(4) Reasons for declaring "Mathematical Breakthrough Award"

1983 Professor Wang first put forward the semi-analytical function theory in the world, and 1988 first put forward and systematically established the analytical function theory of * * * yoke, and successfully applied these two theories to electric field, magnetic field, fluid mechanics, elasticity mechanics and other fields. These two theories have been cited and developed by many experts and scholars, resulting in the emergence of a series of mathematical branches, such as bianalytic functions, polyharmonic functions, multi-analytic functions (k-order analytic functions), semi-bianalytic functions, semi-yoke analytic functions and corresponding boundary value problems, differential equations, integral equations, etc., and this development momentum is strong and unstoppable. This is also an unprecedented large-scale original work made by China scholars on mathematics in the developing world.

Professor Wang's semi-analytic function and * * * yoke analytic function theory and its influence are: the generalization and development of analytic function theory initiated by Cauchy, Riemann, Weisstras, Gauss, Euler and other mathematicians in the world. 18, 19 and even in the 20th century, almost all mathematicians left their footprints in the field of analytic functions.

Another great contribution of Professor Wang to mathematics is that Professor Wang pointed out that social statistics describe variables, while mathematical statistics describe random variables. Variables and random variables are two mathematical concepts that are different and related and can be transformed into each other under certain conditions. Professor Wang's exposition of is a great discovery in mathematics. We know that the concept of "variable" was first put forward by the famous mathematician Descartes in17th century, while the random variable was first put forward by Soviet scholars after 1930s. The difference between these two concepts is three centuries. Up to Professor Wang, no second person in the world has put forward the connection, difference and mutual transformation between variables and random variables.

As we know, the introduction of variables has brought about the emergence and development of a series of major mathematical disciplines, such as function theory, equation theory and calculus, and then triggered the rise of a new industrial revolution in the world. The introduction of random variables laid the foundation for the emergence and development of probability theory, mathematical statistics, information theory, system theory, cybernetics and other sciences, thus triggering the birth of a high-tech era on a global scale. It can be seen that the concepts of variables and random variables are very valuable, so it is not an exaggeration for Professor Wang to put forward the significance of the connection, difference and mutual transformation between variables and random variables for the first time in the world.

Let's return to the theory of "the unity of social statistics and mathematical statistics". Professor Wang pointed out that social statistics describe variables, while mathematical statistics describe random variables. In this way, Professor Wang accurately defined the research scope of social statistics and mathematical statistics, and the relationship that can be transformed into each other under certain conditions, which is the greatest contribution to statistics. It has ended the situation of dozens or even hundreds of statistical scuffles in the past 400 years and brought it back on track.

Because variables appear constantly and last forever, social statistics will not die out, but will continue to grow and develop. Mathematical statistics will also develop and grow because of the continuous emergence of random variables. However, the study of random variables is generally much more complicated than the study of variables, and until today, the study of mathematical statistics is still at a low level and more complicated to use. In the long run, the study of random variables will eventually be transformed into the study of variables, which is the same as why we usually study complex problems into several simple problems. Because social statistics describe variables, and the scope of variable description is extremely wide, it is by no means what some mathematical statisticians say: social statistics only do simple addition, subtraction, multiplication and division. Theoretically speaking, social statistics should cover the operation of most mathematical disciplines except mathematical statistics. For example, the most practical calculus is also included, because calculus also describes variables. Therefore, the theory of "the unity of social statistics and mathematical statistics" put forward by Professor Wang fundamentally corrects the wrong theory that the statistical community has underestimated social statistics for a long time, and shows the broad prospects of social statistics in theory and application.

Since statistics has now risen to the position of methodology, the new statistical theory will play an inestimable role in the development of all sciences, which shows that Professor Wang's discovery in mathematics is huge, not remarkable.