A geometry, Klein said, is defined by a group of transformations, and investigates everything that is invariant under the transformations of this given group. Of symmetry one speaks with respect go a subgrup gamma of the total group.
Physical occurrences happen not only in space but in space and time; the world is spread out not as a three- but as a four-dimensional continuum. The symmetry, relativity, or homogeneity of this four-dimensional medium was firts correctlly described by Einstein.
What Einstein did was this: without bias he collected all the physical evidence we have about the real structure of the four-dimensional space-time continuum and thus derived its true group of automorphisms.
Galois´theory is nothing else but the relativity theory for the set Sigma, a set which, by its discrete and finite character, is conceptually so much simpler than the infinite set of points in space or space-time dealt with by ordinary relativity theory.
A guiding principle in modern mathematics is this lesson: Whenever you have to do with a structure endowed entitiy Sigma try to determine its group of automorphisms, i.e., the group of those element-wise transformations which leave all structural relations undisturbed.
