The phrase "impenetrable mystery" refers to something that is completely unknown or difficult to understand and cannot be comprehended or solved easily. Full definition
What is taught in High School today would be viewed as impenetrable mysteries back then. (religion.blogs.cnn.com)
In the interests of intellectual exactness, social relevance and ecumenical dialogue, liberalism has frequently settled for unresolved tensions, stretchy ambiguities and impenetrable mysteries when dealing with «the truth question.» (religion-online.org)
There is a whiff of social envy (Martin is lower middle - class), a nod at the web of complicity binding society together, a question over the distinction between what is good and what is just, and a gnawing sense of impenetrable mysteries hiding in the silent spaces between human events. (shepherdexpress.com)