Abstract: This article first reviews the background behind the emergence of the discipline of Language and Human Brain Sciences. It then focuses on one of the essential topics within the study of language and brain: the Galilean Challenge. The main viewpoints are as follows: 1) The concept of the Galilean Challenge represents Chomsky’s consistent thoughts on the nature of language. It shares a common theoretical concern with Plato’s Problem of language acquisition, the study of which can trace back to the tradition since the 17th and 18th centuries. This has been one of the driving factors for the intersection and infiltration of linguistics, psychology, neuroscience, biology and other related disciplines; 2) Given the diversity in language externalization, a comprehensive examination of the so-called "patchwork" externalization, encompassing implicit components, is necessary to accurately capture the true essence of the simplicity of I-language; 3) The pursuit of simplicity in studying language and human brain sciences mirrors Einstein's "Miracle Creed" in formulating scientific theories; 4) Employing the strongest cartographic strategy in exploring various explicit or implicit functional heads can significantly enhance our understanding of the Galilean Challenge.