My research goal is to establish a robust mathematical theory that identifies the conditions under which a parameter serves as the temporal parameter in dynamical systems. Mathematical time is typically linked to the real number line, referred to as the minimal model of time. However, this model exhibits significant philosophical contradictions and lacks the structure necessary to describe the dynamic progression or flow of time. While various attempts have been made to address the flow of time, most of the approaches often face ontological inconsistencies and rely on the same objective framework of time represented by the minimal model, offering little advancement in theoretical understanding. Bringing together the various developments in the mathematical theory of time remains a major challenge.