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Please find the details of the upcoming talk below.
Kind regards,
Dagmar Wujastyk
Monday, March 17, 2025, 10:30 am - 12:00 pm EDT
Agathe Keller (Sphere, CNRS / Université Paris Cité)
Some
reflections on the practices of proofs in Sanskrit mathematical texts,
with a special emphasis on Śaṅkara Vāriyar’s work on Mādhava’s procedure
to approximate the circumference of a circle.
In
his commentary on the Līlāvatī—Bhāksara (b.1114) ’s very popular
arithmetical text—Śaṅkara Vāriyar (fl. ca. 1540) launches into a
spectacular presentation of the values that Mādhava (14th century) can
provide to approximate the ratio of the circumference of a circle to its
diameter. He then offers an elaborate proof of one of the highlights of
the “Kerala School of Mathematics” attributed to the same Mādhava: a
rule to approximate the circumference of a circle which is seen as an
equivalent of formulas given later by Gotfried Wilhelm Leibniz
(1646-1716) and James Gregory (1638-1675) prefigurating the birth of
calculus. In this presentation, I will show how Śaṅkara Vāriyar
commentary testifies to new ways of thinking about reasonings and proofs
in mathematics, offering many contrasts with the practices of earlier
authors writing in Sanskrit. More largely I will describe how authors of
mathematical texts in Sanskrit had a great variety of practices of
mathematical reasonings. Not all of these practices were about “proving”
mathematical truths; reasonings could have many different aims— such as
showing that a procedure could be used in different mathematical
disciplines, or that a formal computation could be explained by
providing each step with a meaning. My aim will be to look at how
authors carried out “explanations” (vāsanā) or sought to “establish” a
procedure (sadh-, upapad-), and how this questions standard
historiographies of proof in Sanskrit mathematical literature on the one
hand and of the “Kerala school of mathematics” on the other.