Sciences, Philosophie, Histoire – UMR 7219, laboratoire SPHERE

A bit more than 200 years have elapsed since the publication of Henry Thomas Colebrooke’s Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmagupta and Bhàscara. We will grasp this opportunity to organise a two-day workshop to be held in Paris on the 15th and 16th of April 2019. The conference will concentrate on Colebrooke’s historiography of mathematics and astral sciences, and here are some of the general questions that we invite contributions to this workshop to tackle : In which contexts did Colebrooke’s interest in the mathematics and astral sciences of ancient India take shape ? What was the ensuing impact, in Europe and beyond, of the 1817 publication for the writing of the history of mathematics not only in India, but also worldwide ? What can be said on how Colebrooke translated and worked with Sanskrit sources dealing with mathematics and astral sciences ? How can we situate this work by Colebrooke in the larger context of 18th and 19th century interest for “oriental mathematics and astronomy” ? Does Colebrooke’s early interest for mathematics and astral sciences echo into his other indological studies ? Or, reciprocally, does he translate and study texts of history of mathematics and/or astral sciences in continuity with his other indological studies ?

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

We are in particular interested in the various social environments with which Colebrooke interacted and in which he carried out his work. For example, we know that Colebrooke had close-knit relations actuaries in London, linguists in Germany and Scottish enlightenment mathematicians. Can we trace more specifically how some of these milieux helped structure research questions in the history of mathematics and astral sciences in South Asia ?
We are also interested in how Colebrooke chose to translate the Sanskrit sources for which he set out to provide an English translation, and also on the impact of these translations. For example, one could explore why Colebrooke chose to translate some Sanskrit terms, such as the topics of mathematics known under the term vyavahāras, as “logistics”. This translation has long endured and is still used sometimes today : Why did he use such a translation, where did it come from, why was it retained for such a long time ?

SPEAKERS

• Nalini Balbir (University Paris III, France) / [abstract]

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

• Agathe Keller (SPHERE – CNRS & University Paris Diderot, France) / [abstract]

• Satyanad Kichenassamy (University of Reims) / [abstract]

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

• Rosane Rocher (University of Pennsylvania, USA) / [abstract]

• Ivahn Smadja (University of Nantes, France) / [abstract]

PROGRAM

MONDAY APRIL 15, Room 646A, Mondrian
09:30am	Agathe Keller & Karine Chemla Introduction
09:45am	Rosane Rocher Science in Colebrooke’s universe Comm. : Pascale Rabault-Feuerhahn (UMR 8547 CNRS, Paris)	abstract
11:15am	Break
11:30am	Eric Gurevitch The Whig Interpretation of the Hindu Constitution Comm. : Claude-0livier Doron (Université Paris Diderot, France)	abstract
01:00pm	Lunch
02:00pm	Minakshi Menon Henry Thomas Colebrooke, the Amarakośa, and Botanical Knowledge Making in Colonial India, c. 1800 Comm. : Florence Bretelle-Establet (CNRS, CHSA–SPHERE)	abstract
03:30pm	Break
04:00pm	Nalini Balbir An instance of Colebrooke’s approach to religious science : the Jain tradition Comm. : Rosane Rocher	abstract
TUESDAY APRIL 16, Room 646A, Mondrian
09:30am	Sho Hirose Origin and Observation : Colebrooke on Indian Astronomy Comm. :Victor Gysembergh (CNRS, Centre Léon Robin)	abstract
11:00am	Break
11:30am	Agathe Keller Colebrooke, Commentaries and Proofs Comm. : Vincenzo De Risi (CNRS, SPHERE, & MPWIG Berlin)	abstract
01:00pm	Lunch
02:00pm	Satyanad Kichenassamy Henry Thomas Colebrooke and the nature of Brahmagupta’s mathematical discourse Comm. : Karine Chemla	abstract
03:30pm	Break
04:00pm	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)	abstract
05:30 –6:00pm	General discussion

ABSTRACTS

• Rosane Rocher (University of Pennsylvania)
  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 (University of 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 (University 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 (University of 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 (University of Nantes)
  Some aspects of Colebrooke’s mathematical reception in 19th century Germany : from ancient sources to new questions
  tba

VENUE

Université Paris Diderot, Condorcet Building, Room Mondrian 646A
10 rue Alice Domon et Léonie Duquet 75013 Paris – map

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