A mathematician ruminates on thinking and problem solving:
The Myth and Magic of Generating New Ideas by
Dan Rockmore
“These stories suggest that an initial period of
concentration—conscious, directed attention—needs to be followed by some amount
of unconscious processing. Mathematicians will often speak of the first phase
of this process as “worrying” about a problem or idea. It’s a good word,
because it evokes anxiety and upset while also conjuring an image of
productivity: a dog worrying a bone, chewing at it to get to the marrow—the
rich, meaty part of the problem that will lead to its solution. In this view of
creative momentum, the key to solving a problem is to take a break from
worrying, to move the problem to the back burner, to let the unwatched pot
boil.
All problem solvers and problem inventors have had the
experience of thinking, and then overthinking, themselves into a dead end. The
question we’ve all encountered—and, inevitably, will encounter again—is how to
get things moving and keep them moving. That is, how to get unstuck.”