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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 circum

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.)

FooBarBizBazz 2y ago
> 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. For anyone else reading, I'll mention that I found this book extremely engaging: Rose, Sarah. For All the Tea in China: Espionage, Empire, and the Secret Formula for the World's Favourite Drink.
- srean 2y ago
  Any one who knows his/her tea, opium, coffee and chocolate knows a lot about the world. I don't know enough about cocaine to comment on it. The battle for and between tea and opium is truly bizarre. Today we have war against drugs, the British were fighting for the opposite -- to make China hooked on opium (to counterbalance the import cost of tea) and then blame China -- you opium addled lesser civilization.
griffzhowl 2y ago
The thing is, circumstantial evidence that transmission could have happened, though suggestive, isn't positive evidence that it did happen. The absence of such direct evidence such as translations or quotations from relevant Indian works in Europe is even emphasized in Joseph's book that you give as ref. The claim that Madhava "laid crucial groundwork" for the development of calculus in Europe needs to be backed up with some argument saying exactly what was transmitted and when. The problem with simply observing that his results on infinite series for arctan, sin and cos reappeared in Europe much later is that this doesn't rule out independent discovery in Europe. And the case for independent discovery is strong, because we have the documentary evidence of the logic of discovery: Newton and Gregory both obtained these series from the general binomial series, seemingly independently of each other, and to my knowledge Madhava didn't have this result.[0] They're both clearly basing their works on documented predecessors (who happen to be European) such as Wallis, Fermat, Descartes, Viete, and others, so the trajectory of how the results were obtained seems to be accounted for. So what was the crucial groundwork, and when was it transmitted? There might have been something (e.g. your suggestion about parallels between Wallis and the Yuktibhasa), but I haven't seen a strong argument that gives these details. I would be fascinated if there were though. [0] Stillwell 2010 Mathematics and its History (3rd ed.) - Stillwell is sympathetic to the Kerala school, is very clear in assigning Madhava priority on the arctan, sin and cos series, but concludes, along with most historical scholarship, that it seems there was no transmission of these results to Europe
- canfakt 2y ago
  Firstly, your claim about Stillwell's "conclusion" is a misrepresentation. Stillwell makes no such conclusion about the lack of transmission. In fact, he explicitly states that the Kerala school knew these mathematical series before 1540. This selective reading and distortion of Stillwell's work is intellectually dishonest and undermines genuine historical inquiry. The Jesuits sent to India weren't not your typical bible thumpers; they were highly trained mathematicians and astronomers with a specific mission to study and acquire Indian mathematical and astronomical knowledge. The primary motivation for Europeans to import knowledge from India wasn't mere academic curiosity - it was a matter of practical necessity, particularly in navigation. By the mid-16th century, Europeans were grappling with significant errors in their calendar calculations. The true solar year was about 11.25 minutes shorter than the assumed 365.25 days, an error that had compounded over centuries, leading to serious discrepancies in timekeeping and navigation. Matteo Ricci, the Jesuit astronomer and mathematician in a letter from India to Giovanni Battista Maffei (Italian mathematician) he states that he requires the assistance of an “intelligent Brahmin or an honest Moor” to help him understand the local ways of recording and measuring time. If one wants a smoking gun—a direct admission of knowledge transfer—is either naïve or deliberately obtuse. Do you also believe that tea plants magically teleported from China to India? The British East India Company's industrial espionage in China's tea industry parallels the Jesuits' activities in India perfectly. Both were covert operations aimed at acquiring valuable "know-how" for economic and strategic gain. Do we have a signed confession from Robert Fortune or his kin admitting to tea espionage? The cumulating circumstantial evidence isn't just substantial—it's overwhelming. We have documented records of Jesuits studying Indian texts, teaching Indian concepts, and corresponding with European mathematicians (see my other comment for examples). The methodological similarities between Kerala mathematics and later European work, like the striking parallels between Wallis and the Yuktibhasa (15th century), where Wallis (in 17th Century) is using the exact expression and reasoning as given in the Yuktibhasa, aren't coincidences—they're smoking guns. Your dismissal of this substantial body of evidence goes beyond healthy skepticism. It appears to disregard the complex realities of historical knowledge transfer risks coming off as a deliberate attempt to erase non-European contributions to mathematical history.

FooBarBizBazz 2y ago

> 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. For anyone else reading, I'll mention that I found this book extremely engaging: Rose, Sarah. For All the Tea in China: Espionage, Empire, and the Secret Formula for the World's Favourite Drink.

srean 2y ago
Any one who knows his/her tea, opium, coffee and chocolate knows a lot about the world. I don't know enough about cocaine to comment on it. The battle for and between tea and opium is truly bizarre. Today we have war against drugs, the British were fighting for the opposite -- to make China hooked on opium (to counterbalance the import cost of tea) and then blame China -- you opium addled lesser civilization.

griffzhowl 2y ago

The thing is, circumstantial evidence that transmission could have happened, though suggestive, isn't positive evidence that it did happen. The absence of such direct evidence such as translations or quotations from relevant Indian works in Europe is even emphasized in Joseph's book that you give as ref. The claim that Madhava "laid crucial groundwork" for the development of calculus in Europe needs to be backed up with some argument saying exactly what was transmitted and when. The problem with simply observing that his results on infinite series for arctan, sin and cos reappeared in Europe much later is that this doesn't rule out independent discovery in Europe. And the case for independent discovery is strong, because we have the documentary evidence of the logic of discovery: Newton and Gregory both obtained these series from the general binomial series, seemingly independently of each other, and to my knowledge Madhava didn't have this result.[0] They're both clearly basing their works on documented predecessors (who happen to be European) such as Wallis, Fermat, Descartes, Viete, and others, so the trajectory of how the results were obtained seems to be accounted for. So what was the crucial groundwork, and when was it transmitted? There might have been something (e.g. your suggestion about parallels between Wallis and the Yuktibhasa), but I haven't seen a strong argument that gives these details. I would be fascinated if there were though. [0] Stillwell 2010 Mathematics and its History (3rd ed.) - Stillwell is sympathetic to the Kerala school, is very clear in assigning Madhava priority on the arctan, sin and cos series, but concludes, along with most historical scholarship, that it seems there was no transmission of these results to Europe

canfakt 2y ago
Firstly, your claim about Stillwell's "conclusion" is a misrepresentation. Stillwell makes no such conclusion about the lack of transmission. In fact, he explicitly states that the Kerala school knew these mathematical series before 1540. This selective reading and distortion of Stillwell's work is intellectually dishonest and undermines genuine historical inquiry. The Jesuits sent to India weren't not your typical bible thumpers; they were highly trained mathematicians and astronomers with a specific mission to study and acquire Indian mathematical and astronomical knowledge. The primary motivation for Europeans to import knowledge from India wasn't mere academic curiosity - it was a matter of practical necessity, particularly in navigation. By the mid-16th century, Europeans were grappling with significant errors in their calendar calculations. The true solar year was about 11.25 minutes shorter than the assumed 365.25 days, an error that had compounded over centuries, leading to serious discrepancies in timekeeping and navigation. Matteo Ricci, the Jesuit astronomer and mathematician in a letter from India to Giovanni Battista Maffei (Italian mathematician) he states that he requires the assistance of an “intelligent Brahmin or an honest Moor” to help him understand the local ways of recording and measuring time. If one wants a smoking gun—a direct admission of knowledge transfer—is either naïve or deliberately obtuse. Do you also believe that tea plants magically teleported from China to India? The British East India Company's industrial espionage in China's tea industry parallels the Jesuits' activities in India perfectly. Both were covert operations aimed at acquiring valuable "know-how" for economic and strategic gain. Do we have a signed confession from Robert Fortune or his kin admitting to tea espionage? The cumulating circumstantial evidence isn't just substantial—it's overwhelming. We have documented records of Jesuits studying Indian texts, teaching Indian concepts, and corresponding with European mathematicians (see my other comment for examples). The methodological similarities between Kerala mathematics and later European work, like the striking parallels between Wallis and the Yuktibhasa (15th century), where Wallis (in 17th Century) is using the exact expression and reasoning as given in the Yuktibhasa, aren't coincidences—they're smoking guns. Your dismissal of this substantial body of evidence goes beyond healthy skepticism. It appears to disregard the complex realities of historical knowledge transfer risks coming off as a deliberate attempt to erase non-European contributions to mathematical history.