This paper introduces a new domain of knowledge termed Physical Mathematics, defined as a derived space emerging from the interplay between abstract mathematical axioms and the physical axioms of the universe. Unlike classical mathematics, which exists in a perfect conceptual world, Physical Mathematics studies logical structures constrained by a quantized reality. Its foundation is the Axiom of the Minimal Domain of Existence, which posits that every physical object must oc- cupy a spacetime domain with a non-zero minimum measure, denoted as δ (corresponding to the Planck length, lP ≈ 1.6 × 10−35 m). A core consequence is that every mathematical theorem, when "compiled" into physical reality, carries a quantum signature ϵ(δ), representing the deviation between the abstract mathematical model and physical reality. Classical tools like calculus are repositioned as macroscopic approximations, smoothing a fundamentally discrete reality. Exploring this domain opens an ambitious research program: systematizing the reinterpretation of all mathematical fields—from geometry, algebra, to number theory and topology in the language of the physical universe, to decode the foundational rules governing both logic and reality.