The ground states of all even-even nuclei have angular momentum equal to zero, I 0, and positive parity, π +. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, a predominance of I^π 0⁺ ground states was discovered in 1998 using the two-body random ensemble. Since then many efforts have been devoted to understanding and solving this problem from a lot of viewpoints. Still, the underlying physical origin of the I^π 0⁺ dominance has not been fully understood. Our recent progress in understanding the 0⁺dominance of many-body systems is shown.