Sicily, at the southern tip of the Italian peninsula in 287 BC. Father is a mathematician and astronomer. Archimedes had a good family upbringing since childhood. 1 1 years old, was sent to study in Alexandria, the cultural center of Greece. In this famous city known as the "Capital of Wisdom", Archimedes Job collected books and learned a lot of knowledge, and became a protege of Euclid students erato Sese and Cannon, studying geometric elements.
Later, Archimedes became a great scholar who was both a mathematician and a mechanic, enjoying the reputation of "the father of mechanics". The reason is that he discovered the lever principle through a lot of experiments, and then deduced many lever propositions through geometric derivation and gave strict proofs. Among them is the famous Archimedes principle, and he has also made brilliant achievements in mathematics. Although there are only a dozen works by Archimedes, most of them are geometric works, which have played a decisive role in promoting the development of mathematics.
Sand Calculation is a book devoted to the study of calculation methods and theories. Archimedes wanted to calculate the number of grains of sand in a big sphere full of the universe. He used a very strange imagination, established a new counting method of order of magnitude, determined a new unit, and put forward a model to represent any large number, which is closely related to logarithmic operation.
Using circumscribed circle and 96-plane inscribed circle to measure the circle, the pi is obtained as follows: