In recent years, online education in China has made considerable achievements. But there are also some problems: the teaching quality of online education is unsatisfactory; students’ online learning effects are frustrating, and students’ autonomous learning ability is poor. Based on analysis, teachers’ literacy and Internet technology are important factors restricting the online teaching reform, and online teaching easily falls into the dilemma of “shallow learning.” Digital twins can effectively realize the intelligent interconnection and interaction of the physical world and the information world, optimize the remote teaching process, and provide high-quality remote learning experience for learners. Based on this, the technology is used to the teaching of space geometry to help students understand it and improve their performance. First, the principle and advantages of digital twins are expounded. Second, the platform system based on digital twins is constructed. Then, the corresponding digital model is drawn by using the drawing function of MATLAB software, and the system based on virtual reality (VR) is established. Finally, the students of four classes of the same major are selected as the research subjects to test the teaching effect of advanced mathematics on the digital platform. The results show that students’ scores in the traditional classrooms are form 2.5 to 5.5 and their average score is 4.049, while the scores of the students in the digital twin classrooms are between 5.5 and 9.5 and their average score goes up to 7.986. This shows that students’ performance in the digital twin classrooms is 97.2%, higher than that in the traditional classrooms. A fully digitized spatial geometric model is implemented by using digital twins, and it can help students understand the mathematical theory of spatial analytic geometry, and their learning effect is greatly improved. This study provides a new direction for the application of new technologies in mathematics teaching.