21st-century learners, including in mathematics education, are increasingly utilizing Generative Artificial Intelligence (GenAI). This study examines how various factors influence students' adoption of generative AI in mathematics. It focuses on components of the Unified Theory of Acceptance and Use of Technology (UTAUT) 3 model with external variables such as system accessibility, self-efficacy, knowledge of AI, and perceived privacy concerns. Data were collected from 960 respondents and analyzed using Partial Least Squares-Structural Equation Modeling (PLS-SEM). The results revealed that among the main components of UTAUT 3 model, facilitating conditions, social influence, habit, and knowledge were the strongest and most consistent predictors of students’ behavioral intention to use GenAI tools. In contrast, UTAUT constructs such as performance expectancy, effort expectancy, hedonic motivation, personal innovativeness, price value, and perceived privacy concerns did not directly affect behavioral intention. These findings present a shift in the primary drivers of AI adoption, from perceived usefulness and ease of use to factors rooted in familiarity, social influence, and routine engagement. System accessibility, however, significantly affects key constructs, particularly facilitating conditions, performance expectancy, effort expectancy, and social influence. Moreover, self-efficacy significantly affects hedonic motivation, habit, personal innovativeness, price value, and knowledge, implying their role in supporting AI use. The study emphasizes the importance of AI literacy programs, habitual engagement strategies, and socially supportive learning environments to encourage the meaningful integration of generative AI tools into mathematics education.