This paper is in two parts. The first presents an analysis of the epistemology underlying the practice of classical Indian mathematical astronomy, as presented in three works of Nīlakaṇṭha Somayāji (1444–1545 CE). It is argued that the underlying concepts put great value on careful observation and skill in development of algorithms and use of computation. This is reflected in the technical terminology used to describe scientific method. The keywords in this enterprise include parīkṣā, anumāna, gaṇita, yukti, nyāya, siddhānta, tarka and (...) anveṣaṇa. The concepts that underlie these terms are analysed and compared with such ideas as theory, model, computation, positivism, empiricism etc. In a short second part, it is proposed that the primacy awarded to number and computation in classical Indian science led to an artificial language that did include equations but emphasized displays that facilitated calculation, as in the Bakshali manuscript (800 CE?). It is further argued that echoes of these concepts can be recognized in current science, where computation is once again playing a greater role triggered by spectacular developments in computer technology. (shrink)