The integration of Artificial Intelligence (AI) and Machine Learning (ML) in the financial sector has brought about a profound transformation in decision-making processes, risk management, and predictive analytics. This comprehensive study aims to systematically identify and analyze the foundational theories, emerging themes, and research clusters within the extensive body of AI and ML finance literature through an in-depth bibliometric analysis. By meticulously examining a vast array of publications spanning over two decades, the study uncovers the intricate evolution of AI and ML applications in finance, mapping out key areas of research and providing valuable insights into future research directions. The findings reveal a significant and accelerating growth in the application of AI and ML across various financial domains, notably in fraud detection, portfolio management, and algorithmic trading, demonstrating the substantial impact and transformative potential of these technologies. This study not only charts the current landscape of AI and ML research in finance but also identifies critical gaps and opportunities for future exploration, underscoring the ongoing evolution and maturation of this dynamic field.