Hartmann was born the son of a merchant in Erfurt, in Germany. He was educated at the universities of Tübingen, Berlin, and Leipzig where he obtained his PhD in 1891. He worked first at the Leipzig and Potsdam observatories before being appointed in 1909 as professor of astronomy and director of the Göttingen University Observatory. He remained there until 1921 when he became director of the La Plata Observatory in Argentina, only returning to Göttingen in 1935 a few months before his death.

Hartmann was responsible for the important observation in 1904 that provided the first clear evidence for the existence of interstellar gas. He noted that in the spectrum of the star Delta Orion, a binary system, the calcium lines failed to exhibit any periodic Doppler effect arising from the orbital motion of the stars: when a star moves in its orbit toward the Earth the wavelength of lines in its spectrum are shifted toward the blue, while as it moves away from the Earth its spectral lines are shifted toward the red. That there were what Hartmann described as ‘stationary lines’ of calcium in the spectrum could only mean that the calcium was not part of the atmosphere of Delta Orion and therefore was not participating in the orbital motion. It must occur somewhere between binary system and observer. The existence of interstellar matter and its significance in the estimation of stellar distances was finally demonstrated by Robert Trumpler in 1930.