Could it have been foreseen that - exemplarily - planarity and colorability would turn out to be such important concepts in graph theory (there's almost no textbook on graphs without two chapters devoted to these concepts), or did time have to come and show it? The latter might imply that it's just a historical and evolutionary incident because there are loads of conceivable x-arities, y-abilities and other graph properties. (Maybe the importance of planarity and colorability just has to do with the contingent fact that we live on a (locally) two-dimensional plane and our need of maps?)

But maybe there are more objective reasons internal to mathematics that are formulable?

Related questions: Why-are-planar-graphs-so-exceptional; generalizations-of-planar-graphs;why-is-edge-coloring-less-interesting-than-vertex-coloring

Post-delivered motivation: I wonder why questions for "importance" - of concepts and theorems - are in general not taken as seriously as questions for hard facts. Wouldn't this - taking them equally important - be a real step further in the venture of mathematics? (I admit that questions for importance may be trivial - because importance may be obvious in special cases - or mistaken, because there is no importance at all of trivial concepts.) $\endgroup$ – Hans-Peter Stricker Jan 10 '11 at 20:54