Abstract

The initial mass function of stars is observed to be close to universal in the Milky Way and its satellite galaxies, regardless of the age and the environment of the stellar population. Meanwhile significant IMF variations have been inferred from extragalactic observations: there appears to be an excess of low mass stars in massive elliptical galaxies while there is an excess of high mass stars in ultra faint dwarf galaxies. In this talk I will examine what each of these observations require from an IMF theory then (using appropriate proxies for the different galaxies) I will show that no known star formation model satisfies them all. Furthermore I will show that even generic models (without known physical background) would fail to reproduce all three observations.