Against the backdrop of the synergistic advancement of Industry 4.0 and the dual-carbon strategy, traditional university mathematics education struggles to meet the demands for cultivating engineering talents’ integrated competencies in mathematics, specialization, and application. The STEM education paradigm urgently needs innovation. Guided by sustainable development principles, this study explores integrated approaches to university mathematics teaching for advanced manufacturing. It constructs a four-stage cyclical framework, Concept–Algorithm–Equipment–Evaluation (CAEE), and integrates Fourier Transform systems into industrial inspection workflows, using silicon carbide wafer thickness measurement as a case study. Targeting second-year students in Measurement and Control Technology and Instrumentation, a comparative design involving an experimental and a control group was employed. Comprehensive evaluation utilized AI-powered dynamic questionnaires, multimodal eye-tracking and EEG data, along with mixed-methods research. Results indicate that the assessment tools achieved high reliability and validity (0.906). The experimental group demonstrated significantly superior performance in deep learning proficiency and subject-specific educational structure (effect size 0.67) compared to the control group, along with modest positive enhancements in cognitive engagement and social interaction dimensions. This pedagogical model transcends conventional ‘knowledge collage’ integration, transforming mathematics from an external auxiliary tool into an ‘endogenous variable’ within industrial systems. It establishes a replicable and scalable STEM education practice paradigm.