Some context: as a mathematician, I often hear colleagues argue that we ought to consider the mathematics of historical cultures alongside European mathematics as a part of the history of mathematics. For example, "India" or "China" (historical India/China) had a notion of 0 before Europeans did, therefore that should be acknowledged as a major, non-European mathematical development. I am not entirely confortable with this and I hope you can help. What we understand as "mathematics" is, in the sense that its history is rooted in, European mathematical developments that had little influence from India or China. Therefore, can these examples be considered part of the history of what we understand as mathematics? Is this just a matter of semantics? Or, should we ackowledge that are/were many "mathematics" developed at different points in time to varying degrees and our modern notion ought to encompass them all, even those that terminated at some point in the past?

Edit: I acknowledge that this question is not about a specific event, but rather about historiographical methods.