Olbers, who was born at Arbegen in Germany, was a physician who practiced medicine at Bremen. He became a good amateur astronomer, and converted part of his house into an observatory. He became interested in searching for a planet in the ‘gap’ between Mars and Jupiter, and rediscovered the first minor planet (or asteroid) Ceres after it had been lost by its discoverer Giuseppe Piazzi. In 1802 he discovered the second asteroid, Pallas, and in 1807 the fourth, Vesta. He also devised a method of calculating comet orbits, called Olbers's method, and discovered five comets. The one named for him was last seen in 1956.

Olbers's modern fame, however, rests on his statement of a very simple problem, the solution of which has had a profound impact on modern cosmology. He asked the naive question: why is the sky dark at night? Olbers assumed that the heavens are infinite and unchanging and that the stars are evenly distributed. The amount of light reaching the Earth from very distant stars is very small – in fact, the illumination decreases with the square of the distance. On the other hand, this is compensated for by the increased number of stars – the average number at a given distance increases with the square of the distance. The result is that the whole sky should be about as bright as our Sun. Olbers's solution to this problem was that the light is absorbed by dust in space, but this is an unsatisfactory explanation since the dust would eventually become incandescent and radiate energy. In the 20th century it became clear that the solution lies in the fact that the universe is not uniform, infinite in time, or unchanging; the red shift of the light from distant galaxies results in a reduction of the energy of the radiation from stars. The paradox had been discussed earlier (1744) by J. P. L. Chesaux.