Olbers' paradox

If the universe is infinite and has existed forever, then there should be a star in every direction we look.
This would mean the night sky should be as bright as day because of the infinite amount of stars.
However, the night sky is dark, indicating our assumption about the universe might be wrong.

The universe is not infinite: There's a limit to how far we can see, either due to spatial or temporal boundaries.

We can only see a certain horizon in the universe.
The darkness of the night sky suggests the universe is not infinite, or we cannot see all of it.
The universe is generally the same in every direction on large scales.
The resolution to Olbers' Paradox is that the universe is not infinite, or we can not see the infinite universe.

Proposed in the 1820s by German astronomer Heinrich Wilhelm Olbers, though similar arguments were made earlier by others like Kepler.

If the universe is infinite, static, and has existed forever, then there should be a star in every direction we look.
This means that no matter where you look in the night sky, your line of sight should eventually intersect with a star.
Since every line of sight ends on a star, the night sky should be as bright as the surface of a star, essentially as bright as day, because of the infinite amount of stars.
However, the night sky is dark, indicating our assumption about the universe might be wrong. This stark contradiction is Olbers' Paradox.

The universe is not infinite: There's a limit to how far we can see, either due to spatial or temporal boundaries.
Finite Universe: If the universe has a finite size, then there are not enough stars to cover every line of sight.
Age of the Universe: The universe has not existed forever, so light from very distant stars has not had time to reach us.
Expanding Universe: The expansion of the universe causes the light from distant galaxies to be redshifted, reducing its energy and brightness.
Absorption of Light: Interstellar dust and gas could absorb some of the light, but this is not sufficient to explain the darkness of the night sky.

We can only see a certain horizon in the universe due to the finite speed of light and the expansion of the universe.
The darkness of the night sky suggests the universe is not infinite, or we cannot see all of it.
The universe is generally the same in every direction on large scales (homogeneous and isotropic).
The resolution to Olbers' Paradox is that the universe is not infinite, or we can not see the infinite universe. The most accepted explanation involves the finite age and expansion of the universe.

The Big Bang theory suggests the universe is approximately 13.8 billion years old.
Light from objects farther than 13.8 billion light-years has not reached us yet.
The expansion of the universe stretches the wavelengths of light (redshift), reducing the energy of photons from distant objects.
These factors combined provide a comprehensive explanation for why the night sky is dark.