The least knotted of all knots is a simple closed loop, the “unknot.” Certainly this is easy to spot on its own, but adding even a few twists can make it hard to recognize:

An elaborately draped loop can be quite difficult to distinguish from a knottier knot. Is this an unknot?

(Yes, it is.)

Surprisingly, while research is ongoing, it remains unknown whether the challenge of recognizing unknots is efficiently solvable — whether an algorithm can accomplish the task in polynomial time. It’s an open question.