(a) Ancient India was a land of sages and seers as well as a land of scholars and scientists. It covered all the major branches of human knowledge and activities, including mathematics, astronomy, physics, chemistry, medical science and surgery, fine arts, etc.
Mathematics - Vedic literature is replete with concepts of zero, square root and cube root.
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.
(b) Vastu Shastra:
It is an ancient Indian science to enhance abundance & prosperity by making auspicious buildings. These are texts found on the Indian subcontinent that describe principles of design, layout, measurements, ground preparation. A number of Indian families adhere to the tenets of Vastu Shastra to rid their homes of negativity and unhappiness.