Current Research Projects
Numerical Tables and associated computational algorithms in Sanskrit sources
Numerical tables, a significant yet often overlooked source in the history of mathematics, not only
hold intrinsic mathematical interest with respect to the computational techniques they embody, but
also more broadly as they speak to scientific practices, assumptions, and aspirations of those that
compiled them. However the significance of mathematical tables and computational
techniques often goes unnoticed, due largely to their subordinate role in classical and modern
mathematics. Neglect of these subjects in the history of mathematics has led to a widespread failure
to understand the role of computational practices in shaping scientific ideas. This research project
undertakes to remedy this situation by an in-depth investigation of tables and computation
algorithms in the mathematics of India in the second millennium, documenting and analyzing the
growing importance and eventual dominance of computational mathematics in the Sanskrit exact
The History of Mathematical Astronomy in the Indian subcontinent
The astral sciences in the Indian subcontinent---that is, mathematics, astronomy, and related
disciplines---have been flourishing for over two and a half millennia, and this culture of inquiry has
produced insights and techniques that are central to many of our scientific practices today, such as
the base ten decimal place value system and trigonometry. Indeed, many of their technical
procedures, such as infinite series expansions for various mathematical relations predated those
that were developed with the advent of the Calculus, but notably in contrasting intellectual
circumstances with distinctly different epistemic priorities. However, while many histories of
science have centered on the so-called `western miracle' in their analysis of the ignition and
flourishing of modern science, they have done so at the expense of other non-European traditions.
Yet these traditions can provide some powerful contrasts and cross-cultural comparisons for our
attempts to delineate and illuminate the scope of scientific activity more broadly. This
comprehensive and far reaching research programme aims to rectify this disparity by bringing more
prominently into the mainstream key perspectives, features, and themes of this important, yet
understudied, tradition of scientific inquiry.
Greek and Arabic diagrammatic reasoning
The investigation of Greek texts and manuscripts on mathematics and astronomy, with particular
emphasis on the role and nature of their technical diagrams. Diagrams represent an element of
mathematical reasoning which is not part of the written text. Are they complementary or independent
of the text?
The Zīj al-Sanjarī
The critical edition and commentary of the twelfth century Arabic work in mathematical astronomy, the Zīj al-Sanjarī by Al-Khāzinī. Zīj is a term derived from middle-Persian that was used to refer to compositions containing astronomical tables and accompanying descriptions intended for practical astronomical use. They typically include chronological systems and calendar conversions, mean motions and corresponding planetary equations, trigonometric functions, stellar coordinates, eclipses, and so on.
The role and function of mathematical notation and symbolism. What are some of the various notational conventions in mathematics and why and how did they develop? What do they reveal about the mathematical object in question? How does notation play an important role in facilitating mathematical insights? These question are
particularly interesting when considering the emergence of symbols for various aspects of calculus in the seventeenth century and beyond.