From the Wikipedia article:

Szymanski's conjecture states that every permutation on the n-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths. That is, if the permutation σ matches each vertex v to another vertex σ(v), then for each v there exists a path in the hypercube graph from v to σ(v) such that no two paths for two different vertices u and v use the same edge in the same direction.

Example of routing on the cube (n=3):

We know that it's true for n ≤ 4, but is it true for all n?

Will resolve to YES if there's a widely accepted proof that the conjecture is true and NO if there's a widely accepted proof that the conjecture is false.