The mathematical prediction equation (MPE) will give the mathematical definition of prediction / forecast to various physical motion (wave) fields. MPE of space-time infinite order accuracy in the Taylor series was proposed in this study (MPE is also an infinite series), and its sufficient and necessary convergence condition was reported, which whold take place of the famous CFL (Courant-Friedrichs-levy) calculation stability condition in textbooks of modern numerical weather forecast. Meanwhile, simplified derivation or inference was given for MPE (it is hoped that the mathematical circle will perfectly prove MPE). The mathematical definition of prediction was provided during derivation, including mathematical relationships between the Euler constant equation and Newton displacement, velocity and acceleration. Furthermore, by combining MPE and its convergence condition with the cubic spline function, closed prediction equations of ideal gas pressure, temperature, and flow fields with space-time second-order accuracy were established. And the success of modern numerical predictions, such as weather forecast, implies the existence of MPE. (It is also hoped that the physics circle will investigate the application of MPE in quantum fields, to discuss the mathematical definition and difference between Newton displacement and Einstein displacement).