In retrospect, it appears that mathematicians missed a great opportunity to obtain important scientific results simply because they ignored the study of the nonlinear diffusion equation. An exception was the work of A. N. Kolmogorov, I. G. Petrovsky, and N. S. Piskunov. "Investigation of the diffusion equation associated with an increase in the amount of substance..." They showed that any initial disturbance in the form of a difference tends to the same isolated stationary solution of the traveling wave type. The authors studied this solution using the phase plane and obtained an explicit expression for the velocity. ... The fact that mathematicians failed to study the Kolmogorov-Petrovsky-Piskunov equation in time cannot be explained by the weakness of their technique in the face of enormous mathematical difficulties... The obstacle probably lay in the fact that mathematicians automatically transferred the conclusion about the non-wave behavior of solutions of the linear diffusion equation to the nonlinear case.