Abstract
The historiography of mathematics of the non-Western world long appeared immune to the influence of cultural studies or of critiques of Orientalism. The turn to “ethno-mathematics” and the interrogation of the historiography of proof as boundary marker (Chemla 2012), the internal challenge to foundationalism, etc., have all played a role in pluralizing conceptions of mathematics—though inklings of the idea can be found in the work of a thinker scholars have, understandably, treated with kid gloves: namely, Oswald Spengler. And yet the practice of mathematics continues to manifest a dynamic and positive relationship with its past and the different ways of doing mathematics: How else is one to understand why mathematicians pursue problems that are 300 years old, or why the theoretical astrophysicist and Nobel laureate S. Chandrasekhar produced a book on Newton’s Principia at the end of the twentieth century (Chandrasekhar 1995)? Furthermore, recent studies on the historiography of non-Western mathematical traditions in Western histories of mathematics produced at the end of the eighteenth and the beginning of the nineteenth century in Europe actually reveal the shaping of the historiographical landscape by the changing representations of the Orient in European historical discourse—splintered, of course, across varying “national interpretative traditions” (Said 1994). Thus, as I have argued elsewhere, the Scottish reading of the Indian mathematical tradition was at variance with the French one (Raina 2001, 2012a). This paper sidesteps the preoccupation of historians with priority disputes and looks more closely at the similarities and differences that might stimulate the development of a cognitively just history of mathematics. This requires closer scrutiny of the historiography of European and Indian mathematics, the modality of construction of the Indian and West-East mathematical divide, and its relationship with modernity.
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Notes
- 1.
In a section below, we shall briefly mention the role of historiography of proof as boundary marker.
- 2.
Disciplinary histories of mathematics and astronomy began to be produced in the second half of the eighteenth and early nineteenth centuries. One of the earliest was Montucla’s History of Mathematics. The cover of the book elaborates upon the title Dans laquelle on rend compte de leur progrès depuis leur origine jusqu’à nos jours; où l’on expose le tableau et le développement des principales découvertes dans toutes les parties des Mathématiques, les contestations qui se sont élévées entre les Mathematiciens, et les principaux traits de la vie des plus célèbres (Montucla 1759).
- 3.
- 4.
See also Gillies 1992.
- 5.
Grattan-Guinness points out that the ‘quadrature of curves’ served as one axis for the determination of particular areas. On the other hand, the inverse tangent problem, requiring the determination of a curve from some given property of its tangent, served as the other axis for the evolution of calculus (Grattan-Guinness 1997, 248).
- 6.
While this task was going on, M. D. Srinivas, Sriram and others were busy in Chennai translating the most significant of the salient texts, namely the Yuktibhasa.
- 7.
A joint AHRB project undertaken examined two hypotheses: (1) Null Hypothesis: the development of calculus in Europe was independent of earlier developments in Kerala; and (2) the alternative hypothesis: the development of calculus in Europe was influenced by the transmission of earlier Kerala mathematics (Joseph 2009b, 4). Concluding the findings of the team, George G. Joseph writes: “There has been little direct evidence of any transmission in the correspondence of the Renaissance mathematicians that have been studied thus far …” (ibid., 5).
- 8.
Ballantyne was the Superintendent of Banaras College between 1846 and 1861.
- 9.
This was one of the schools of Indian philosophy dealing with logic.
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Raina, D. (2020). A History of Circulation vs. an ‘Episodic’ History of Mathematics in South Asia: Titrating the Historiography and Social Theory of Science and Mathematics. In: Feichtinger, J., Bhatti, A., Hülmbauer, C. (eds) How to Write the Global History of Knowledge-Making. Studies in History and Philosophy of Science, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-37922-3_6
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