Advanced technologies and mathematical metacognition: The present and future orientation.

The intersection of mathematical cognition, metacognition, and advanced technologies presents a frontier with profound implications for human learning and artificial intelligence. This paper traces the historical roots of these concepts from the Pythagoreans and Aristotle to modern cognitive science and explores their relevance to contemporary technological applications. We examine how the Pythagoreans' view of mathematics as fundamental to understanding the universe and Aristotle's contributions to logic and categorization have shaped our current understanding of mathematical cognition and metacognition. The paper investigates the role of Boolean logic in computational processes and its relationship to human logical reasoning, as well as the significance of Bayesian inference and fuzzy logic in modelling uncertainty in human cognition and decision-making. We also explore the emerging field of Chemical Artificial Intelligence and its potential applications. We argue for unifying mathematical metacognition with advanced technologies, including artificial intelligence and robotics, while identifying the multifaceted benefits and challenges of such unification. The present paper examines essential research directions for integrating cognitive sciences and advanced technologies, discussing applications in education, healthcare, and business management. We provide suggestions for developing cognitive robots using specific cognitive tasks and explore the ethical implications of these advancements. Our analysis underscores the need for interdisciplinary collaboration to realize the full potential of this integration while mitigating potential risks.