The stellar initial mass function (IMF) is usually assumed to be a probability density distribution function. Recent data appear to question this interpretation though, and I will discuss alternative applications and results concerning the possibly true nature of the IMF. Empirical evidence has emerged that the IMF becomes top-heavy in intense star bursts and at low metallicity. Related to the IMF are binary star distribution functions, and these evolve through dynamical processes in embedded star clusters. The insights gained from these considerations lead to a mathematically computable method for calculating stellar populations in galaxies, with possibly important implications for the matter cycle in galaxies. It turns out that the galaxy-wide IMF, the IGIMF, becomes increasingly top-heavy with increasing galaxy-wide star formation rate, while at the same time the binary fraction in the galactic field decreases.