Indian mathematical texts usually stated results in compressed verse and left the reasoning to a teacher. Jyeṣṭhadeva, a later mathematician of the Kerala School broke that habit. After Madhava of Sangamagrama (c. 1340 – 1425 CE) first invented Calculus, Jyeṣṭhadeva (a later mathematician of the Kerala School) wrote the world’s first explicit textbook on calculus in c. 1530 CE. It was written in Malayalam for greater consumption. The Yuktibhāṣā was revolutionary because it didn't just state the mathematical rules; it provided the complete rationale, proofs, and derivations (known as yukti) for those discoveries. The book contains detailed, geometric proofs for integration, differentiation, and infinite power series. While the West spent centuries fighting over whether England (Isaac Newton published his work in c.1704 CE) or Germany (Gottfried Wilhelm Leibniz published his work in c.1684 CE) invented calculus, modern research from institutions like the University of Manchester has shown that the fundamental operational components of calculus, such as infinite series, limits, and mathematical proofs of these expansions, were already fully operational in southwest India. Western scholars expanded the Calculus invented by Indians to Force Mechanics. Europeans often claim that they had “no knowledge” of Indian mathematics, historical evidence shows that Jesuit missionaries were highly active in the Kerala region during the 16th centuries. These missionaries were actively translating and sending mathematical and astronomical texts back to Europe, leading many modern historians to suggest that the "sudden" leap in European mathematics may have been directly or indirectly sparked by imported Indian knowledge. Following Vasco da Gama’s arrival in Kerala in 1499, a direct maritime route opened between Europe and south-west India. By the mid-16th century, Jesuit missionaries had established a heavy presence in the region. Historians like Dr. George Gheverghese Joseph of the University of Manchester have compiled extensive circumstantial evidence tracking how these missionaries interacted with Indian knowledge. The Vatican was deeply invested in exploration, which required accurate navigation, map-making, and calendar correction. Pope Gregory XIII set up a committee to reform the Julian calendar in the late 1500s. Jesuits in India were explicitly instructed to learn local languages and gather mathematical and astronomical data to solve these problems. Jesuits like Johann Ernst Hanxleden (known as Arnos Paatiri) and others became highly fluent in Sanskrit and Malayalam (the languages of the Kerala texts). They translated local works and maintained direct communication networks back to European scientific hubs. #Yuktibhasha #KeralaSchool #IndianScience