The real problem is there are too many people who treat mathematical/scientific history as some kind of olympic games, where the goal is to rack up medals for y

The real problem is there are too many people who treat mathematical/scientific history as some kind of olympic games, where the goal is to rack up medals for your preferred team (country, region, religious group, ...), with the result that any discussion becomes counterproductively politicized. Trying to argue about whether one tribe's or another tribe's 50-generations-ago ancestor was the first one to do this or that thing seems to me like completely missing the point, when all of these steps were part of a long and gradual historical process, building ideas and tools up over centuries. (Similarly, it's annoying how many debates center on various ancient figures' ethnicity or religious affiliation, usually without much evidence.) To anyone who tries researching ancient (or more recent) mathematics, it's clear that there usually isn't a single aha moment changing everything, but a broader culture that gradually evolves. We can see different flavors/aspects of a concept like "zero" which were developed different times and places (China, Mesopotamia, India, Greece, North America), none of which really draws any obvious line in the sand. With regard to Indian innovations, however, it seems pretty clear that written arithmetic per se (performed on a "sand board") was developed there, as credited by all of the oldest extant texts on the subject from writers in Arabic (which call it something like "Indian arithmetic" or "Indian numbers"). Written arithmetic was then substantially elaborated in the Islamic world with a switch to using pen and paper, before making its way to Europe where it eventually kicked off the development of modern mathematical notation. The earlier Mesopotamian/Egyptian/Greek/European tradition, as well as the Chinese tradition, were generally based on using finger counting or some form of counting board, with written numerals used as a serialization format rather than a calculation tool. Arguably the invention and spread of physical materials like cheap good quality paper, writing implements, ink, and eventually printing presses were as important as the theoretical developments.