Abstract
It is well recognized that since the Bronze Age about 5000 years ago mathematical ideas have circulated across the Eurasian region between the agrarian civilizations that emerged in the river valleys of the Tigris-Euphrates, the Nile, the Indus, and the Hwang-Ho. Over time these exchanges became more intensive and extensive as deeper connections between these civilizations developed through empires, religions, and commerce. Although the global turn in the history of mathematics has led to many studies of mathematical connections between cultures there have been few investigations of how the flow of mathematics over the region crucially shaped the growth of mathematics within civilizations. Most scholarship has largely focused on histories of mathematics which trace the development of ideas within civilizations in isolation from each other. Such histories do not allow us to see those historical processes and epistemological reorientations brought about by inter-civilizational fusions. This is what is explored in this chapter.
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Notes
- 1.
This paper began as an attempt to draw together the muti-civilizational exchanges that nurtured the growth of mathematical knowledge. However, over time, I found myself health-wise unable to complete the chapter. Instead I thought it would be a good idea to draw together dialogical connections I discussed in the course of writings about the mathematics of different civilizations in my book The Crest of the Peacock: Non-European Roots of Mathematics into one narrative by exploring how they integrate together. This approach has some drawbacks that have to be admitted. First I have been unable to address more recent work in the areas I discuss. Second, I have had to largely see dialogue in terms of non-European contributions without adequtely covering the Greek and European contributions to the mathematics of other civilizations since my original study was focussed on the non-European mathematical traditions. Nevertheless, I think the study does reflect the broad general pattern of mathematical exchanges across civilizations and cultures. I also wish to thank Arun Bala for his invaluable help in not only kindly assisting me in the process by putting together dialogical connections discussed in this chapter that are drawn from my book, but also the numerous fruitful exchanges we had which helped to weave this material into a continuous and coherent narrative.
References
Friberg. 2005. Unexpected Links Between Egyptian and Babylonian Mathematics. Singapore: World Scientific.
Friberg. 2007a. A Remarkable Collection of Babylonian Mathematical Texts. New York: Springer.
Friberg. 2007b. Amazing Traces of a Babylonian Origin in Greek Mathematics. Singapore: World Scientific.
Joseph, George Gheverghese, and (with Nelson, David and Williams, Julian). 1993. Multicultural Mathematics: Teaching Mathematics from a Global Perspective. Oxford: Oxford University Press.
Joseph, George Gheverghese. 2009. Kerala Mathematics: History and Its Possible Transmission to Europe. Delhi: B.R. Publishing Corporation.
Joseph, George Gheverghese. 2011. The Crest of the Peacock: Non-European Roots of Mathematics. Princeton: Princeton University Press.
Joseph, George Gheverghese. 2016. Indian Mathematics: Engaging With the World from Ancient to Modern Times. Singapore: World Scientific.
Joseph, George Gheverghese. 2018. A Passage to Infinity: Medieval Indian Mathematics from Kerala and its Impact. New Delhi: SAGE Publications Pvt. Ltd.
Kasir, Daoud S. 1931. The Algebra of Omar Khayyam. New York: Teachers College, Columbia University, January 1.
Katz, V., and B. Lumpkin. 1995. The Relationship of Egyptian to Greek Mathematics. History and Pedagogy of Mathematics Newsletter 35: 10–13.
Katz, Victor, ed. 2007. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton: Princeton University Press.
Kuhn, Thomas. 1962. The Structure of Scientific Revolutions. Chicago: University of Chicago Press.
Lach, D.F. 1965. Asia in the Making of Europe, 2 vols. Chicago: university of Chicago Press.
Lumpkin, B. 2000. The Mathematical Legacy of Ancient Egypt: A Response to Robert Palter. In Debating Black Athena, ed. Bernal Martin. NC: Duke University Press.
McEvilley, Thomas C. 2001. The Shape of Ancient Thought. Comparative Studies in Greek and Indian Philosophies. Allworth.
Needham, Joseph. 1954. Science and Civilisation in China, Volume 1: Introductory Orientations. Cambridge: Cambridge University Press.
Needham, Joseph. 1970. Clerks and Craftsmen in China and the West. Cambridge: Cambridge University Press.
Neugebauer, Otto. 1969. The Exact Sciences in Antiquity, 2 ed., vol. 9. New York: Dover Publications.
Parker, R.A. 1972. Demotic Mathematical Papyri. Brown Egyptological Studies 7. Providence: Brown University Press.
Saliba, George. 2007. Islamic Science and the Making of the European Renaissance. Cambridge, MA: MIT Press.
Shigeru and Rosenfeld. 1997. Seki Kowa. In Encyclopedia of the History of Science, Technology and Medicine in Non-Western Cultures, ed. H. Selin. Dordrecht: Kluwer Academic Publishers.
Sigler, L.E. 2003. Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. New York: Springer.
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Joseph, G.G. (2024). Liberating Mathematics from Civilizations. In: Bala, A., Lau, R.W.K., Mei, J. (eds) Multicivilizational Exchanges in the Making of Modern Science. Palgrave Macmillan, Singapore. https://doi.org/10.1007/978-981-97-3541-9_8
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