/kloc-At the end of 0/3, China was unified by the Yuan Dynasty, and the destroyed economy and culture soon flourished. For the sake of national prosperity and national security, Mongolian rulers began to respect knowledge and select a large number of talents, which pushed the development of various sciences to a new peak.
At that time, Kublai Khan recruited a large number of Han intellectuals to form a think tank, including Wang Xun, Guo Shoujing, Li Zhi and others. The members of this think tank are proficient in mathematics and calendars.
At this time, Zhu Shijie also inherited the main achievement of northern mathematics-astrophysics, and extended it from binary and ternary to the solution of quaternary equations. Zhu Shijie not only accepted the mathematical achievements of the North, but also absorbed the mathematical achievements of the South, especially various daily algorithms, business arithmetic and popular ballads.
Before the Yuan Dynasty destroyed the Southern Song Dynasty, North-South exchanges, especially academic exchanges, were almost cut off. Mathematicians in the south know nothing about celestial science in the north, and mathematicians in the north are rarely influenced by the south. Zhu Shijie once traveled around the world. After more than 20 years' study tour and lectures, he finally published and engraved his two mathematical masterpieces, The Enlightenment of Arithmetic and Four Jade Juanjian, in Yangzhou 1299 and 1303.
Arithmetic enlightenment included all aspects of mathematics at that time, from multiplication and division and its agile algorithm to square root, celestial element and equation, and formed a relatively complete system from shallow to deep. Before the text, the 18 items such as 99-99 Song formula, Divide by Song formula, Divide by Zero Song formula, calculation and position identification system, decimal method of size, measurement system, pi, law of addition, subtraction, multiplication and division, and square root law are summarized. As the preparatory knowledge of this book, the law of addition, subtraction, multiplication and division not only appears in Chinese mathematical works, but also appears for the first time in the world. Many rhymes are more complete and accurate than Yang Hui's, and some are almost the same as modern abacus formulas.
Meeting with Siyuan is Zhu Shijie's most outstanding work. In this book, he recorded his views on the solution of multivariate higher-order equations, higher-order arithmetic progression summation and higher-order interpolation. It is highly praised by researchers in the history of modern mathematics, and is regarded as the most important and greatest mathematical masterpiece in China's ancient mathematical science works.
Another great contribution of Zhu Shijie is the study of "piling". He studied a series of new summation problems of crib series, from which he obtained the formula of "triangular crib", and actually obtained a systematic and universal solution to this kind of summation problem of arbitrary high-order arithmetic series. Zhu Shijie also introduced the triangle crib formula into the unique skill, pointing out that the coefficient in the unique skill formula is just the product of the triangle crib in turn, thus obtaining the unique skill formula with the fourth difference. He also extended this formula to include any higher-order difference, which is the first time in the history of mathematics in the world.
In the history of Chinese mathematics, Zhu Shijie formally put forward the correct law of positive and negative multiplication for the first time; He discussed the calculation of the surface area of a sphere, which is the only discussion in China's classical mathematics. Although the conclusion is incorrect, the spirit of innovation is commendable. In "Arithmetic Enlightenment", he recorded a complete "nine-point" formula, which is almost the same as the abacus formula.
In a word, Zhu Shijie inherited and developed the mathematical achievements of predecessors and made indelible contributions to the development of ancient mathematical science in China. Zhu Shijie deserves to be a famous mathematician in the history of mathematics in China and even in the world.