Zu Chongzhi's main achievement lies in the calculation of pi. According to Sui Shu's records, Zu Chongzhi determined that the approximate value of pi was 3. 14 15926, and the approximate value of pi was 3. 14 15927, which was the first time in the world to make pi accurate to the seventh place after the decimal point. It was not until the 6th century A.D./KLOC-that the Arab mathematician Al Cassie broke this record. Zu Chongzhi actually gave the error range of pi.

Zu Chongzhi and his son, Zuxuan, solved the problem of calculating the volume of the ball with ingenious methods. In "Nine Chapters Arithmetic", it is considered that the volume ratio of the circumscribed cylinder to the spherical surface is equal to the area ratio of the square and its inscribed circle. Liu Hui, when commenting on Nine Chapters Arithmetic, pointed out that the statement in the original book was incorrect, only the ratio of "square cover" (the volume of the same part where two cylinders intersect vertically) to the volume of a sphere was exactly equal to the area ratio of a square and its inscribed circle. However, Liu Hui did not get the volume formula of the vertical intersection of two cylinders, so he could not get the spherical volume formula. Zu Chongzhi and his son applied the principle that the volumes of two solids with the same cross-sectional area at the same height must be equal, and calculated the volume of the square cover of Mohe River. The volume of the sphere is equal to π/4 times the volume of the square cover, and finally the volume of the sphere is π D3/6 (D is the diameter of the sphere), which is the famous "axiom of ancestor's declaration". When westerners got this axiom, it was 1000 years since Zu Chongzhi and his son. Zu Chongzhi also studied the problems of "open difference power" and "open difference station", which involved the problem of finding the roots of quadratic and cubic equations. Zu Chongzhi even "takes both positive and negative arguments" in his solution, which shows his high level of research.

Zu Chongzhi and his son's achievements in mathematical research are all included in his mathematical monograph Composition. This book is so profound that "scholars can't study its profundity, so they ignore it." In the official school of the Tang Dynasty, Zhuanshu was also listed as one of the top ten required books, and the study time was four years, with the number of years being the first of all books. Later, seal script spread to North Korea, but after 10 century, seal script was gradually lost in various countries.