We haven't resolved whether every possible tangle of a rope, when idealized mathematically, can be untangled using a provably minimal number of moves.
open
Global / Unspecified, Global
WS01267
Knot theory offers tools for identifying and classifying tangles, but calculating a guaranteed minimal ontangling path for every possible knot remains computationally unresolved. This connects abstract mathematics to physical intuition about rope and cords.