Liberating Mathematics from Civilizations

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.