  A critical discourse is provided on the current status of the astrophysics of
galaxies in view of open fundamental questions on the law of gravitation and
the physics-driven variation of the galaxy-wide stellar initial mass function
(GWIMF). The Einstein/Newtonian plus cold or warm dark-matter-based models face
many significant but unresolved tensions (e.g. planes of satellites, the highly
organised and symmetrical structure of the Local Group, the local Gpc-scale
void). The accumulating nature of these indicates quite compellingly the need
for a different theoretical framework. An example is the prediction, made in
1997, of the existence of satellite galaxies with near-exact properties to the
Hercules dwarf spheroidal satellite galaxy discovered in 2007 if it is a tidal
dwarf galaxy void of dark matter. Such results indicate that once the evidence
is accepted that dark matter particles have no role in galaxies with
gravitation being effectively Milgromian, then the resulting theoretical
understanding of galaxies becomes much simpler and highly predictive with
remarkable successes. Along with these scientific advancements, the recent
observational data solidify the existence of one of the most important
relations in star-formation theory, namely the mmax-Mecl relation. The data
rule out stochastic star formation and confirm that the IMF becomes
increasingly top-heavy with increasing star-formation rate density. Galaxies
and their embedded-star-cluster building blocks are therefore self-regulated
dynamical systems which are computationally accessible. Finding a theory for
the formation of galaxies involves the development of a new cosmological model,
which may differ substantially from the dark-matter based one. Very significant
new opportunities have thus emerged for inquisitive and daring researchers
which may appear risky now but almost certainly lead to major breakthroughs.
