Abstract: Based on the brief review of generation process of the two core-system hypothesis, the essay mainly analyses the core point, working mechanism and experimental basis of the two core-system hypothesis, including the experimental basis on the small precise representative system and large approximate representative system。Finally, the problem and dispute of behavior and brain physiological mechanism are discussed, as well as the contradiction result and method limitation, and seven urgent problems are explored such as the baby’s number cognition depends on independent system or multiple systems and so on

Key words: infants, approximate representative system, precise representative system, the two core-system hypothesis, primary mathematical abilities