This study aims to analyze in-depth students' conceptual knowledge and reasoning when
solving problems using mathematical proof as a rigorous mathematical thinking paradigm.
The research uses a qualitative method with a case study approach that analyzes the mathematical proof ability of nine students who represent different cognitive functions from
each level of rigorous mathematical thinking. The results showed that each level of rigorous mathematical thinking meant other indicators according to their ability to master conceptual knowledge and implement mathematical ideas through reasoning. This research
has an impact on the treatment that the teacher must give in determining the learning
model and evaluation instrument that can raise students' conceptual knowledge and reasoning.