The limits of mathematics in physics

Mathematics is considered the language of physics. Starting from idealizations and kinematics, geometric-mathematical physics with paradigms such as flexible spacetime and dark energy has emerged whose physical reality has not been clarified. By analyzing processes regarding their causes and the functional dependencies of energies, this work identifies shortcomings in the basic energy concepts of physics, which cannot be remedied with mathematics. While formal transformations of process equations such as integration are mathematically correct, they do conceal vital physical information, suggesting that mathematics should be used with caution. We propose a physically justified approach that reconciles the mechanical and thermodynamic energy concepts and provides a revised interpretation of E = mc2. Our results suggest that geometric approaches were built too early on a shaky physical foundation, leading to undesirable developments in recent centuries. The language of physics should be physics, not just mathematics.