This study explores the design and implementation of an intelligent mathematics teaching classroom based on principal component analysis (PCA) and neural network (NN) algorithms. This design aims to utilize advanced data analysis techniques and machine learning algorithms to enhance the effectiveness and efficiency of mathematics teaching. Firstly, the PCA algorithm is used to reduce the dimensionality of mathematics teaching resources and student learning data, extract key features, and simplify data structures and highlight important information. Then, an intelligent teaching model is constructed using the NN algorithm, which can automatically adjust teaching strategies and content based on student learning data and grades to achieve personalized teaching. This study verified the effectiveness of PCA-NN algorithm in the design of intelligent mathematics teaching classrooms through empirical analysis, and the results showed that the algorithm can significantly improve students’ learning performance and interest. Meanwhile, this study also discusses the challenges and future development directions of intelligent classroom design, providing useful references for future mathematics teaching reforms.