Indian Mathematicians and Astronomers

Kanada (also known as Kashyapa) founded the Vaisheshika school of Hindu philosophy, which proposed that all matter is composed of indivisible atoms called 'paramanu'. This atomic theory dates back to around 6th-2nd century BCE, making it one of the earliest atomic theories in the world. The other options were mathematicians and astronomers but not associated with atomic theory.

Aryabhatta is credited with the invention and use of zero as a number in the 5th century CE. While the concept existed in earlier civilizations, Aryabhatta formalized zero's use in mathematical calculations and the decimal system. Bhaskara, Varahamihira were later astronomers, and Archimedes was Greek.

Aryabhatta (5th century CE) proposed a heliocentric model in his treatise Aryabhatiya, explaining that the earth rotates on its axis and revolves around the sun. This was remarkably advanced for his time. Vatsyayana is known for Kamasutra, Susruta for medicine, and Vishnugupta (Chanakya) for Arthashastra.

Pythagoras is documented to have visited India around the 6th century BCE. Ancient Greek sources and Indian traditions mention his travels to learn from Indian scholars and priests. This exchange is believed to have influenced his philosophical and mathematical ideas.

Aryabhatta, the ancient Indian mathematician and astronomer (5th century CE), is credited with developing the concept of zero as a number and its mathematical operations. His work revolutionized mathematics and formed the foundation of the decimal system.

'Numbers rule the universe' was said by Pythagoras.

The birth centenary of S. Ramanujam was celebrated in India in 1987.

The 'Aryabhateeya' was written by 'Aaryabhatta - 1'.

Aryabhatta (5th century CE) is credited with using zero as a number in Indian mathematics, though Brahmagupta later formalized its operations. However, the concept evolved over centuries - Babylonians used zero as a placeholder earlier. Within the Indian context of this question's options, Aryabhatta is the intended answer. Ramanujam is modern (20th century), Patanjali is known for Yoga sutras.

Adi Shankaracharya established four cardinal institutions (Mathas) in the four corners of India: Sringeri (South), Puri (East), Dwaraka (West), and Jyotirmath (North). These centers were created to sustain and propagate Advaita Vedanta.

Aryabhatta is widely credited with foundational work in algebra and astronomy in ancient India, including the concept of zero and the decimal system.

Srinivasa Ramanujan was a self-taught Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, and infinite series.

Aryabhatta was a renowned ancient Indian mathematician and astronomer who wrote the Aryabhatiya. Charak was a physician, and Shudrak was a playwright.

Aryabhata is widely regarded as the first of the major mathematician-astronomers from the classical age of Indian mathematics and astronomy.