In his works, Yang Hui collected many valuable calculation problems and algorithms that have been lost in various ancient mathematical works, and preserved many very valuable mathematical historical materials of the Song Dynasty. He has deeply studied the roots of any higher power, binomial expansion, the solution of higher equations, higher arithmetic progression, vertical and horizontal graphs, etc. Yang Hui attaches great importance to mathematics education and carries out his educational thoughts in his own practice. Yang Hui has made a detailed study on stacking problem (high-order arithmetic progression) and magic square.
Because he mentioned Jia Xian's research on binomial in his works, the "Jia Xian Triangle" is also called "Yang Hui Triangle". This is almost 500 years earlier than the similar research on Pascal Triangle in Europe in the17th century. In "Multiplication and Division into Treasure", Yang Hui created the formula of "Nine Returns" and introduced various fast algorithms for calculating multiplication and division. Yang Hui listed various vertical and horizontal diagrams (Rubik's Cube) in "Algorithm for Extracting Odds from Ancient Stories", which is the most important work to study Rubik's Cube and Magic Circle in Song Dynasty. Yang Hui not only made a profound study of China's ancient Rubik's Cube, but also created four-order concentric Rubik's Cube and several serial Rubik's Cube.