India never invaded any country in her last 100000 years of history.
When many cultures were only nomadic forest dwellers over 5000 years ago, Indians established Harappan culture in Sindhu Valley (Indus Valley Civilization)
The name 'India' is derived from the River Indus, the valleys around which were the home of the early settlers. The Aryan worshippers referred to the river Indus as the Sindhu.
The Persian invaders converted it into Hindu. The name 'Hindustan' combines Sindhu and Hindu and thus refers to the land of the Hindus.
Algebra, Trigonometry and Calculus are studies, which originated in India.