Shu Shu is a set of mathematical problems. This book has nearly seventy titles. Some topics are named after calculation methods, such as multiplication, division and multiplication, approximate division, combined division and radial division. Some are named after the subject words in the text of the question, such as * * * buying materials, fox customs clearance, interest money, drinking paint, tax field, salt, millet begging for rice, negative charcoal, sharing money, square field and brick cover. This book is written in the style of "topic-answer-skill". "Problem" refers to a proposition, that is, a mathematical problem; "Answer" refers to the answer, that is, the answer to the example; "Skill" refers to the general algorithm of this kind of problem summarized from the answers of examples. According to the content, the book can be divided into two categories: one is the four algorithms of integers and fractions; The other is all kinds of application problems and solutions closely related to the actual production and life at that time. For example, "Feather Arrow" is an application problem related to making arrows, "spinning millet" is an application problem related to agricultural yield estimation, and "interest money" is an application problem related to lending. According to the classification of modern mathematics, some of these application problems belong to arithmetic problems and some belong to geometry problems. Archaeologists believe that Shu Shu may be a textbook and reference book for officials in Qin and Han dynasties, especially those in charge of economic management, to learn mathematical knowledge.
Shu Shu is about 200 years earlier than Nine Chapters Arithmetic handed down from ancient times. Its unearthed, make us to the 2nd century BC, even earlier, the level of China's mathematical development and the level of the compilation of mathematical monographs, formed the following understanding:
First, Numbers recorded the most advanced quartering and proportional algorithm in the world at that time. The scientific concept and algorithm of fractions were established by China's ancient algebra. The ancient Egyptians used to have a relatively complete fractional form, but it was too complicated to calculate. This influenced the development of arithmetic in ancient Egypt and set obstacles for the later development of Greek mathematics. In Greek mathematics, the laws of fractional reduction and general division are lacking, and the operation of fractional four is even later. In the 7th century, the concept and algorithm of systematic score became popular in India, but it was much later in Europe.
Second, the technique of surplus and deficiency appeared in China no later than the 2nd century BC. In the early mathematical works in Arabia and Europe, it was called "Khitan algorithm". "Qidan" was the name given to China by the West and Arabs at that time. Therefore, the complementary method is the original creation of China's ancient algebra. In the 9th century, the Arab mathematician Huala Mizi put forward the double hypothesis method, which was more than 1000 years later than the ancient mathematicians in China. China remainder technique is an algorithmic calculus program based on ratio theory. It provides an application method that can be operated according to the program for people who don't know arithmetic, and pushes the application of arithmetic to the peak.
Third, Shu Shu's title "Differentiation" is jealousy. According to Liu Hui, an outstanding mathematician in Wei and Jin Dynasties, jealousy is "a tunnel". For example, it is a wedge, and its volume solution formula is the first in China's ancient algebra.
Fourthly, Shu Shu's writing style of "Question-Answer-Technique" has the advantages of paying attention to practicality, development and easy popularization. The mathematical problems raised by examples come from social practice. With the development of social practice, new problems can be continuously incorporated to promote the development of mathematics. For example, from the Spring and Autumn Period and the Warring States Period, lacquerware gradually rose, eventually replacing bronzes in the Qin and Han Dynasties. Lacquer production has a growing demand for raw lacquer. Rhus verniciflua can only grow in parts of the middle reaches of the Yellow River and parts of the Yangtze River basin, and its output is very limited. In order to ensure the supply of raw lacquer, the government set up a lacquer garden in the origin of raw lacquer, and assigned special personnel to manage it. Raw lacquer needs drinking water, and the amount of drinking water determines the quality of raw lacquer. According to the law, the collection of raw lacquer should go to the government to test water and drink water. Managers must master the calculation method of drinking water. Shu Shu's "drinking lacquer" is a calculation method to test the quality of raw lacquer. It was definitely included in Shu Shu later than Tian Fang. In the method of solving problems, we start with specific examples, and then summarize the general solution of similar problems, that is, the "technique" behind "answer". Judging from the style and structure of the book, it is an open inductive system. This compiling style directly influenced Nine Chapters Arithmetic and became the tradition of China's ancient mathematical works.