Bhaskara II, the derivative and Rolle's theorem
AI-drafted · awaiting admin review
Bhaskara II (1150) noted that a planet's instantaneous speed is zero at its extreme position, an idea close to Rolle's theorem (1691). It was a specific astronomical result, not a general theorem.
Indian contribution, later developed elsewhereMathematics & astronomy
Indian claim
Bhaskaracharya knew the derivative and Rolle's theorem more than 500 years before Europe.
Evidence for the Indian claim
- In the Siddhanta Shiromani (1150), Bhaskara II uses instantaneous motion (tatkalika gati) and says that where a planet is at its farthest point, its instantaneous speed is zero.
- MacTutor's Indian mathematics project describes this as an early form of Rolle's theorem and a hint of the differential.
- A mean value result was later stated by Parameshvara (15th century) of the Kerala school.
Commonly credited to
Michel Rolle stated the theorem in 1691, and the derivative as a general concept comes from Newton and Leibniz.
Evidence for the other claim
- Bhaskara's statements are tied to planetary motion; he does not define a derivative for general functions.
- Rolle's 1691 statement was about polynomials and was later generalised in European analysis.
What historians and scientists say
Bhaskara II genuinely used the idea of an instantaneous rate and its vanishing at an extreme point. Historians see this as an important early step, while the general theory came later in Europe.