Wu Wenjun is one of the founders of mathematical mechanization research in China, an academician of China Academy of Sciences and the Third World Academy of Sciences. He used to be chairman of the Chinese Mathematical Society (1985 ~ 1987), director of the Department of Mathematics and Physics of China Academy of Sciences (1992 ~ 1994), member and member of the Standing Committee of Chinese People's Political Consultative Conference (1979 ~1).
Wu Wenjun has made outstanding contributions in the fields of topology, automatic reasoning, machine proof, algebraic geometry, the history of Chinese mathematics and game theory, and enjoys a high reputation at home and abroad. He has made a series of important achievements in the study of indicator class and embedded class of topology. Indicator class and embedded class are the basic work in topology and have many important applications. His "Wu method" has a great influence in the field of international machine certification and has a wide range of important application values. At present, the mainstream symbolic computing software in the world has realized Professor Wu Wenjun's algorithm.
Wu Wenjun's great contribution to mathematics.
In topology, Wu Wenjun has made a series of achievements in the field of representation and embedding, obtained many famous formulas, and pointed out the wide application of these theories and methods. He also has creative work on topological invariants, algebraic manifolds and other issues. From 65438 to 0956, Wu Wenjun won the first prize of China Natural Science Award for his outstanding achievements in the representation and embedding of topology.
In the aspect of mathematical mechanization or machine proof, Wu Wenjun started with elementary geometry, proved a kind of difficult theorems on the computer, found some new theorems at the same time, and further discussed the theorem proof of differential geometry. A new method of proving and discovering geometric theorems with machines is proposed. This work has opened up a new field of mathematical research and will have a far-reaching impact on the revolution of mathematics. 1978, this achievement won the major scientific and technological achievement award of the National Science Conference.
In the history of Chinese mathematics, Wu Wenjun thought that the characteristics of ancient mathematics in China were: starting from practical problems, analyzing and improving, then abstracting general principles, principles and methods, and finally achieving the purpose of solving a large class of problems. He also put forward incisive views on the achievements of China's ancient mathematics in number theory, algebra and geometry.
Wu Wenjun's mathematical research activities can be divided into two periods, involving several fields of mathematics. From 1947 to 1970s, I mainly studied algebraic topology, and my contributions mainly included two aspects:
Indicative class research
Through the Grassmann manifold, this paper systematically discusses the demonstrative classes introduced by Steefel of Switzerland, Whitney of the United States, Pontrogakin of the Soviet Union and Chen Shengshen in the 1930s, determines the names, probes into the corresponding relations, and applies them to the construction of manifolds. The homology class he introduced was later called Wu's demonstrative class in the literature, and his two formulas containing topological invariance and homotopy invariance were later called Wu's formula. Because of their basic importance, these results have been widely used in many problems, such as1Dold in Germany in the 1950s,1Hirzebruch in Germany in the 1960s and Novikov in the Soviet Union, for which they won the Fields Prize.
Research on indicator embedded class
He introduced a general construction method with homotopy topological invariants, and systematically applied it to the embedding problem, introduced the complex shape embedding class, and studied the immersion problem and the homotopy problem in the same way, and introduced similar immersion classes and trace classes. Haefiger of Switzerland listened to his lecture on the above-mentioned embedded classes in 1958, and extended the embedding problem in 196 1, thus becoming a major topology expert in Switzerland. Smale of the United States applied his work to Poincare conjecture with dimension greater than 4, and won the Fields Prize for it. Later, he applied the results of embedding class to the circuit routing problem, and gave a new criterion for judging the planarity of linear graphs, which was completely different from the previous criterion in nature, especially computable.
It should be noted that the importance of his research results completed before 1956 was revealed many years later, and it is still widely cited in the world.
Wu Wenjun's later mathematical research began in 1976, mainly engaged in machine proof and mathematical mechanization.
The method of proving geometric theorems by computer is fundamentally different from the commonly used methods based on mathematical logic, showing unparalleled advantages, changing the face of automatic reasoning research in the world, being called the pioneering work in the field of automatic reasoning, and thus winning the Gerbrand Award for Outstanding Achievement in Automatic Reasoning. The following is an introduction and evaluation of Wu Wenjun's work at the 14 International Conference on Automatic Reasoning.
Wu Wenjun is famous for the method he invented in 1977 in the field of automatic reasoning. This method is a breakthrough in the field of automatic proof of geometric theorems.
The automatic proof of geometric theorems was first studied by HerbertGerlenter in the 1950s. Although some meaningful results have been achieved, little progress has been made in this field in the twenty years before the appearance of Wu method.
In a few fields of automatic reasoning, this passive situation is completely reversed by one person. Wu Wenjun is obviously such a person. Wu's work turned an unsuccessful geometric theorem proving automatic reasoning field into one of the most successful fields. In a few fields, we can attribute machine proof to a person's work. Geometric theorem proving is such a field.
Wu method for solving nonlinear algebraic equations introduced by Wu Wenjun is one of the most complete methods for solving exact solutions of algebraic equations. It has been successfully used to solve many problems and has been implemented in popular symbolic computing software. There is also a special software package for Wu method in the POSSO project funded by the European Union.
Wu method has also been applied to many high-tech fields and achieved a series of international leading results. Including surface modeling, robot mechanism position analysis, intelligent CAD system (computer aided design), robot, image compression and so on.
At the end of 1980s, he put forward the full-order method of partial differential-algebraic equations, which is a complete constructive method to deal with partial differential-algebraic equations at present. This method has been applied to the machine proof of differential geometry theorem and the solution of partial differential equations. The classical numbers of algebraic clusters, which are usually limited to the case without singularities, are extended to the classical numbers and Chen Shu with arbitrary singularities, and the definition of computability is formed, which forms a new chapter in the mechanization of algebraic geometry.
He gave the zero-point structure theorem of multivariate polynomial groups, which is an important symbol of the development of constructive algebraic geometry.