“The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture. Without one or the other, you will spend a lot of time blundering around in the dark.”<p>Well put! In empirical research, there is an analogy where intuition and <i>systematic data collection from experiment</i> are both important. Without good intuition, you won’t recognize when your experimental results are likely wrong or failing to pick up on a real effect (eg from bad design, insufficient statistical power, wrong context, wrong target outcome, dumb mistakes). And without experimental confirmation, your intuition is just untested hunches, and lacks the refinement and finessing that comes from contact with the detailed structure of the real world.<p>As Terry says, the feeling of stumbling around in the dark suggests you are missing one of the two.