What are 7 of ancient india's best advancements and why?

Mathematics - Vedic literature is replete with concepts of zero, the techniques of algebra and algorithm, square root and cube root. Arguably, the origins of Calculus lie in India 300 years before Leibnitz and Newton.
Astronomy - Rig Veda (2000 BC) refers to astronomy.

Physics - Concepts of atom and theory of relativity were explicitly stated by an Indian Philosopher around 600 BC.

Chemistry - Principles of chemistry did not remain abstract but also found expression in distillation of perfumes, aromatic liquids, manufacturing of dyes and pigments, and extraction of sugar.

Medical science & surgery - Around 800 BC, first compendium on medicine and surgery was complied in ancient India.

Mechanical & production technology - Greek historians have testified to smelting of certain metals in India in the 4th century BC.

Civil engineering & architecture - The discovery of urban settlements of Mohenjodaro and Harappa indicate existence of civil engineering & architecture, which blossomed to a highly precise science of civil engineering and architecture and found expression in innumerable monuments of ancient India.

Shipbuilding & navigation - Sanskrit and Pali texts have several references to maritime activity by ancient Indians.Sports & games - Ancient India is the birth place of chess, ludo, snakes and ladders and playing cards.