This study examines the relationship between curiosity and exploratory mathematical abilities, as well as the role of basic mathematical knowledge in shaping this relationship. Three distinct dimensions of curiosity relevant to mathematics education were identified: trait curiosity, mathematical curiosity, and mathematical state curiosity. A sample of 71 Grade 6 students participated in the study. Data on the three curiosity dimensions were collected through self-report questionnaires, while two written mathematical tests were administered: one assessing students’ performance on exploratory mathematical tasks and another assessing students’ knowledge of foundational mathematical concepts and procedures. Partial Least Squares Structural Equation Modeling (PLS-SEM) was used to analyze the data and model the relationships among these variables. The results revealed that trait curiosity strongly predicted mathematical curiosity, which in turn significantly predicted mathematical state curiosity, suggesting an important indirect pathway linking stable personality traits to momentary engagement. Mathematical state curiosity and basic mathematical knowledge were found to significantly predict exploratory mathematical abilities, indicating a direct effect. These findings contribute to a deeper conceptualization of curiosity in mathematical learning and underscore the importance of fostering both curiosity-driven engagement and basic mathematical knowledge to support students’ mathematical exploration abilities.