A mental model for a mathematic proof.

You start off in a pitch black house.

The only way to make progress is by fumbling around, using touch.

Over time you develop an intuitive map of the space, even though you can't see it.

At some point you find the light switch, and now you can see everything clearly.

You already had developed an intuition for the space, but now you can see it and show it to others.

If you only get the lightswitch moment, you miss the learning from fumbling around by touch.