[INDOLOGY] Upcoming talk on Monday, March 17 at CHSTM History of Science in Early South Asia

[Dagmar Wujastyk]

Dear colleagues,

Please join us for the next talk for the online CHSTM series History of
Science in Early South Asia  this Monday, at 10am EDT. Agthe Keller
(Sphere, CNRS / Université Paris Cité) will be talking about:
*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.*

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https://www.chstm.org/group/history-science-early-south-asia

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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.
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