They are not advancing the field. At least they didn't in the case of the N-S debacle. The model most likely used the conversation text of a mathematician which had discovered and was pursuing a new avenue towards the goal, then pumped millions upon millions to hurry up ahead to an opaque solution which leaves no-one the wiser, beyond just settling a theoretical question. The only impact on science is to deflate the potential minds who might have been motivated to join the effort.