Encounter with Siyuan is a book about multivariate higher-order equations and higher-order arithmetic progression, in which the general formula of higher-order error is exactly the same as Newton's later formula. His research level has surpassed that of Qin, Zhou and Qing Dynasties. In his Introduction to the History of Science, Sutton, a famous American historian of science, said that Zhu Shijie was "an outstanding mathematician of his time" and his "Meeting with the Source" was "the most important mathematical work in China and one of the most outstanding mathematical works in the Middle Ages". Obviously, Zhu Shijie's achievements have gone beyond the scope of China's classical works on ancient mathematics. His achievements also surpassed China's tradition of only studying practical problems in mathematics.