As far as I know, in the CAD world Z is typically up/down. It makes sense if you look at the scene from above, like an architect a floor plan - world-space X and Y map to screen-space X and Y, and Z is then the depth. In a 3D virtual world, on the other hand, the perspective is usually of a person embedded in the world, in which case "Y is up" is more intuitive.

OK, thinking about the architecture angle finally made it click for me.

When I took Calculus III, Z was up. When I took Engineering Physics the same semester, Y was up.

According to legend, this is why the Math and Physics departments hate each other.

So the difference between Math and Physics can be described as a single rotation matrix?

I thought it was coming from the fact Nobel's wife had an affair with a mathematician. Thus explaining why there is no Nobel Price for Mathematics.

There are several reasons to believe that that urban legend isn't true. One of them being that Nobel was never married.

With the right rotation, any direction can be pointing "up".

It makes sense if you think of the X and Y axis as being drawn on paper, which usually lies flat on the desk.

Sort of, kind of, but it's a stretch. "Up and down" on a page are not oriented according to gravity, but according to the top and bottom of the page. If you say "Well, we'll make the z-axis vertical because vertical is perpendicular to the plane of the desk, and that's depth", and then you put the z-axis toward the top of the page, you're using two completely different definitions of "vertical" in the same sentence.

I always use Z for up/down even though I'm a programmer. For some reason I just find it easier to reason about. In fairness, my first forays into 3D were extending a 2D top-down game with an "altitude".