There's provability ("math"), and testability / falsifiability ("science"), and then there's just making it work amidst a deluge of trade-offs ("engineering"). If in the end, you simply can't make it work, the entire exercise becomes futile. In that sense, I do not really believe in favouring the formalisms of provability and testability at just any cost. If the person can actually solve the practical problem, then that should allow us to move on, no? That is why I like having that kind of people on my team.