Higher mathematics is a compulsory basic course of general education in colleges and universities, which is crucial to the cultivation of students’ innovative thinking, logical reasoning and other abilities. The teaching quality of higher mathematics directly affects the realization of talent cultivation goals in colleges and universities. Through analyzing the current situation of higher mathematics teaching in colleges and universities, we will sort out the main problems in teaching from four dimensions: intrinsic factors, extrinsic factors, major factors and minor factors, and conduct exploratory thinking on the teaching content, teaching mode, teaching evaluation and teaching responsibility of higher mathematics from three dimensions: sufficient conditions, necessary conditions and supporting conditions, so as to provide theoretical support for improving the quality of higher mathematics teaching.