Why Fundamental Physical Equations Are of Second Order?

In this paper, we use a deep mathematical result (namely, a minor modi cation of Kolmogorov's solution to Hilbert's 13th problem) to explain why fundamental physical equations are of second order. This same result explain why all these fundamental equations naturally lead to nonsmooth solutions like singularity. Formulation of the problem. Most physical phenomena are described in terms of partial di erential equations. These di erential equations can be arbitrarily complicated; in particular, they can be of high order: e.g., the equations of elasticity theory (see, e.g., [8]) are of fourth order (i.e., involve derivatives of fourth order). However, amazingly, these higher order equations only occur in the description of non-fundamental phenomena, i.e., phenomena which (like elasticity) can be reduced to more fundamental forces and elds, while fundamental physical equations, i.e., equations which describe the evolution of fundamental