MacTutor
Indian Mathematics - Redressing the balance
Ian G Pearce
Keralese mathematics: IV. Possible transmission of Keralese mathematics to Europe
In addition to my discussion, there is a very recent paper (written by D Almeida, J John and A Zadorozhnyy) of great interest, which goes as far as to suggest Keralese mathematics may have been transmitted to Europe. It is true that Kerala was in continuous contact with China, Arabia, and at the turn of the 16th century, Europe, thus transmission might well have been possible. However the current theory is that Keralese calculus remained localised until its discovery by Charles Whish in the late 19th century. There is no evidence of direct transmission by way of relevant manuscripts but there is evidence of methodological similarities, communication routes and a suitable chronology for transmission.
A key development of pre-calculus Europe, that of generalisation on the basis of induction, has deep methodological similarities with the corresponding Kerala development (200 years before). There is further evidence that John Wallis (1665) gave a recurrence relation and proof of Pythagoras theorem exactly as Bhaskara II did. The only way European scholars at this time could have been aware of the work of Bhaskara would have been through Keralese 'routes'.
The need for greater calendar accuracy and inadequacies in sea navigation techniques are thought to have led Europeans to seek knowledge from their colonies throughout the 16th and 17th centuries. The requirements of calendar reform were imperative with the dating of Easter proving extremely problematic, by the 16th century the European 'Julian' calendar was becoming so inaccurate that without correction Easter would eventually take place in summer! There were significant financial rewards for 'anyone' who could 'assist' in the improvement of navigation techniques. It is thought 'information' was sought from India in particular due to the influence of 11th century Arabic translations of earlier Indian navigational methods.
Events also suggest it is quite possible that Jesuits (Christian missionaries) in Kerala were 'encouraged' to acquire mathematical knowledge while there.
It is feasible that these observations are mere coincidence but if indeed it is true that transmission of ideas and results between Europe and Kerala occurred, then the 'role' of later Indian mathematics is even more important than previously thought.
A key development of pre-calculus Europe, that of generalisation on the basis of induction, has deep methodological similarities with the corresponding Kerala development (200 years before). There is further evidence that John Wallis (1665) gave a recurrence relation and proof of Pythagoras theorem exactly as Bhaskara II did. The only way European scholars at this time could have been aware of the work of Bhaskara would have been through Keralese 'routes'.
The need for greater calendar accuracy and inadequacies in sea navigation techniques are thought to have led Europeans to seek knowledge from their colonies throughout the 16th and 17th centuries. The requirements of calendar reform were imperative with the dating of Easter proving extremely problematic, by the 16th century the European 'Julian' calendar was becoming so inaccurate that without correction Easter would eventually take place in summer! There were significant financial rewards for 'anyone' who could 'assist' in the improvement of navigation techniques. It is thought 'information' was sought from India in particular due to the influence of 11th century Arabic translations of earlier Indian navigational methods.
Events also suggest it is quite possible that Jesuits (Christian missionaries) in Kerala were 'encouraged' to acquire mathematical knowledge while there.
It is feasible that these observations are mere coincidence but if indeed it is true that transmission of ideas and results between Europe and Kerala occurred, then the 'role' of later Indian mathematics is even more important than previously thought.