Olbers' paradox

Remarks

The argument: let $n$ be the number density of stars and $L$ their mean luminosity. A thin shell of radius $r$ and thickness $dr$ around the observer contains $4 \pi r^2 n \, dr$ stars, each of which sends a flux $L / (4 \pi r^2)$. So each shell contributes the same flux $n L \, dr$, and the sum over all shells diverges. Since near stars hide far ones, the sky instead reaches the surface brightness of a star.

Status: resolved within physical cosmology. The universe has a finite age, so light reaches us only from a finite region, and stars have finite lifetimes. These facts alone make the sky dark. The mean distance along a line of sight to a stellar surface is far larger than the distance light has travelled since stars formed. The expansion of the universe adds a further dimming through the cosmological redshift of distant light.

The question is named after Olbers, who wrote about it in 1823; it had been raised earlier, for example by Kepler in 1610 and by de Chéseaux in 1744.