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 S^{2} in **R**^{3} 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.