Happiness is often thought of as a subjective experience that could not be formally analyzed. This paper proposes a mathematical framework in which happiness is modeled as a time dependent function defined by differential and stochastic dynamics. Instead of coming up with a universal formula for happiness, the framework provides tools for analyzing how happiness evolves over time, and how it responds to intentional life choices, how it adapts, and how it is disrupted by random external shocks. By combining pragmatic axioms with dynamical models, the paper redefine happiness as an evolving process rather than an unanalyzable human experience.