A Philosophical Origin of the Mathematical Zero.

We investigate if philosophical ideas of nothing could have given rise to the mathematical zero, which is distinct from nothing and is an independent number with a set of basic operations defined. This investigation should be complementary to other studies, e.g., those based on epigraphic and paleographic evidence in order to probe the origin of zero. First, we argue that a practical need did not give rise to the mathematical zero. Moreover, neither a place-value number system nor a placeholder in such a system was required to conceptualize zero. Therefore, we insist that zero and its basic operations were intellectually premised, which likely required a philosophical base of nonexistence, and not that of emptiness or void as commonly assumed. The prevalence of a philosophy of nothing in ancient India and the appearance of the first clear prescription of basic operations of zero in an Indian book of the first millennium CE point to a development of the concept of zero in India. We back this up with 'living evidence' of word-numerals developed in India, and propose that the comments of the Syrian Bishop Severus Sebokht, which are often used to argue against the Indian origin of zero, do not provide evidence against such an origin. [ABSTRACT FROM AUTHOR]