Who invented calculus?
AI-drafted · awaiting admin review
Kerala mathematicians used key ideas of calculus, such as infinite series and limits, long before Newton and Leibniz. Calculus as a general method with its own notation was built in 17th-century Europe.
Indian contribution, later developed elsewhereMathematics & astronomy
Indian claim
Calculus was invented in India: Bhaskara II and the Kerala school used its methods centuries before Newton and Leibniz.
Evidence for the Indian claim
- Bhaskara II (1150) used instantaneous motion (tatkalika gati) in planetary calculations.
- Madhava (c. 1400) summed infinite series, and the Yuktibhasa (c. 1530) derives them using what are in effect limits and term-by-term summation.
- Historians such as those cited by MacTutor describe this as a substantial part of what later became calculus.
Commonly credited to
Newton and Leibniz invented calculus as a general method, with the fundamental theorem linking derivatives and integrals.
Evidence for the other claim
- Newton (from 1665–66) and Leibniz (published 1684) gave general rules for differentiation and integration that apply to any function, with notation still in use.
- They stated the fundamental theorem of calculus as a general principle; it is not stated in that general form in the Indian texts.
- Greek mathematicians such as Archimedes also used limit-like methods (method of exhaustion) for areas and volumes.
What historians and scientists say
Indian mathematicians, especially in Kerala, discovered important parts of calculus first. Calculus as a unified general theory was developed in Europe. Both statements are true at once.