Summary: - Differential calculus is defined as a systematic theory of differentiation, integration and the connecting fundamental theorem, which did not exist anywhere outside Europe before the 17th century. - India did not invent differential calculus because no Indian tradition had developed general, algorithmic methods for differentiating and integrating broad classes of curves. - Mathematics before the 17th century in India, the Islamic world and Greece contained isolated tricks for infinities and results for special cases, not unified differential calculus. - The key historical error behind the claim that "India invented differential calculus" is to confuse specific problem-solving methods with a general theory that applies to all problems. - Leibniz's 1684 article is presented as the first public announcement of a truly systematic differential calculus with general rules, such as the product and quotient rules. - Leibniz's later publications (in 1686 on integration and in 1693 on the Fundamental Theorem) are described as completing the systematic framework of differential calculus. - Newton and Leibniz are credited (by Katz) as inventors because they unified the ideas of derivatives and integrals and combined them into a powerful general tool. - The claim that European differential calculus originated from Indian methods handed down by the Jesuits is rejected as unsupported by historical evidence. - Plofker is quoted saying that no Latin translations or abstracts of 16th-17th century Kerala texts are known, and that no European innovator gives credit to Indian sources. - Plofker is also quoted saying that early European infinitesimal techniques resemble Hellenistic predecessors rather than Indian methods. - Bressoud is quoted saying that Indian work on series was not known outside India (or even outside Kerala) until the 19th century. - Katz argues that non-European mathematics did not have a significant impact on European development, and knowing this fact would have spared Europeans centuries of duplicated effort. - Baldini argues that the scenario of knowledge transfer by the Jesuits is unlikely, since the Jesuits focused mainly on Chinese mathematics, and access to "proprietary" Hindu texts by religious rivals would have been unlikely.