Mathematics, the mathematical sciences, and historical contingency: Some thoughts on reading Netz

ABSTRACT The history of mathematics is replete with multidimensionality and multiculturalism. This essay attempts to use the history of astronomy (one of the mathematical sciences) to emphasize the multiple traditions from various cultural zones that contributed to that history. In doing so, it supplements, but also challenges, the more unidimensional story that Reviel Netz puts forth in his own essay on the importance of the Archimedean tradition. Specifically, the essay uses examples from Babylonian, Greek, Indian, and, especially, Islamic astronomy to show how traditions not tied to Archimedes were of major importance on the often circuitous path to modern science. The notion of contingency is also explored, in particular the idea that without Greek mathematics in general, and Archimedes in particular, early modern and modern science might not have been possible. Counter to this, the essay explores other possible scenarios, whereby different mathematical traditions in other cultural settings could have plausibly led to major breakthroughs associated with the scientific revolution.