Often the usefulness of a theorem is justified by saying examples which don't meet the assumptions (counterexamples) are pathological. A famous case is the Alexander horned sphere, a counterexample showing that embedding topologically a sphere S2 in R3 may fail to separate the space cleanly, unless an extra condition of tameness is used to suppress possible wild behaviour.
One can therefore say that (particularly in mathematical analysis) those searching for the 'pathological' are like experimentalists, interested in knocking down potential theorems proposed (by 'theorists'); though this should all take place within mathematics. What is created especially can have some undesirable, unusual, or other properties that make it difficult to contain or explain within a theory. But that point of view is probably biased, by preconceptions.