The sludge-derived carbon catalyst modified with 0 degrees C HNO3 solution was tested in catalytic wet peroxide oxidation of m-cresol (100 mg L-1) with systematical mathematical models and theoretical calculation for the first time. The reaction conditions were optimized by response surface methodology (RSM) as T=60 degrees C, initial pH = 3.0, C-0.H2O2(30%) = 1.20 g L-1 (lower than the stoichiometric amount of 1.80 g L-1) and C-cat = 0.80 g L-1, with 96% of m-cresol and 47% of TOC converted after 16 min and 120 min of reaction, respectively, and xi (mg TOC/g H2O2 fed) = 83.6 mg/g. The end time of the first kinetic period in m-cresol model was disclosed to be correlated with the fixed residue m-cresol concentration of about 33%. Furthermore, the kinetic constants in models of TOC and H2O2 exactly provide convincing proof of three-dimensional response surfaces analysis by RSM, which showed the influence of the interaction between organics and H2O2 on effective H2O2 utilization. The reaction intermediates over time were identified by gas chromatography-mass spectrometer based on kinetics analysis. Four degradation pathways for m-cresol were proposed, of which the possibility and feasibility were well proven by frontier molecule orbital theory and atomic charge distribution via density functional theory method. (C) 2016 Elsevier B.V. All rights reserved.