New computational research by the International Journal of Ancient Mathematics has analyzed rare variants of Bhaskara II's 12th-century masterpiece, the Siddhanta-Shiromani. The study utilizes advanced OCR and linguistic modeling to demonstrate that the text contains formal mathematical proofs for instantaneous velocity—specifically the concept of tatkaliki gati—which predates the Western development of differential calculus by several centuries.
By examining the commentary layers on planetary motion, researchers identified a sophisticated use of infinitesimal fluxions to calculate the precise change in a planet's position over a null interval. This finding elevates the historical understanding of the Kerala School of Mathematics' early foundations, suggesting that the mathematical framework for calculus was deeply integrated into Indian astronomical modeling long before European contact.