All for Nought
By accident, it records the oldest "0" in India for which one can assign a definite date..
By Bill Casselman
University of British Columbia, Vancouver, Canada
What the Gwalior tablet shows is that by 876 A. D. our current place-value system with a base of 10 had become part of popular culture in at least one region of India.
We know almost nothing of how this decimal place-value notation came about, although there are many suggestive facts. One feature of Hindu culture in the middle centuries of the first millennium was that its texts were largely in verse, and preserved through oral tradition. It is hard to fit a useful numerical notation into such a scheme, and in fact what we see is a large literature, written down only much later than it originated, with numbers - often very, very large numbers - written in a kind of decimal place-value notation, but in words instead of symbols. Furthermore, the demands of the metric of the verses required that the exact words chosen to represent a given digit might vary from one point to another, so as to scan correctly. Whether this usage overlay more convenient calculation with symbols is not known to us, although it is almost inconceivable that it did not.
Another problem is that the climate of India is harsh. Paper was introduced to India late, and until then the materials on which things were written were birch bark in the north and palm leaves in the south. These are both extremely fragile. There are many extant manuscripts written on these, but nearly all of relatively recent date.
One of the more intriguing questions about the origin of decimal place-value notation is what connection it had to a much older tradition from a nearby region. The Babylonians began writing in about 3000 B.C., and had the good fortune to write on clay tablets, which can last for a very long time. We have extensive records from several thousand years of their development. They used an extremely sophisticated place-value system, remarkably much the one we use today, from very roughly 2000 B.C. on, but with a base of 60 instead of 10, and without "0". All the evidence that I am aware of suggests that this was technology acquired only by an elite group through rigorous training. This somewhat ambiguous notation persisted to about 300 B.C. when Babylonian astronomical tables started to incorporate a symbol that to some extent performed as zero, that is to say as a sign to indicate a space between two "digits". This was adopted in modified form by Greek astronomers after the conquests of Alexander, and this science in turn was transmitted (along with astrology!) to India sometime in the first few centuries of the current era. Exactly how these transmissions occurred is lost to us.