The ground state spins of even-even nuclei are always 0 without an exception, which is believed to be a consequence of the attractive short-range interaction. However, it was recently discovered that spin 0 ground state (0 g.s.) dominance can be found in many-body systems with random interactions. This discovery is very interesting because, just as pointed out in a paper by Johnson, Bertsch, Dean and Talmi, we are interested in asking: "how arbitrary can an interaction be and still `be` nuclear physics?" It is well known that the low-lying excitations of quite a few many-body systems, such as atomic nuclei or molecules, often display a pattern suggestive of group symmetries, such as rotational or vibrational bands, despite that these many-body systems are so different, complicated. The symmetries are quite unclear from those complicated interactions. This raises a question that how much these "key" properties can be remained if we relax our interactions in our calculation? or we ask for a specific case: what type of interactions produce a generic collectivity, say, rotation? The result that dominance of 0 a.s. separated with a gap from the excited states may be obtained by random interactions indicate that at least one of the key properties (0 g.s. dominance) of nucleus does not really require our previous assumptions: the strong attractive pairing. Then we can ask: what is the origin of this robust observation? Many efforts were made to understand this unexpected discovery. There are also a lot of works related to this, e.g., generic collectivity in systems with random interactions, the behavior of average energies etc. In my seminar I shall present the recent development, in particular the progresses contributed by my collaborators and myself, in understanding the 0 g.s. dominance of many-body systems, and related topics, such as generic rotation and other regular features of fermions and boson systems, etc.