In this question I am coming from a mathematical perspective. Apologies if this question has already been answered in layman's terms. But here I am trying to understand the issues in mathematical terms.
Consider travelling between two points which are very far appart, say the distance of 1000 times the distance to our nearest neighbouring galaxy, Canis Major. Say you travel directly toward that location, then since our universe is flat, you will pretty much travel in an straight line. To a good approximation, anyway.
Our spacetime will be embedded in an higher dimensional flat space, like the way a 2D sheet of paper exists in 3D. If the spacetime metric was a true metric (distance must be positive) then by the axiom of the triangle inequality, any detour out of the plane of flat space would be a greater distance of travel; as it would be a curved path between the same two points.
QUESTION. Can a detour through a wormhole really be shorter in distance or time than the straight line path?
As the spacetime metric is a pseudo-metric (distance can be negative), I realise that triangle inequality will probably no longer apply. Is that the reason why wormholes can allow a faster journey between the two points?