Geometry includes theorem proving, geometric drawing and geometric inequality proving. Under the influence and enlightenment of Mr. Wu's pioneering achievements, Chinese scholars have made fruitful achievements in geometric mechanization, such as theorem machine proof, geometric automatic drawing, geometric inequality machine proof and so on. This field has also begun to attract foreign scholars to learn from us.

As we all know, geometric concepts such as lines and planes can be described by linear algebraic equations, while polynomial equations are used to describe curves and surfaces. In mathematical science, the first leap from linearity to nonlinearity is observed by polynomials. Therefore, the solution of polynomial equation is the most basic subject of nonlinear mathematics, and the research on this problem has been carried out for hundreds of years. Many problems in different branches of mathematics, many problems in different fields of natural science and many problems in high technology can be transformed into polynomial equations to solve. In the process of mechanical proof of geometric theorem, the zero structure of polynomial equation must be clarified. This demand prompted Mr. Wu to establish a theory and method for solving polynomial equations, which is called "characteristic column method" or "Wu elimination method" internationally. Mr. Wu also extended these methods to differential cases, and established the mechanized theory and method of machine proof of differential geometry theorem and solution of differential algebraic equations. Naturally, compared with the case of algebra, the application of differential algebra is wider, and the research of problems is more complicated and difficult.