Sciences, Philosophie, Histoire – UMR 7219, laboratoire SPHERE

Un peu plus de 200 ans se sont écoulés depuis la publication de Algebra with arithmetic and mensuration from the Sanskrit of Brahmagupta and Bhascara, 1817, de Henry Thomas Colebrooke. La conférence se concentrera sur l’historiographie des mathématiques et des sciences astrales de Colebrooke. Voici certaines des questions générales auxquelles nous vous invitons à contribuer au cours de ce workshop.

Dans quels contextes l’intérêt de Colebrooke pour les mathématiques et les sciences astrales de l’Inde ancienne a-t-il pris forme ? Quel a été l’impact, en Europe et au-delà, de la publication de 1817 sur la rédaction de l’histoire des mathématiques non seulement en Inde, mais aussi dans le monde entier ? Que peut-on dire sur la façon dont Colebrooke a traduit et travaillé avec des sources sanscrites traitant des mathématiques et des sciences astrales ? Comment pouvons-nous situer cette œuvre de Colebrooke dans le contexte plus large de l’intérêt des 18e et 19e siècles pour « les mathématiques orientales et l’astronomie » ? L’intérêt précoce de Colebrooke pour les mathématiques et les sciences astrales fait-il écho à ses autres études indologiques ? Ou, réciproquement, traduit-il et étudie-t-il des textes d’histoire des mathématiques et / ou des sciences astrales dans la continuité de ses autres études indologiques ?

Colebrooke’s annotated copy of Pṛthūdhaka’s 10th century commentary
on Brahmagupta’s Brāhmasphuṭasiddhānta (628). [British Library, IOSAN1304]

Nous nous intéresserons en particulier aux différents milieux sociaux avec lesquels Colebrooke a dialogué et dans lequel il a effectué ses travaux. Par exemple, nous savons qu’il était en relation avec des actuaires à Londres, des linguistes en Allemagne et des mathématiciens des Lumières écossais. Pouvons-nous déterminer plus précisément comment certains de ces milieux ont aidé à structurer des questions de recherche en histoire des mathématiques et des sciences astrales en Asie du Sud ?
Nous nous intéressons également à la façon dont Colebrooke a choisi de traduire les sources en sanscrit, pour lesquelles il a entrepris de fournir une traduction en anglais, ainsi qu’à l’impact de ces traductions. Par exemple, on pourrait explorer les raisons pour lesquelles Colebrooke a choisi de traduire certains termes sanscrits, tels que les thèmes de mathématiques connus sous le terme de vyavahāras, appelés logistique. Cette traduction a longtemps perduré et est encore utilisée parfois de nos jours : pourquoi a-t-il utilisé une telle traduction, d’où vient-elle, pourquoi a-t-elle été conservée aussi longtemps ?

INTERVENANTS

• Nalini Balbir (Université Paris III, France) / [résumé]

• Sho Hirose (ETH, Zürich, Suisse) / [résumé]

• Agathe Keller (CNRS, SPHERE & Université Paris Diderot, France) / [résumé]

• Satyanad Kichenassamy (Université de Reims) / [résumé]

• Minakshi Menon (Max Planck Institute for the History of Science, Allemagne) / [résumé]

• Rosane Rocher (Université de Pennsylvania, USA) / [résumé]

• Ivahn Smadja (Université de Nantes, France) / [résumé]

PROGRAMME

LUNDI 15 AVRIL, salle 646A, Mondrian
09:30	Agathe Keller & Karine Chemla Introduction
09:45	Rosane Rocher Science in Colebrooke’s universe Comm. : Pascale Rabault-Feuerhahn (UMR 8547 CNRS, Paris)	résumé
11:15	pause
11:30	Eric Gurevitch The Whig Interpretation of the Hindu Constitution Comm. : Claude-0livier Doron (Université Paris Diderot, France)	résumé
13:00	Déjeuner
14:00	Minakshi Menon Henry Thomas Colebrooke, the Amarakośa, and Botanical Knowledge Making in Colonial India, c. 1800 Comm. :	résumé
15:30	pause
16:00	Nalini Balbir An instance of Colebrooke’s approach to religious science : the Jain tradition Comm. : Rosane Rocher	résumé
MARDI 16 AVRIL, salle 646A, Mondrian
09:30	Sho Hirose Origin and Observation : Colebrooke on Indian Astronomy Comm. : Victor Gysembergh (CNRS, Centre Léon Robin)	résumé
11:00	Break
11:30	Agathe Keller Colebrooke, Commentaries and Proofs Comm. : Vincenzo De Risi (CNRS, SPHERE, & MPWIG Berlin)	résumé
13:00	déjeuner
14:00	Satyanad Kichenassamy Henry Thomas Colebrooke and the nature of Brahmagupta’s mathematical discourse Comm. : Alain Bernard	résumé
15:30	Break
16:00	Ivahn Smadja Some aspects of Colebrooke’s mathematical reception in 19th century Germany : from ancient sources to new questions Comm. : AJ Misra (MPWIG, Berlin, Germany)	résumé
17:30 –18:00	discussion générale

RÉSUMÉS

• Rosane Rocher (Université de Pennsylvanie)
  Science in Colebrooke’s universe
  The paper focuses on Colebrooke’s lifelong engagement with the sciences and traces the arc it followed. After a period of exploration and initiation (1786–1801) came one of intense activity and intervention (1802–1814), leading up to its scholarly pinnacle in 1817 with the publication of Algebra. Colebrooke’s involvement with the sciences then transitioned to a representational phase. The periodization of Colebrooke’s engagement with the sciences is not unrelated to his mundane working circumstances, but it is not entirely conditioned by them. It is also independ-ent –neither in lockstep nor in complementary distribution– from his progression in other branches of scholarship.

• Eric Gurevitch (Université de Chicago)
  The Whig Interpretation of the Hindu Constitution
  In 1880, Rajkumar Sarvadhikari—a professor of Sanskrit and law—delivered a series of 15 lectures at the University of Calcutta. In these lectures, Sarvadhikari provided a nuanced critique of the legal reasoning of Henry Thomas Colebrooke founded on new philological research, which allowed him to integrate Sanskrit legal texts into the social-evolutionary theory of Herbert Spencer, and which led to his work being taken up by Henry Sumner Maine. The reception of Colebrooke’s legal reasoning in the late 19th century helps to show the methods and presumptions contained in Colebrooke’s views of history and tradition, and has implications for his scholarship on other genres of Sanskrit text. In particular, Colebrooke’s arguments regarding the coherence of legal and philosophic “schools” would be contested and reassessed throughout the 19th century, with new debates over scientific and positivist history emphasizing new aspects of Colebrooke’s work. Thinking with Sarvadhikari can help us to situate the complex uptake of Colebrooke’s broad-ranging researches in the production of science in the late-Victorian Empire and within India on the eve of the nationalist movement.

• Minakshi Menon (Max Planck Institute for the History of Science)
  Henry Thomas Colebrooke, the Amarakośa, and Botanical Knowledge Making in Colo-nial India, c. 1800
  In 1808, the English East India Company published a translation of the famous Sanskrit verse lexicon, the Amarakośa. The Amara was the best known and most widely used of all Sanskrit lexicons, composed c. 500 CE by Amarasiṃha, a Buddhist, who may have been a minor poet.
  The English translation of the Amara, was undertaken by Henry Thomas Colebrooke (1765-1837), usually considered the “father of Indology”. Colebrooke explained the rationale for the publication in his Preface to the author’s edition of the Amara thus : “The compilation of a Sanscrit dictionary having been undertaken early after the institution of the College of Fort William, it was at the same time thought advisable to print, in Sanscrit and English, the work which has been chosen for the basis of the compilation… with the view of furnishing an use-ful vocabulary, which might serve until an ampler dictionary could be prepared and published.”
  In this paper, I examine the Amara as an important tool in botanical knowledge making in East India Company India. Whatever its pedagogical uses, Colebrooke himself, as well as other orientalists such as Sir William Jones (1746-1794), used the Amara as a source for Sanskrit plant names. Colebrooke worked hard to stabilize such names by linking them to their equivalents in the Indian vernaculars. He used forms of visualizing plant names – lists and tables – which would have been impossible without rectangular sheets of European paper, marking the imbrication of the material and the epistemic in his knowledge making. I show how Colebrooke’s process of translation re-visualized and re-structured the information in the Amara, producing new observational and triangulation practices for identifying Indian plants.

• Nalini Balbir (Université Paris 3)
  An instance of Colebrooke’s approach to religious science : the Jain tradition
  In this paper we will try to explain how Colebrooke participated in creating a new scientific object in the beginning of the 19th century, namely knowledge about the Jain tradition. We will focus on the sources he used, his team, his methodology, and the contents of his discourse. His contributions to the Asiatick Researches (1807) and the collection of Jain manuscripts he man-aged to get will form the main basis of our investigation. The case arising, we will compare Colebrooke’s scientific approach to Jainism with other contemporary approaches.

• Sho Hirose (ETH)
  Origin and Observation : Colebrooke on Indian Astronomy
  In his article "On the Indian and Arabian Divisions of the Zodiac", Colebrooke attempts to identify the stars in the Indian lunar mansions with the aim to discuss whether they have a common origin with their Arabic counterparts. Colebrooke’s views on Indian astronomy is articulated therein. He assumes that observation played an important role in astronomy and conjectures that the lunar mansions were established in India and probably introduced to the Arabs later. This talk focuses on how Colebrooke’s notions on origin and observation in Indian astronomy were formed and how they were received in Europe.

• Agathe Keller (CNRS, SPHERE)
  Colebrooke, Commentaries and Proofs
  H.T Colebrooke published in 1817 English translations of mathematical texts by Bhrahmagupta and Bhāskara. Footnotes to these translations included extracts of commentaries by Gaṇeśa, Sūryadāsa, Kṛṣṇadaivajña, Pṛthūdhakasvāmin : Colebrooke translated glosses of technical terms, solved numerical examples and proofs of the rules when he could. In this paper I look at how by fragmenting the commentaries and thus sectioning from them parts devoted to reasonings/proofs, Colebrooke shaped texts corresponding to moments of what he called geometrical proofs and algebraical analysis, overlooking what might have been other values by which commentators were trying to explain a rule. This operation has deeply influenced our perception of reasonings in Sanskrit mathematical texts, but it also opens new questions we can address to them.

• Satyanad Kichenassamy (Université de Reims)
  Henry Thomas Colebrooke and the nature of Brahmagupta’s mathematical discourse
  We analyse Colebrooke’s study of Brahmagupta’s mathematical discourse in the light of recent research, and stress its relevance for current problems. Colebrooke’s early and highly influential attempt at a global history of medieval mathematics identified Brahmagupta as the possible initiator of several major advances, whose importance was dimmed by partial breaks in the continuity of tradition. Unfortunately, the only commentary on his work that Colebrooke had access to was flippant ; in addition, Bhāskara II, the only other mathematician that Colebrooke translated, had misunderstood Brahmagupta. Colebrooke therefore merely endeavored to establish Brahmagupta’s and Āryabhaṭa’s priority, implying that they had not obtained any results that were not, in essentials, contained in the mathematics of his time. Now, close reading (2010, 2012) shows that the derivation of the area of a cyclic quadrilateral that Brahmagupta presents differs from all those proposed after him, even in India. It is couched in the form of an apodictic discourse, a discourse that carries conviction without coercion. Other examples are known. This leads to the following conclusions : (i) Colebrooke perceived the originality and importance of Brahmagupta’s work, but the lack of a self-reflective knowledge of contemporary mathematics prevented him from identifying a new form of mathematical discourse. (ii) Apodictic discourse is conducive to the production of new knowledge. (iii) Such knowledge, when partially lost, can apparently not be recovered by deductive means, but only by close reading. This analysis also helps solve open problems in the study of the Euclidean tradition (2015), some of them also alluded to by Colebrooke.

• Ivahn Smadja (Université de Nantes)
  Some aspects of Colebrooke’s mathematical reception in 19th century Germany : from ancient sources to new questions
  tba

ACCES
Salle Mondrian 646A,
bâtiment Condorcet, Université Paris Diderot, 4 rue Elsa Morante, 75013 Paris– plan d’accès.

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