... In the case of ordinary differential equations, the arbitrary elements being numerical parameters, we have to determine them by an equal number o… - Jacques Hadamard

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.

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.

... Let a perturbation be produced anywhere, like sound; it is not immediately perceived at every other point. There are then points in space which the action has not reached in any given time. Therefore the wave, in that sense a surface, separates the medium into two portions (regions): the part which is at rest, and the other which is in motion due to the initial vibration. These two portions of space are contiguous. It was only in 1887 that Hugoniot, a French mathematician, who died prematurely, showed what the surface of the wave can be; and even his work was not well known until Duhem pointed out its importance in his work on mathematical physics.