The History of Mathematical Proof in Ancient Traditions

6 Overlooking mathematical justifi cations

in the Sanskrit tradition: the nuanced case

of G. F. W. Th ibaut

Agathe Keller

Introduction

Until the 1990s, the historiography of Indian mathematics largely held that

Indians did not use ‘proofs’ in their mathematical texts. 1 Dhruv Raina has

shown that this interpretation arose partly from the fact that during the

second half of the nineteenth century, the French mathematicians who

analysed Indian astronomical and mathematical texts considered geometry

to be the measure of mathematical activity.^2 Th e French mathematicians

relied on the work of the English philologers of the previous generation,

who considered the computational reasonings and algorithmic verifi ca-

tions merely ‘practical’ and devoid of the rigour and prestige of a real logical

and geometrical demonstration. Against this historiographical backdrop,

the German philologer Georg Friedrich Wilhelm Th ibaut (1848–1914)

published the oldest known mathematical texts in Sanskrit, which are

devoted only to geometry.

Th ese texts, śulbasūtra s (sometimes called the sulvasūtra s) contain

treatises by diff erent authors (Baudhāyana, Āpastamba, Kātyāyana and

Mānava) and consider the geometry of the Vedic altar. 3 Th ese texts were

written in the style typical of aphoristic sūtra s between 600 and 200 bce.

Th ey were sometimes accompanied by later commentaries, the earliest

of which may be assigned to roughly the thirteenth century. In order

to understand the methods that he openly employed for this corpus of

texts, Th ibaut must be situated as a scholar. Th is analysis will focus on

Th ibaut’s historiography of mathematics, especially on his perception

of mathematical justifi cations.

(^1) Srinivas 1990 ; H1995.
(^2) See Raina 1999 : chapter vi.
(^3) I will adopt the usual transliteration of Sanskrit words, which will be marked in italics, except
260 for the word Veda, which is found in English dictionaries.