Who among the following has worked in the field of mathematical astronomy ?

Correct Answer: Aryabhatta and Bhaskara I

Explanation:

Both Aryabhatta and Bhaskara I were prominent ancient Indian mathematicians and astronomers who made fundamental contributions to the field of mathematical astronomy.

1. Aryabhatta (476–550 CE):
He authored the famous treatise Aryabhatiya, which covers both mathematics and astronomy. He pioneered concepts such as the heliocentric principles of planetary motion, calculated the length of the solar year, explained the causes of solar and lunar eclipses, and provided accurate approximations for π (pi).

2. Bhaskara I (c. 600–680 CE):
He was a 7th-century astronomer and mathematician who wrote commentaries on Aryabhatta's work (such as Aryabhatiyabhasya) and composed two major astronomical works: Mahabhaskariya and Laghubhaskariya. He is also famous for providing a unique rational approximation of the sine function.

While Srinivasa Ramanujan was a legendary 20th-century mathematician (focusing on number theory and mathematical analysis) and Mahavira was a 9th-century Jain mathematician (author of Ganita-sara-samgraha), it is Aryabhatta and Bhaskara I who are explicitly recognized for their extensive foundational work in mathematical astronomy.