Alan Dow and Frank Tall recently proved the consistency of the statement Every hereditarily normal manifold of dimension at least two is metrizable.
See: Dow, Alan; Tall, Franklin D., Hereditarily normal manifolds of dimension greater than one may all be metrizable, Trans. Am. Math. Soc. 372, No. 10, 6805-6851 (2019). ZBL1427.54006.
This suggests a natural question:
Is it true in ZFC that every monotonically normal manifold of dimension at least two is metrizable?
The Long Line is an example of a one-dimensional non-metrizable monotonically normal manifold.
NOTE: By "manifold" I mean a Hausdorff space which is locally euclidean.