Why is the sky dark at night? - Olbers's paradox

Heinrich Olbers, a German astronomer and physician who lived in the 18th and 19th centuries, proposed the question : why isn't the night sky at least as bright as it is during the day? This is referred to as Olbers's paradox or dark night sky paradox. In essence, it states that if the universe is static (homogenous, i.e relatively consistent at a large scale e.g stars and galaxies present throughout) then any and all fields of view from earth must end at a bright surface of a star, thus the night sky should be bright, which obviously isn't the case.

Heinrich Olbers

The paradox in detail

The night sky should be bright in place of dark due to the existence of an infinite number of stars in an infinite universe. This can be best understood using the concept of concentric shells. In short, the first concentric shell will have 1 square, i.e 1^2. The second concentric shell will have 2^2 squares, or 4. This pattern continues infinitely. Each square represents a certain number of stars. 

Concentric shells to help portray the paradox

Say the first shell is 1 billion light years away (this distance is chosen specifically for purposes of easier explanation) from the observer, which could be someone on earth. Since the universe is static and homogenous generally speaking, there would be 4 times as many stars as in the 1st square. And because the second shell is twice as far away, it would appear at 25% of the brightness of the stars that are 1 billion light years away (inverse square law). So, it can be inferred that the first set of stars  at a distance of 1b light years are as bright as the next set that are twice as far away, and this pattern continues indefinitely. As mentioned before, this would only work in an infinite universe or an infinite amount of stars. So, it could mean that the universe is potentially finite and not infinite as previously thought.

Explanations

Astronomers and physicists alike have proposed several explanations : 

1) Cosmic dust between celestial objects blocks the light from reaching us. However, this isn't quite accurate as then the dust would absorb the light and heat energy. However, there isn't enough dust in the universe to block out light sources from all points, and our own sun shines daily without cosmic dust in the way, so this isn't quite as reliable as the others.

2) Finite universe - The concentric shells idea used to show the paradox would not work if the universe is finite, it assumes that the universe is infinite. Thus, there could be a limited amount of stars in the universe which is one explanation. But, even if there are a finite amount of stars, there's still too many for the paradox to be explained correctly.

3) Light from stars hasn't reached us yet. The universe is relatively young : only about 14b years old, so it's quite possible that light from stars has yet to reach us.