Brown and Walter provide a wide variety of situations implementing this strategy
including a discussion of the development of non-Euclidean geometry. After many years
of attempting to prove the parallel postulate as a theorem, mathematicians began to ask
"What if it were not the case that through a given external point there was exactly one
line parallel to the given line? What if there were two? None? What would that do to the
structure of geometry?" (p.47). Although these ideas seem promising, there is little
explicit research reported on problem posing.