The mathematical prediction equation (MPE) will give the mathematical definition of prediction to various physical motion (wave) fields. The MPE of space-time infinite order accuracy was proposed in this study (MPE is also an infinite series), and its sufficient and necessary convergence condition was reported. Meanwhile, simplified derivation or inference was given for the MPE (it is hoped that the mathematical circle will perfectly prove the 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 MPEs and convergence conditions with the cubic spline function, closed prediction equations of ideal gas pressure, temperature, and flow fields with space-time second-order accuracy were established, (it is also hoped that the physics circle will investigat the application of MPE in quantum fields, to discuss the mathematical definition and difference between Newton displacement and Einstein displacement).