Vernacular Mathematics in Pre-Modern India (EAP1063)

Aims and objectives

This project will collect materials from three regional vernacular mathematical cultures in India. The Material includes a variety of pre modern mathematical sources, which reflect the entire textual scope of vernacular mathematical cultures: Palm leaf manuscripts of mathematical treatises in vernacular languages (non Sanskrit), palm leaves of village, temple and merchant account registers, manuals of merchants, accountants and artisans (e.g. sculptors, boat makers), and pedagogical mathematical texts. The regional (linguistic) focus of the project is: Kerala (Malayalam), Tamil Nadu (Tamil), and Uttar Pradesh and Uttarakhand (Hindi). The material will enable research into social and cognitive contexts of pre-modern Indian mathematics.

So far, scholarship on Indian mathematics has mostly been interested in an abstract and universalised view of mathematics. It therefore focused on canonical Sanskrit treatises that emphasise abstract and universal aspects of mathematics, and on comparisons with foreign high mathematical cultures. This approach to knowledge risks leading to anachronistic reconstructions of Indian mathematics, instead of interpreting it in the context of Indian knowledge and society itself. This result feeds back into the myth that mathematics is a universal and abstract form of knowledge, rather than a locally embedded set of practices, closing a vicious circle.

This project aims at highlighting the local logics of mathematics and the contextual motivations for the development and presentation of mathematical texts. To achieve that, we must complement the Sanskrit sources with vernacular sources that cover the complex continuum of education, accounting, commerce, bureaucracy, artisanal practice and higher theoretical knowledge. This continuum spans a comprehensive social context, and prevents us from identifying one kind of sources (Sanskrit) as the only ‘national tradition’.

Collecting such sources will provide us with the means to analyse how mathematical practices and texts functioned as social and cognitive agents, linking (or setting apart) schools, workshops, civil administration, markets and centres of higher learning. This analysis will shed new light on the pre modern social, economic and intellectual history of several Indian regions, and add to our understanding of local power dynamics in the pre-modern Indian world, highlighting how practices of accounting and compartmentalisation of mathematical knowledge allowed indigenous affluent communities to assert their dominance over lower castes. A similar approach has proved useful in the study of Egyptian, Babylonian, and late medieval European vernacular mathematics, increasing our understanding of the cognitive and social background of higher and lower mathematics.

Moreover, during the 14th-16th centuries Kerala was the home of the world’s most advanced mathematical knowledge, foreshadowing some results of the calculus that were obtained in Europe only in the 17th and 18th centuries. Both the question of the internal processes that led to this breakthrough as well as the question of the transfer of knowledge between Kerala and Europe remain unresolved by studying the canonical texts alone. Looking into vernacular practical texts may shed new light on these questions.

The repositories to be reviewed were chosen in order to obtain as rich a sample as possible of different sources relating to vernacular mathematics in pre-modern India: established national libraries, an East India Company survey, educational and professional training institute archives, temple and village repositories, and private collections. This way we will sample higher mathematical knowledge, educational materials for schoolchildren, practical manuals for apprentices and professionals (merchants, accountants, artisans), and actual accounts and surveys. In turn, this will provide a complete overview of mathematical culture from its most elementary instances to its highest manifestations. The selection of specific repositories is based on published catalogues, secondary literature in local languages, colonial surveys, the research experience of the project staff, academic networks (e.g. the KV Sarma research centre and National Mission for Manuscripts) and informal amateur networks.

The multi-regional and multi-lingual approach will allow for a comparative analysis. Instead of seeing India as one undifferentiated mass, the different regional histories can be correlated with different regional practices to deepen our understanding of the contextual role and development of mathematical knowledge.

Materials in private collections, community centres and libraries are often in a fragile condition due to age, insects, weather and lack of optimal preservation conditions. Many manuscripts reach professional libraries after they had been damaged, so even if they are provided with good preservation conditions, their life expectancy is short. Some of the manuscripts seen in established Kerala libraries literally started breaking or decomposing when opened. Other manuscripts listed in catalogues have already been lost or misplaced.

Poor community libraries cannot afford to invest in preventing rain or fire damage. The little precarious grants that these libraries get are spent on what they consider the most valuable possessions of the library, leaving other materials for slow decay in locked shelves that are rarely opened for the public. Some of the rare, practically invaluable lithographed or printed texts from the nineteenth and early twentieth century housed in various community libraries such as in Lucknow are in the process of decomposition due to the poor infrastructures of libraries.

A particular danger for materials housed in poor local libraries is property feuds. If the library loses ownership of the property, materials are either picked up by people or burnt. For example, a library located in the market of Munger (Bihar) was subjected to the property dispute in May, 2015, and 12,000 rare Urdu books were dumped into the River Ganga forever.

In private collections, when owners no longer have use or access to the knowledge contained in manuscripts, they sometimes ceremoniously burn them or simply discard them. Even if the manuscripts make it to libraries, the obscure and technical nature of the content makes it difficult for the librarians to catalogue them, so they sometimes just set them aside.


As had been envisaged when conceiving of the project, historical materials include several versions of Tamil and Malayalm mathematical treatises, which can be grouped under the rubric of the Kanakkatikaram genre were discovered. Now, not only the locations and the kinds of extant texts is understood, it is also possible to map the various editions and publications of these texts. The second interesting aspect from the survey is the surprisingly large amount of manuscripts concerning architecture, which are often called the Manaiyadi Sastiram or Manai Alankaram, which have received little attention from historians.

The project produced a survey detailing the manuscripts found during exploratory visits to institutions and private collectors.


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