Illams of individual teachers, whose fame attracted students from far and near to stay for extended periods of time, was important in a society where knowledge was passed on from person to person

In medieval Kerala, people lived in scattered settlements. Their contacts with outside world was through travel and hence learning was acquired in three main ways. First, scholars were invited to certain cultural centres. These centres were established or patronised by notables, often of royal birth, some of whom were considerable scholars or artists in their own right. Second, in certain temples, rich people donated part of their wealth to art and learning as an expression of their piety. Part of this donation was used to support scholarly activities. The temple was also a place of pilgrimage where people travelled long distances to see the divine in different forms: in sculpture, architecture and ceremonial drama or in priests and scholars given to a life of devotion or cultivation of intellectual pursuits. Third, and more commonly in the case of the Nambuthiris, there were homes (illams) of individual teachers whose fame attracted students from far and near to stay for extended periods of time. This type of transmission was important in a society where knowledge was passed on from person to person without recourse to books or similar aids.
It was the practice among the students and teachers of the Kerala School to live and work in these illams. The typical illam had one or two internal courtyards without a roof and was built either as a square or double square around them. The roof was tiled, or more commonly in the olden days thatched with coconut leaves. The thatched roof had to be replaced annually. The floor was bare, just constructed from mud: no form of cement or marble was used. There would be a shed some distance away for the cows and a sizeable stack of hay to feed them. Membership of a number of these illams were often limited, as we saw earlier, to a leisured class of younger sons of land-owning families whose economic needs were provided for by their families and whom custom dictated could not marry. A few of them chose to take up the study of astronomy and mathematics as an intellectual activity and not for earning their livelihood by constructing calendars or casting horoscopes. The latter was generally undertaken by another group consisting of professional astrologers (kaniyans) whose technical knowledge of these areas rarely went beyond a minimum basic competence passed on through families and through referring occasionally to certain elementary manuals. However, a symbiotic relationship apparently developed between some members of the Kerala School and certain kaniyans, transcending caste barriers, providing a stronger ‘application’ orientation to the work of the former group and improving the mathematical and astronomical skills of the latter. It is interesting how, even in a highly rigid caste system, contacts were maintained between two groups who were socially far apart, raising the wider question of the extent to which scientific ideas percolated into the wider society.
In a number of illams which specialised in mathematical astronomy, a small, self-selected and highly motivated group of students were set to memorise verses summarising results from the past. It is from the works of these scholars that we can piece together the Kerala episode of Indian mathematics. And for the most part, the writings of these scholars rarely circulated much beyond their locality. Contrast this with the wider campus within which the proliferation of mathematical discoveries occurred in Europe during the seventeenth and eighteenth centuries and perhaps we have some clue as to the different course of mathematical development in the two cultures
Source:
George Gheverghese Joseph, A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact, Sage India, First edition (11 November 2009), pp. 34-35