Innovations in Indian Mathematical Astronomy

Innovations in Indian Mathematical Astronomy

Kim Plofker

Other involved Scholars: 

Clemency Montelle (Project "The Development of Computational Procedures and Numerical Tables in Sanskrit Mathematics in the Second Millennium")

Cooperation Partners: 

University of Canterbury, U.K., New Zealand Royal Society


A page from a manuscript of a sixteenth-century Sanskrit text combines tables and computational algorithms in verse to solve astronomical problems.

The aim of this project is to clarify the approaches employed by Indian mathematician-astronomers to develop innovations in their traditional models and practices.  The default historiographic assumption, heavily influenced by modern scientific practices, is that mathematical astronomy evolves via a systematic and continuous program of observations that are then used to test and refine targeted features of existing models.  However, it is by no means established that this pattern was typically followed by Indian scholars in their scientific endeavours---in fact, many aspects of their practice suggest otherwise.

Previous attempts to investigate this question have resulted in something of a stalemate between two opposing historiographic approaches. One perspective, championed by scholars such as Roger Billard,  was based on the assumption that the parameters retrieved from original sources and those reconstructed from modern retro-cast astronomical alignments could be meaningfully compared and used to generate historical inferences.  This line of investigation was used to rationalize and reinterpret developments in this tradition as well as to shed light on the relationship between observation and theory.  In contrast, scholars in recent times have advocated alternative points of view.  David Pingree, for instance, pointed to textual evidence to argue that data was dealt with and manipulated in a way that was, at times, contrary to the basic assumption that these practitioners were driven by modern scientific standards.  Such an approach disputed the claim that improving the correspondence between computed and observed phenomena was the overwhelming imperative for these scholars.  However, this position has never been systematically verified. While various instances of mathematical "tinkering" with the data have been adduced from the texts to support this interpretation, it has remained beyond the scope of scholarship to coherently and convincingly account for change and innovation in Indian mathematical astronomy. 

The proposed project will compare these hypotheses to the methods and computational strategies found in studying Sanskrit astronomical handbooks and tables, and will use the results to reconstruct a more coherent and comprehensive narrative accounting for the scientific practice of  Indian scholars.  The content of numerical tables, computational procedures, parameter selection, and textual comparisons will provide concrete, systematic, and contextualized evidence to support the analysis.