Ok so me and a few of my physics (& Maths) friends were arguing this. I argued that it must be finite in size, since the universe contains a finite amount of matter and since no space is truly empty, how could the universe be finite. My friend who's a mathematician said that in her geometry subject this question was actually brought up. She said that the universe may be a 3-manifold (3D surface?) and it depends on the curvature (negative or positive) as to whether the universe is finite or not. I just want to know what the consensus is.