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I encountered this topic a while, back and had a deep look into it, I will be sharing my insights and formed opinion based on the facts that I encountered. @Dx

I encountered this topic a while, back and had a deep look into it, I will be sharing my insights and formed opinion based on the facts that I encountered. @Dx51Q I appreciate your perspective, but I'd like to clarify a few points regarding Madhava's contributions to calculus. While it's true that Madhava and his school may not have created a unifying framework like Newton and Leibniz did, their work laid crucial groundwork for what we now consider calculus. Madhava is credited with developing infinite series for trigonometric functions such as sine and cosine, which are equivalent to the Taylor series we use today. For example, his series for sin(x) and cos(x) predate those discovered in Europe by over 200 years[1][2]. His followers, like Jyeṣṭhadeva, further elaborated on these concepts in texts like the Yuktibhāṣā, providing proofs and demonstrating their applications[3][5]. Moreover, Madhava's methods for approximating pi were remarkably accurate, achieving values correct to 11 decimal places, showcasing his advanced understanding of numerical analysis[2][4]. This indicates that he was indeed engaging with concepts foundational to calculus, such as limits and convergence. Thus, while Madhava's work may not fit neatly into the modern definition of calculus, it represents a significant and sophisticated mathematical tradition that deserves recognition as a precursor to later developments in the field. While we are on this topic, we can stop for a second and ponder on why the ancient Indians needed these mathematical formulation. The answer is astronomy, and thus needing a language/framework to understand the cosmos, i.e. mathematics. Additionally, I wanted to share some interesting insights about the Jesuit transmission of both calculus and the Gregorian calendar from Kerala to Europe. The Jesuit missionaries were not only spreading Christianity through their work, but they were scholars in their own right and could see the value of the advance mathematics they encountered by the Kerala (India) school of mathematics by madhava and the advanced calendar, more accurate than the julian calendar used in Europe at the time. Jesuit missionaries, especially Matteo Ricci, were really fascinated by the advanced mathematical knowledge coming from the Kerala school. They connected with local scholars, like Brahmins and Kshatriyas, to learn about their mathematical concepts, including those found in texts like the Yuktibhāṣā and Tantrasangraha [5]. This collaboration was part of the Jesuits' efforts to understand local cultures and improve their missionary work. It’s fascinating to think that this exchange not only contributed to the Gregorian calendar reform in 1582 but also helped introduce key calculus concepts into European mathematics. As to why this is not common knowledge, it’s partly the British colonial policies that muddied the waters and/or suppressed the source of information. But If one looks at it with time, the evidence is there Citations: [1] https://www.linkedin.com/pulse/madhava-man-who-taught-trigonometry-world-sunila-jha https://www.linkedin.com/pulse/madhava-man-who-taught-trigon... [2] https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama [3] https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ [4] https://en.wikipedia.org/wiki/Madhava_series https://en.wikipedia.org/wiki/Madhava_series [5] https://indicmandala.com/the-kerala-school-european-mathematics/ https://indicmandala.com/the-kerala-school-european-mathemat...

empath75 2y ago
Going to preface this by saying that it's completely uncontroversial that the Kerala school discovered a lot of foundational mathematical concepts independently and in many cases earlier than Europeans, but the evidence for any transmission of those ideas to europe is _extremely_ thin, and you can see the organic development of it mostly within Europe in the textual record after the introduction of Arabic numbers and Arabic mathematical texts to Europe (which of course themselves where _hugely_ influenced by Indian mathematics themselves). You can of course make the argument that colonialist historians are motivated to erase the contributions of foreign mathemeticians, but the _mathematicians themselves_ were not shy about crediting the influence of arabic philosophers and mathematicians, so it would have to be explained why they were fine with crediting al-Khwārizmī but drew the line at crediting Madhava. If they did have direct access to the works of the Kerala school, they'd have developed Calculus much more quickly, that's for sure. It's very possible that there was some extremely vague indirect transmission through word of mouth where the source was obscure even to the mathematicians themselves, but I think it's hard to make the argument that "if not for Madhava, calculus would not have been discovered in Europe." There were many scientists and mathematicans all circling around the same problems and several of them solved aspects of it independently at the same time from different directions. And the idea that _Euler_ only discovered power series with help from Indian mathematics is ridiculous. You can see in his own books and his correspondence with others how he gradually worked them out from first principles over time. There's no mystery as to where it came from. If he had just read about them from a book, he would have used them and not spent several years trying to figure it out. The development of math in Europe was _absolutely_ dependent on the introduction of Indian mathematical ideas through Arabic texts, though.
- canfakt 2y ago
  The claim of "extremely thin evidence" for the transmission of Kerala mathematics to Europe by Jesuits is far from accurate. In fact, there's a wealth of circumstantial evidence supporting this possibility. Jesuits were present in Kerala from 1540-1670, with many, like Matteo Ricci, being highly trained mathematicians tasked with studying Indian sciences. We have clear documentation of their interest in local mathematics, astronomy, and timekeeping, even incorporating subjects like jyotisa into their curricula. Numerous examples show Jesuits actively gathering and transmitting knowledge, from Ricci's inquiries about Indian calendars to Schreck's astronomical observations sent to Kepler. Their close relationships with the Court of Cochin provided access to valuable mathematical manuscripts, and there's evidence of collaboration with Brahmins in translating Sanskrit works. The Jesuits were strongly motivated by practical needs in navigation and calendar reform. Moreover, Marin Mersenne's extensive correspondence network demonstrates that awareness of Indian mathematical knowledge was circulating in Europe. Intriguingly, there are methodological similarities between Kerala mathematics and later European developments, such as parallels between methods used by Wallis and those in the Yuktibhasa. I believe it's crucial to consider the historical context of knowledge transmission between cultures, which often involved clandestine methods. A prime example is the case of Robert Fortune, a Scottish botanist, who in 1848 undertook a covert mission for the British East India Company. Fortune, disguised as a Chinese merchant from a distant province, infiltrated China's heavily guarded tea-growing regions. His objective was to acquire tea plants and seeds, along with the closely guarded secrets of tea production. Fortune's mission was successful; he managed to remove thousands of tea plants and seeds from China, effectively ending the Chinese monopoly on tea production. This act of industrial espionage had far-reaching consequences, leading to the establishment of vast tea plantations in India and Ceylon (now Sri Lanka), and fundamentally altering the global tea trade. While this example pertains to botany rather than mathematics, it illustrates the lengths to which nations went extract knowledge. (Source: Joseph, G. G. (2011). The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition). Princeton University Press.)

empath75 2y ago

Going to preface this by saying that it's completely uncontroversial that the Kerala school discovered a lot of foundational mathematical concepts independently and in many cases earlier than Europeans, but the evidence for any transmission of those ideas to europe is _extremely_ thin, and you can see the organic development of it mostly within Europe in the textual record after the introduction of Arabic numbers and Arabic mathematical texts to Europe (which of course themselves where _hugely_ influenced by Indian mathematics themselves). You can of course make the argument that colonialist historians are motivated to erase the contributions of foreign mathemeticians, but the _mathematicians themselves_ were not shy about crediting the influence of arabic philosophers and mathematicians, so it would have to be explained why they were fine with crediting al-Khwārizmī but drew the line at crediting Madhava. If they did have direct access to the works of the Kerala school, they'd have developed Calculus much more quickly, that's for sure. It's very possible that there was some extremely vague indirect transmission through word of mouth where the source was obscure even to the mathematicians themselves, but I think it's hard to make the argument that "if not for Madhava, calculus would not have been discovered in Europe." There were many scientists and mathematicans all circling around the same problems and several of them solved aspects of it independently at the same time from different directions. And the idea that _Euler_ only discovered power series with help from Indian mathematics is ridiculous. You can see in his own books and his correspondence with others how he gradually worked them out from first principles over time. There's no mystery as to where it came from. If he had just read about them from a book, he would have used them and not spent several years trying to figure it out. The development of math in Europe was _absolutely_ dependent on the introduction of Indian mathematical ideas through Arabic texts, though.

canfakt 2y ago
The claim of "extremely thin evidence" for the transmission of Kerala mathematics to Europe by Jesuits is far from accurate. In fact, there's a wealth of circumstantial evidence supporting this possibility. Jesuits were present in Kerala from 1540-1670, with many, like Matteo Ricci, being highly trained mathematicians tasked with studying Indian sciences. We have clear documentation of their interest in local mathematics, astronomy, and timekeeping, even incorporating subjects like jyotisa into their curricula. Numerous examples show Jesuits actively gathering and transmitting knowledge, from Ricci's inquiries about Indian calendars to Schreck's astronomical observations sent to Kepler. Their close relationships with the Court of Cochin provided access to valuable mathematical manuscripts, and there's evidence of collaboration with Brahmins in translating Sanskrit works. The Jesuits were strongly motivated by practical needs in navigation and calendar reform. Moreover, Marin Mersenne's extensive correspondence network demonstrates that awareness of Indian mathematical knowledge was circulating in Europe. Intriguingly, there are methodological similarities between Kerala mathematics and later European developments, such as parallels between methods used by Wallis and those in the Yuktibhasa. I believe it's crucial to consider the historical context of knowledge transmission between cultures, which often involved clandestine methods. A prime example is the case of Robert Fortune, a Scottish botanist, who in 1848 undertook a covert mission for the British East India Company. Fortune, disguised as a Chinese merchant from a distant province, infiltrated China's heavily guarded tea-growing regions. His objective was to acquire tea plants and seeds, along with the closely guarded secrets of tea production. Fortune's mission was successful; he managed to remove thousands of tea plants and seeds from China, effectively ending the Chinese monopoly on tea production. This act of industrial espionage had far-reaching consequences, leading to the establishment of vast tea plantations in India and Ceylon (now Sri Lanka), and fundamentally altering the global tea trade. While this example pertains to botany rather than mathematics, it illustrates the lengths to which nations went extract knowledge. (Source: Joseph, G. G. (2011). The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition). Princeton University Press.)