promoting alternative sciences-that is, traditional "scientific" systems as opposed to modern "We... more promoting alternative sciences-that is, traditional "scientific" systems as opposed to modern "Western" scienceare part of a wider reflection in South Asia on how to shape the future. History of science, then, is a very politicized affair. We will describe how two contrasting practices of numbers, measures and computations can be documented in South India as they appear in early Sanskrit mathematical treatises and commentaries (seventh-twelfth centuries) and also in elementary mathematical curricula in Tamil (seventeenth-twentieth centuries). We will question whether they should be described as two different mathematical ontologies.
Popular attention has recently been captured by the results of the Bodleian Library's 2017 projec... more Popular attention has recently been captured by the results of the Bodleian Library's 2017 project of radiocarbon dating portions of the birch-bark fragments constituting what is known as the Bakhshālī Manuscript. In this paper, we disagree with the interpretation of the findings announced by the Bodleian team. In particular, we argue that the earliest dated folio of this manuscript is unlikely to be the date of the whole text. Rather, the latest dateable folio is logically the date of the scribal activity. This fits well with past estimates of the date of the Bakhshālī Manuscript based on historical, philological and palaeographical arguments.. And we argue that the Bakhshālī Manuscript does include written zeros that function as arithmetical operators, i.e., as numbers in their own right, and not merely as place-holders, as asserted by the Bodleian team. Finally, we express regret that the Bodleian Library chose to announce scientific results without peer-review and through a press release to newspapers and a YouTube video.
Comment on a écrit les nombres dans le sous-continent indien, histoires et enjeux Cette présentat... more Comment on a écrit les nombres dans le sous-continent indien, histoires et enjeux Cette présentation expose les débats qui ont eu lieu au cours du XIXème et au début du XXème siècle concernant l'origine de la numération positionnelle décimale. Elle se focalisera en particulier sur les échos que ce débat eut dans le souscontinent Indien, notamment les échanges qu'eurent G. R Kaye et Saradakanta Ganguly. Ces enjeux historiographiques confrontés à un ensemble de textes sanskrits du VIIème -XIIème siècle, soulèveront des questions sur la notion de position dans l'écriture des nombres.
How did the narratives on the history of mathematics in India omit the tradition of mathematical ... more How did the narratives on the history of mathematics in India omit the tradition of mathematical justifications that existed in medieval Sanskrit commentaries? This article will look at a key moment of the history of mathematics in India, when in 1874 and 1875, the German philologer G. F. Thibaut published a translation of a set of Vedic geometrical texts, thus establishing that India had known other mathematical activities than "practical calculations". We will observe how his philological work and historiographical values influences his approach of these texts, providing a bias for his approach of the reasonings and efforts that may have existed to assert the validity of algorithms existing in this set of texts.
Comptes-rendus des séances de l année - Académie des inscriptions et belles-lettres, 2006
Comment on a écrit les nombres dans le sous-continent indien, histoires et enjeux Cette présentat... more Comment on a écrit les nombres dans le sous-continent indien, histoires et enjeux Cette présentation expose les débats qui ont eu lieu au cours du XIXème et au début du XXème siècle concernant l'origine de la numération positionnelle décimale. Elle se focalisera en particulier sur les échos que ce débat eut dans le souscontinent Indien, notamment les échanges qu'eurent G. R Kaye et Saradakanta Ganguly. Ces enjeux historiographiques confrontés à un ensemble de textes sanskrits du VIIème -XIIème siècle, soulèveront des questions sur la notion de position dans l'écriture des nombres.
Rules for extracting square roots written in Sanskrit in two treatises and their commentaries (fr... more Rules for extracting square roots written in Sanskrit in two treatises and their commentaries (from the Vth to the Xth century) are approached with questions inspired by textology and Speach Act Theory. An analysis of the number and order of steps spelled out is used to show that their aims were not limited to describing how to carry out the algorithm. The intentions of authors of mathematical texts in Sanskrit are questioned by lending an ear to the expressivity of relations established between world and text.
A renewed interest for contextualization in indological studies 1 , is but slowly affecting publi... more A renewed interest for contextualization in indological studies 1 , is but slowly affecting publications on Indian mathematics. The isolation of history of mathematics within the general field of indology derives partly from a lively historiographical trend of technical and patriotic history of mathematics which remains oblivious to social science. Preservation plays a role as well: precious little information exists on the context in which mathematics and astronomy were practiced in India in the past 2 . To overcome this problem some historians of science have turned to periods (XVIth-XIXth century) and places where institutions, libraries and many texts help us contextualize their mathematical and astronomical ideas 3 .
This article will analyze the vocabulary and the reasonings that Bhāskara (629 A. D.) uses to gro... more This article will analyze the vocabulary and the reasonings that Bhāskara (629 A. D.) uses to ground the procedures exposed in the mathematical chapter of theĀryabhat .ī ya, a Sanskrit astronomical treatise of the fifth century. We will see that explaining, showing and verifying procedures are part of the general endeavor of the commentary to defend his interpretation of the procedures and their correctness. These attempts are in no way systematic, and when they appear, they are often fragmentary as if they where carried out orally. We will nevertheless argue, that one of the modes of mathematically grounding a procedure was to reread it with the help of an alternative procedure. We will see that the Rule of Three and the Pythagoras Theorem have a special value in this context.
This paper concerns the influence of Peacock's history of arithmetic, a text plublished in the En... more This paper concerns the influence of Peacock's history of arithmetic, a text plublished in the Encyclopaedia Metropolitana in the Indian subcontinent. After questioning the material and intellectual diffusion of the Encyclopaedia Metropolitana in India, it explores the early historiography of arithmetic, as written by Indian authors in English. This article's focus is on the debate that raged at the end of the XIXth century and in the early decades of the XXth century concerning the origin of Indian numerals, concentrating specifically on the origins of the decimal place value notation. It describes the arguments exchanged on this subject by a number of authors including S. Ganguly and G. R. Kaye thus attempting to map out a portion of the historiography of arithmetic in India.
Page 1. Peacock in the Land of the Peacock ? George Peacock's Arithmetic in the ch... more Page 1. Peacock in the Land of the Peacock ? George Peacock's Arithmetic in the changing landscape of the history of mathematics in India Agathe Keller SPHère, UMR 7219, Université Paris VII-CNRS, Case 7064, 5 rue Thomas Mann 75205 PARIS CEDEX 13, France. ...
This article is a survey of the numerous questions raised by the diagrams in a seventh-century Sa... more This article is a survey of the numerous questions raised by the diagrams in a seventh-century Sanskrit mathematical commentary. Exploring the links between the original text, the manuscripts, and the edition of Bhāskara I's Aryabhat .ī yabhās . ya, the enquiry ranges from the tools employed to draw geometrical figures to the diverse functions that were assigned to drawings in geometry. Whether technical objects set down on a working surface or testimonies of an oral explanation, diagrams deal with a part of mathematical reasoning which was not formulated through written speech. 2004 Elsevier Inc. All rights reserved.
promoting alternative sciences-that is, traditional "scientific" systems as opposed to modern "We... more promoting alternative sciences-that is, traditional "scientific" systems as opposed to modern "Western" scienceare part of a wider reflection in South Asia on how to shape the future. History of science, then, is a very politicized affair. We will describe how two contrasting practices of numbers, measures and computations can be documented in South India as they appear in early Sanskrit mathematical treatises and commentaries (seventh-twelfth centuries) and also in elementary mathematical curricula in Tamil (seventeenth-twentieth centuries). We will question whether they should be described as two different mathematical ontologies.
Popular attention has recently been captured by the results of the Bodleian Library's 2017 projec... more Popular attention has recently been captured by the results of the Bodleian Library's 2017 project of radiocarbon dating portions of the birch-bark fragments constituting what is known as the Bakhshālī Manuscript. In this paper, we disagree with the interpretation of the findings announced by the Bodleian team. In particular, we argue that the earliest dated folio of this manuscript is unlikely to be the date of the whole text. Rather, the latest dateable folio is logically the date of the scribal activity. This fits well with past estimates of the date of the Bakhshālī Manuscript based on historical, philological and palaeographical arguments.. And we argue that the Bakhshālī Manuscript does include written zeros that function as arithmetical operators, i.e., as numbers in their own right, and not merely as place-holders, as asserted by the Bodleian team. Finally, we express regret that the Bodleian Library chose to announce scientific results without peer-review and through a press release to newspapers and a YouTube video.
Comment on a écrit les nombres dans le sous-continent indien, histoires et enjeux Cette présentat... more Comment on a écrit les nombres dans le sous-continent indien, histoires et enjeux Cette présentation expose les débats qui ont eu lieu au cours du XIXème et au début du XXème siècle concernant l'origine de la numération positionnelle décimale. Elle se focalisera en particulier sur les échos que ce débat eut dans le souscontinent Indien, notamment les échanges qu'eurent G. R Kaye et Saradakanta Ganguly. Ces enjeux historiographiques confrontés à un ensemble de textes sanskrits du VIIème -XIIème siècle, soulèveront des questions sur la notion de position dans l'écriture des nombres.
How did the narratives on the history of mathematics in India omit the tradition of mathematical ... more How did the narratives on the history of mathematics in India omit the tradition of mathematical justifications that existed in medieval Sanskrit commentaries? This article will look at a key moment of the history of mathematics in India, when in 1874 and 1875, the German philologer G. F. Thibaut published a translation of a set of Vedic geometrical texts, thus establishing that India had known other mathematical activities than "practical calculations". We will observe how his philological work and historiographical values influences his approach of these texts, providing a bias for his approach of the reasonings and efforts that may have existed to assert the validity of algorithms existing in this set of texts.
Comptes-rendus des séances de l année - Académie des inscriptions et belles-lettres, 2006
Comment on a écrit les nombres dans le sous-continent indien, histoires et enjeux Cette présentat... more Comment on a écrit les nombres dans le sous-continent indien, histoires et enjeux Cette présentation expose les débats qui ont eu lieu au cours du XIXème et au début du XXème siècle concernant l'origine de la numération positionnelle décimale. Elle se focalisera en particulier sur les échos que ce débat eut dans le souscontinent Indien, notamment les échanges qu'eurent G. R Kaye et Saradakanta Ganguly. Ces enjeux historiographiques confrontés à un ensemble de textes sanskrits du VIIème -XIIème siècle, soulèveront des questions sur la notion de position dans l'écriture des nombres.
Rules for extracting square roots written in Sanskrit in two treatises and their commentaries (fr... more Rules for extracting square roots written in Sanskrit in two treatises and their commentaries (from the Vth to the Xth century) are approached with questions inspired by textology and Speach Act Theory. An analysis of the number and order of steps spelled out is used to show that their aims were not limited to describing how to carry out the algorithm. The intentions of authors of mathematical texts in Sanskrit are questioned by lending an ear to the expressivity of relations established between world and text.
A renewed interest for contextualization in indological studies 1 , is but slowly affecting publi... more A renewed interest for contextualization in indological studies 1 , is but slowly affecting publications on Indian mathematics. The isolation of history of mathematics within the general field of indology derives partly from a lively historiographical trend of technical and patriotic history of mathematics which remains oblivious to social science. Preservation plays a role as well: precious little information exists on the context in which mathematics and astronomy were practiced in India in the past 2 . To overcome this problem some historians of science have turned to periods (XVIth-XIXth century) and places where institutions, libraries and many texts help us contextualize their mathematical and astronomical ideas 3 .
This article will analyze the vocabulary and the reasonings that Bhāskara (629 A. D.) uses to gro... more This article will analyze the vocabulary and the reasonings that Bhāskara (629 A. D.) uses to ground the procedures exposed in the mathematical chapter of theĀryabhat .ī ya, a Sanskrit astronomical treatise of the fifth century. We will see that explaining, showing and verifying procedures are part of the general endeavor of the commentary to defend his interpretation of the procedures and their correctness. These attempts are in no way systematic, and when they appear, they are often fragmentary as if they where carried out orally. We will nevertheless argue, that one of the modes of mathematically grounding a procedure was to reread it with the help of an alternative procedure. We will see that the Rule of Three and the Pythagoras Theorem have a special value in this context.
This paper concerns the influence of Peacock's history of arithmetic, a text plublished in the En... more This paper concerns the influence of Peacock's history of arithmetic, a text plublished in the Encyclopaedia Metropolitana in the Indian subcontinent. After questioning the material and intellectual diffusion of the Encyclopaedia Metropolitana in India, it explores the early historiography of arithmetic, as written by Indian authors in English. This article's focus is on the debate that raged at the end of the XIXth century and in the early decades of the XXth century concerning the origin of Indian numerals, concentrating specifically on the origins of the decimal place value notation. It describes the arguments exchanged on this subject by a number of authors including S. Ganguly and G. R. Kaye thus attempting to map out a portion of the historiography of arithmetic in India.
Page 1. Peacock in the Land of the Peacock ? George Peacock's Arithmetic in the ch... more Page 1. Peacock in the Land of the Peacock ? George Peacock's Arithmetic in the changing landscape of the history of mathematics in India Agathe Keller SPHère, UMR 7219, Université Paris VII-CNRS, Case 7064, 5 rue Thomas Mann 75205 PARIS CEDEX 13, France. ...
This article is a survey of the numerous questions raised by the diagrams in a seventh-century Sa... more This article is a survey of the numerous questions raised by the diagrams in a seventh-century Sanskrit mathematical commentary. Exploring the links between the original text, the manuscripts, and the edition of Bhāskara I's Aryabhat .ī yabhās . ya, the enquiry ranges from the tools employed to draw geometrical figures to the diverse functions that were assigned to drawings in geometry. Whether technical objects set down on a working surface or testimonies of an oral explanation, diagrams deal with a part of mathematical reasoning which was not formulated through written speech. 2004 Elsevier Inc. All rights reserved.
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