This note gives an in-depth discussion on feasible mathematics and bounded arithmetic with a focus on Cook's theory PV (STOC'75). We present an informal characterization of PV based on three intuitive postulates and formulate the Feasible Mathematics Thesis, which asserts the equivalence between this informal framework and the formal system PV. To support this thesis, we provide a detailed exposition demonstrating how advanced programming and reasoning tools can be systematically constructed within the seemingly weak theory PV.