Total newbie with basically no physics knowledge here :) I would welcome any correction to the steps of my reasoning that lead to my question, which could easily turn out to be invalid :)
My current understanding is that General Relativity is definitely accepted by the vast majority of scientists, and that according to General Relativity spacetime is curved by the presence of mass.
I also seem to understand that not as many scientists (although probably still the majority) agree that extra dimensions of space exist.
But if we agree that spacetime can "curve", aren't we automatically saying that extra dimensions of space exist?
I mean, if I grab a stick and I bend it, it becomes curved with respect to our good old 3D space. The stick needs to be in a 3D space, with respect to which it can be straight or curved.
So, if the thing that gets curved is not an object in space but space itself, doesn't space need to be in "another" space in order to be curved?
I apologize in advance if I used inaccurate terms here, which I most likely did :)