First of all, let me tell you that I'm not a physicist but rather a computer scientist with a mere interest in physics at nowhere near a professional level so feel free to close this question if it doesn't make any sense.
I remember a physicist friend mentioning me about an argument about the finiteness of the universe. I have looked it up and it turned out to be Olbers' Paradox.
We computer scientist like to use astronomical numbers to help us imagine the complexity of an algorithm. One of the most common one is the number of atoms in the Observable Universe (which we take as $10^{80}$) so I have a crude understanding about the observable universe concept.
I had known these two for some time hence I woke up with the dilemma today. So my question is, how come it can be argued that universe is finite just because it is dark if we know that we can only observe a finite portion of it? Can't it be the case that the universe is infinite even if the sky is dark because not all the light from all the stars reach the earth?
I have searched this a little bit but I think I need an explanation in simpler terms (like popular physics). A historical perspective would also be welcomed.