This study examines how AI supports students in developing their mathematical problem-solving and problem-posing skills. The study examines 101 articles from approximately the last 55 years and shows that there is an increasing focus on problem-solving research, perhaps due to its ease of application and assessment. However, studies of problem sets are gaining in importance as their importance in fostering mathematical creativity is recognized. Findings suggest that AI tools hold promise for improving problem-solving skills, especially among high school and college students. The impact on problem-posing skills is less conclusive and suggests the need for further research in this area. Popular AI systems such as ALEKS and intelligent tutoring systems (ITS) are considered to be widely used in these studies because they provide personalized guidance and immediate feedback. Research in this context has mostly focused on solving arithmetic and algebraic problems in AI-supported environments, while studies on geometric problems are relatively rare. The findings of this study and implications for future research and educational applications are discussed.