Xu Lizhi is outgoing, enthusiastic and open-minded. These characteristics are embodied in his extensive knowledge, interesting research results, clear papers and few obscure ones.
Xu Lizhi's research scope is very wide, and the research depth in related fields is also considerable. It may be superficial to look for the answer only from his profound knowledge, wide interests and brilliant talents. As Lu You pointed out when talking about poetry, "Kung Fu lies outside poetry", and Xu Lizhi's attainments in mathematics should also look for answers outside mathematics. In this way, we can not only find his non-intellectual factors such as ambition, perseverance and interest, but also find the necessary qualities for success. It is precisely because of his profound academic thought system, including mathematical education thought, mathematical research method, mathematical aesthetics, mathematical philosophy, etc., that he has formed a complete mathematical system theory-a general methodology between philosophy and mathematical science. Unfortunately, the theory of mathematical systems is only hidden in the minds of a few "strategic" and "tactical" mathematicians. If we can extract it, sort it out systematically and dedicate it to the world, its
Professor Xu Lizhi is trying his best to do it sincerely. He not only involved philosophy in the research of mathematical foundation, but also used philosophical thoughts to guide scientific research. He skillfully analyzes the contradictory transformation process of concept development and is good at discovering the * * * in personality. He often abstracts general concepts from individual concepts and draws general conclusions from special conclusions. He firmly believes that the source of mathematics lies in the objective world, and the achievements of predecessors are only the flow of mathematics. He believes that beauty is not only the exclusive product of writers and artists, but also the best realm of mathematical exploration. He analyzed the harmonious beauty and singular beauty in mathematics, and pointed out that "beauty is true beauty, but beauty is not necessarily true", which is a necessary condition to test the authenticity of mathematical achievements. On the one hand, he proposed that mathematical intuition = aesthetic intuition+relational intuition+truth perception; On the other hand, he supplemented mathematical creativity with the logical product formula put forward by psychologists: creativity = divergent thinking ability × perspective essential ability × effective knowledge. Xu believes in Paulia's view that mathematical knowledge has the duality of deduction and induction, and vigorously promotes his educational thought. Xu not only attaches importance to the logical thinking process of strict deduction, but also is good at using intuitive judgment method based on numerical calculation. In view of a large number of mapping means and inverse problem-solving phenomena in the development of mathematics, he summed up the general principles of relationship, mapping and inverse for the first time, that is, the so-called RMI principle, which has general methodological guiding significance. At home, he first opened a course of mathematical methodology and wrote a book, which is by no means a simple tick to concretize philosophical methodology in mathematical research. It is the perfect combination of mathematics and research methods, which embodies a series of painstaking management experiences such as "eating grass, ruminating and digesting". He advocates that mathematics students should learn literature well and care about art, because this is not only one of the means to improve their cultural quality, but also because there are many internal similarities between mathematics research and literary and artistic creation, which is conducive to the exertion of imagination and creativity.
It is not difficult to see that Xu Lizhi's extensive knowledge is closely related to his extensive interests and extensive reading. In fact, his extensive achievements are based on his "outline" (taking mathematical system theory as the key link) and "collar" (mathematics field), and he has built his own knowledge structure.
Hua once said: "among my disciples, my research field is the widest and my thoughts are the most active." China's evaluation is just right. However, when it comes to his disciples, he is just an ordinary student of Hua, just as Xu is also a student of Xu He. Strictly speaking, Xu Lizhi has no teachers-no tutors, only teachers. In contrast, young people nowadays are enviable. When Xu Lizhi was a child, there was no tutor. He finds his own topic, sets his own direction, conducts his own research and contributes his own articles. He didn't rely on any "big trees" to "enjoy the cool". Later, Xu found so many research directions with his own knowledge and achieved many results.
Although Xu himself has no tutor, his "direct disciple" has a tutor who is as amiable as him. Xu Lizhi is approachable, unassuming, pays attention to academic democracy, is not conservative in knowledge, and despises the meanness of private knowledge. He is convinced that knowledge belongs to all mankind and has no reservations about seekers. In the eyes of his disciples, he is a mentor and a friend, and he forgets to make friends. He also asked young people not to have only one. Instead, we should learn from others. He gave scientific research and teaching guidance to young and middle-aged teachers, and his young and middle-aged teaching assistants made rapid progress, such as Wang, Zhu Wuyi, Lin and others. Among them, Wang Yizhi is a doctoral supervisor. 1982, Wang, Liang and Zhou Yunshi won the third prize of National Natural Science. Is Xu Lizhi right? Guide and help them solve their academic difficulties and be willing to cooperate with them. Wang Xinghua, a middle-aged doctoral supervisor at Hangda University, has a close relationship with Xu Lizhi. The second edition of Selected Lectures on Mathematical Analysis Methods and Examples co-authored by Xu and Wang won the National Excellent Textbook Award 1988. Xi 'an's seminar on approximation theory has been directed by Xu Lizhi.
After graduation, Zhu Wu was detained as an assistant in Xu Lizhi. Later, Zhu was wrongly classified as a "Rightist" and sent back to his hometown in Jiangsu. Although Xu Lizhi was in adversity and his salary dropped by two grades, he still often sent him money to support himself. They wrote more than 400 letters, talking about ideas and learning. They have achieved the same success. Because of Xu Lizhi's extensive research, academic democracy and easygoing, his.
Xu Lizhi has several academic characteristics: keen thinking and being good at capturing the development direction. For example, in the 1960s, he emphasized that approximation theory should be pluralistic and clear. Later, the international development in this field showed that his views were ahead. He has a wide range of interests and likes to browse other people's works, but his thoughts are not bound by others and he can "go in and out"; He is not conservative and willing to support new things. For example, some scholars at home and abroad think that fuzzy set theory is superficial and worthless, and non-standard analysis is of little significance. However, Xu Lizhi saw their great prospects through the "scaffolding" that has not been dismantled in this discipline, and encouraged young people to engage in research in this field. He is devoted to his work, but rich in analogy and good at association, and combines "divergent thinking" with "convergent thinking"; He is not afraid of calculation, but patiently induces laws and verifies conclusions from complex calculations.
The key to his success lies in: young people are determined, poor family and chaotic years have honed his will and made him stronger, while interest in learning has strengthened his will on the other hand; The cultivation of self-study ability laid a solid foundation for him outside the classroom study, especially after reading some classic works on mathematics, he was edified, his ability increased with the accumulation of knowledge, and his creativity was enhanced in his study; In the end, he seized the opportunity of the fork in the road with tenacious perseverance. He has a wide range of interests, active thoughts, always standing on the high ground, and always letting vivid academic views guide his research.