1925, Finnish mathematician Naiwanglinna created a theory in the study of function value distribution theory, which holds that among a large number of common and important functions, most functions take each value in a similar time, with a few exceptions. These abnormal values are called "deficient values". For a long time, the study of "deficient value" has become a major topic in the theoretical study of function value distribution. In addition, when studying the changes of a large number of common and important functions, in some parts of the range of independent variables, the function values are particularly large and the changes are extremely intense, which is called "singular direction" in mathematics. The study of this "singular direction" constitutes another important topic in the theory of function value distribution. In order to solve these two problems, many outstanding experts in the international mathematics field have devoted countless efforts for a long time. Yang Le and Zhang Guanghou, mathematicians in China, in their research, made a breakthrough with a brand-new way of thinking, and finally made a new discovery. They realize that "deficient value" is a whole concept, which reflects the loss and gradual change of function value, while "singular direction" is a local concept. It reflects the situation that the function takes many values and changes dramatically; "Deficiency" and "singular direction" constitute a pair of contradictions. The relationship between them is not antagonistic or exclusive, but a unified concept based on interdependence and organic connection. Their discovery with decades of hard work and wisdom has built a colorful bridge between two long-divided mathematical research fields. From 1965 to 1977, Yang Le and Zhang Guanghou jointly published nearly 10 important papers on function theory, which not only discovered the relationship between "deficient value" and "singular direction", but also completely solved the problem of singular direction distribution that has not been solved in recent 50 years. Their achievements have promoted the development of function theory and caused a sensation in the international mathematics field. International mathematicians call it "Xi Zhang Theorem" or "Xi Zhang Inequality".

1978 On April 13, at the International Mathematics Conference in Zurich, Yang Le reported his and Zhang Guanghou's research results, which aroused strong repercussions. Mathematicians attending the meeting praised this as an "amazing achievement". The founder of modern function value distribution theory, Dutch mathematician Naiwanglinna said to Yang Le, "Just now, you said you came to learn from European mathematicians. I think European mathematicians should learn from you now. " A mathematical research report published in the United States quoted Yang Le and Zhang Guanghou's theorems completely, and evaluated them as "novel and profound". Like Goldbach's conjecture research, it is a "first-class work" in pure mathematics. Ju Leixin, a famous American expert on function theory, said: "Yang Le and Zhang Guanghou are leading a fruitful and prosperous Beijing school."