Zhang Dingming is knowledgeable and enjoys a high reputation in the field of mathematics. He is unique in studying integral equations and functionals. He first obtained the relationship between eigenvalue and singular value of integral equation, and solved the long-standing unsolved problem in the international mathematics field. He proved and popularized the theorems of famous mathematicians such as Dulesgo, Hill and Tamagen, and thus established the theory of combinatorial product kernel, which was highly praised by the mathematical circles at home and abroad. He has published more than 20 academic papers in famous magazines at home and abroad, and has been introduced by authoritative magazines such as Federal German Mathematical Abstracts, Journal of Abstracts of the Former Soviet Union, and American Mathematical Review. 1949 published a paper on the distribution of singular values and eigenvalues of linear integral equations in the Journal of the American Mathematical Society. Experts at home and abroad believe that it lays a foundation for studying the relationship between singular values and eigenvalues of trace operators, and it is still a classic document. He has also done a lot of work in the study of normal kernel integral equations.
Zhang Dingming is a member of the China Democratic League and has been elected to the Standing Committee of the Sichuan Provincial Political Consultative Conference for many times. He wrote to Premier Zhou Enlai, presenting eight pieces of evidence on the Sino-Indian and Sino-Soviet border issues, proving that 90,000 square kilometers south of Xinjiang McMahon Line and Aksu have been China's territory since ancient times, which was praised by the Ministry of Foreign Affairs. In addition to teaching, he has been engaged in mathematical research all his life. In his later years, he studied Fermat's Last Theorem, a famous problem in computational mathematics, day and night, and finally died from overwork in 1985.