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.

In order to join the zoom, you need to login into the CHSTM website and get the zoom link here:

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

Please note that you can only log in if you are signed up to the group. People have had trouble with signing up, and we advise you to sign up a few days in advance if you would like to join. It's free and you will only receive emails once a month when we announce the next talk or discussion session.

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.