This article is really just a gloss on Kaplan's book (which I have read so it stands out) with a bit of gratuitous randomness thrown in.
Much as I have a rather low-level atavistic desire to credit India with the zero/nil, as there was so much exchange between mesopotamia and the early indus regions (just look at the idea of the alphabet going one way and then digits going the other), the sumerian "origins" are quite likely. More importantly, the vedic tradition didn't give rise to the formalisms developed by the later Greeks and, centuries later, their Islamic students. Thus for a long time, scholarly dissertations from the subcontinent on mathematics, philosophy etc tended to essays and explorations of conjectures, which makes pinning responsibility hard to do, the way you can, say, "Wiles did prove Fermat's Last Theorem".
Personally I find invention requires so much history and intertwined communication that the idea of "inventor" is kind of bogus anyway.
BTW in case this sounds like I'm dissing ancient indian scholars: you see this in the early days of any scientific field: early neuroscience in the early 20th century, the same with cognitive science in the mid 50s-70s (at least) etc. In fact most of contemporary ML just has a light layer of formalism painted on too. It feels like fields need names, but only really get them when they have attained some early level of abstraction and emerging rigor.
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.
What adds to the absurdity is that an ancient spartan or dalmatian would have seen folks like Socrates as foreigners, and so people who descend from ancient Spartans would have no reason to feel proud of the achievements of Greek philosophy were it not for the 20th century myth of the nation state. The situation is even worse in India.
The intellectually honest account is that great people came at random from accommodating societies and cultures with the requisite technology and opportunity for those geniuses. There are countless stories of kings beheading inventors because their inventions risk offending the social order, or the gods, their pride, or some such. Just as there were in all likelihood millions of geniuses all over the world who were determined at birth to be subsistence farmers or slaves.
Isn’t India’s contribution the base 10 number system and using zero for the first time to represent numbers like we do today? I don’t think having a concept of nothing means much otherwise.
Base ten number systems were invented repeatedly. The oldest positional number system we know about is the (base 60) system from Mesopotamia. Other ancient people also used positional base 10 systems for calculation, including in China, Egypt, and Greece, but their written numerals were not positional in the same way. India is the first place where we have evidence of a base-ten number-writing system with 10 symbolic digits whose contribution to a number depends on the place.
Much as I have a rather low-level atavistic desire to credit India with the zero/nil, as there was so much exchange between mesopotamia and the early indus regions (just look at the idea of the alphabet going one way and then digits going the other), the sumerian "origins" are quite likely. More importantly, the vedic tradition didn't give rise to the formalisms developed by the later Greeks and, centuries later, their Islamic students. Thus for a long time, scholarly dissertations from the subcontinent on mathematics, philosophy etc tended to essays and explorations of conjectures, which makes pinning responsibility hard to do, the way you can, say, "Wiles did prove Fermat's Last Theorem".
Personally I find invention requires so much history and intertwined communication that the idea of "inventor" is kind of bogus anyway.
BTW in case this sounds like I'm dissing ancient indian scholars: you see this in the early days of any scientific field: early neuroscience in the early 20th century, the same with cognitive science in the mid 50s-70s (at least) etc. In fact most of contemporary ML just has a light layer of formalism painted on too. It feels like fields need names, but only really get them when they have attained some early level of abstraction and emerging rigor.
Sorry, that moved on beyond zero!