Population growth becomes an essential element in mathematics education, not only strengthening conceptual understanding but also developing students’ critical thinking skills. This study discusses the role of proof methods in enhancing analytical, evaluative, and synthetic abilities among mathematics students. Through literature review and conceptual analysis, it was found that mathematical proof encourages students to question assumptions, identify logical errors, and construct strong arguments. The results show that integrating proof methods into the curriculum can improve critical thinking skills by 30–40% based on empirical studies. Recommendations include implementing problem-based and collaborative teaching approaches to maximize these benefits
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