Mathematics education is commonly confronted with the contradiction between large-scale classroom teaching and personalized tutoring, while traditional photo-based question-searching software hinders students' in-depth thinking by directly providing answers. Therefore, this paper firstly proposed a new paradigm for intelligent tutoring termed the “Diagnostic Socratic Dialogue” model. Then, relying on this model, an intelligent mathematics tutoring system based on Socratic Dialogue was designed. Integrating large language model, OCR technology and Socratic Dialogue, the system replaced directly providing answers with dynamically questioning chains to guide students toward independent thinking, overcoming the limitations of traditional tools. Finally, the system was applied at a primary school. By analyzing system usage log data, student questionnaire data and semi-structured interview transcripts, this paper revealed that the system featured user-friendly operation and prompt feedback, effectively improving students' learning efficiency, mathematical comprehension and learning confidence, with its core educational functions well recognized. The designed intelligent mathematics tutoring system based on Socratic Dialogue in this paper had prominent application value in real teaching scenarios, which could provide feasible solutions to the dilemma of personalized mathematics tutoring and promote the deep integration of artificial intelligence and education, as well as facilitate the paradigm innovation of intelligent tutoring tools.