Maybe, I'm slightly over enthusiastic (as a converted Hinduist), still, many scholars, learned in the field, express a similar opinion. (Or, at least, that Indian culture is not less profound, then Chinese, without placing first and second places, because it's not a competition). But. If we talk about the direct influence of one culture on another, then, of course, the Indian influenced the Chinese much more strongly (through Buddhism) than in the opposite direction.
I can't really speak about school and preschool education for children, because I'm not an Indian, but it's rather question to your state and local governments. For example, we here have precisely
one piece of early culture (XII CE, for India it's the start of
modern period, while for us it's the
ancient history
), and it's part of obligatory course of national literature, be it state-issued or any private alternative course (they can't, really, implement private course without state permission).
Don't they at least teach you about the
Mahābhārata and
Rāmāyaṇa at school? About the
Laws of Manu? About
Arthaśāstra? About the astronomical treatises of Aryabhatta and Varahamihira? About the six schools of philosophy and their foundational texts and commentaries? About the six great poems (
mahākāvya)? About didactic literature, such as
Pañcatantra and
Hitopadeśa (
stories that actually spread throughout Eurasia from the British Isles to Japan, but were born in India)? I am silent about the
Saṃhitās of the
Vedas, the
Upaniṣads, the
Purāṇas, poetry, both religious and secular, in Sanskrit and vernacular languages, works on the theory of grammar, theater, music, poetry, medicine, etc., etc. It really is the botomless ocean.
What do you mean by "nothing really interesting"? Just history of India not one bit poorer, that history of China. In all other (especially crucial for good story material) fields India exceeds China: religion, philosophy, mythology, all kinds of literature, self-cultivation systems, and so on, and so forth.
