Bhaskaracharya (Bhaskara II)

Bhāskarācārya, commonly distinguished as Bhāskara II to separate him from an earlier astronomer of the same name, lived from 1114 to 1185 CE and headed the astronomical observatory at Ujjain, continuing a tradition of Indian mathematical astronomy stretching back through Brahmagupta to Āryabhaṭa and Lagadha before them.

His Līlāvatī, on arithmetic, and Bījagaṇita, on algebra, are traditionally said (per later, not fully verifiable, legend) to have been named for his daughter. Whatever the truth of that story, the Bījagaṇita contains a general method — the chakravāla (cyclic) method — for solving what would later be called Pell's equation in European mathematics, a class of problem that resisted general solution in the West for centuries after Bhāskara's treatment.

The Siddhānta Śiromaṇi, his major astronomical work, describes an attractive force by which the Earth draws objects toward itself — language that anticipates, in qualitative form, the concept of gravitational attraction articulated far more rigorously by Newton roughly five centuries later. In the same text, Bhāskara's treatment of a planet's instantaneous velocity — its rate of motion at a single moment rather than averaged over an interval — is frequently cited as containing reasoning structurally close to the core intuition behind differential calculus, developed independently and more fully by Newton and Leibniz in the 17th century.

Bhāskara II is generally regarded as marking the high point of medieval Indian mathematics and astronomy, drawing algebra, number theory, trigonometry, and observational astronomy into a single, rigorously argued body of work. As with Āryabhaṭa's rotating Earth, the honest framing of his gravitational and calculus-adjacent ideas is that they are strikingly early qualitative intuitions arrived at through a different mathematical tradition — not a fully-formed anticipation of Newtonian mechanics, but a genuine and independent step in that direction.