... Let a perturbation be produced anywhere, like sound; it is not immediately perceived at every other point. There are then points in space which t… - Jacques Hadamard

We are going to speak of the role of analysis situs in our modern mathematics. This theory is also called the geometry of situation. It is the study of connection between different parts of geometrical configurations which are not altered by any continuouse deformation. For instance, a sphere and a cube are considered as one and the same thing from the point of view of the geometry of situation, because one can be transformed into the other without separating parts, or uniting parts which formerly were separated.

Just after the discovery of infinitesmal calculus, physicists began by needing only very simple methods of integration, the problems in general reducing to elementary differential equations. But when higher partial differential equations were introduced, the corresponding problems almost immediatelly proved to be far above the level of those which contemporary mathematics could treat.

In the case of partial differential equations employed in connection with physical problems, their use must be given up in most circumstances, for two reasons: first, it is in general impossible to get the general solution or general integral, and second, it is in general of no use even when it is obtained.