Research commissioned by the University of Oxford’s Bodleian Libraries on an ancient Indian text known as the Bakhshali manuscript has moved the use of zero in Indian mathematics back five hundred years to between the 2nd and 4th centuries CE. The discovery, through radiocarbon dating, is significant because it more clearly indicates the place in history of the solid dot used as the placeholder for zero in the Bakhshali manuscript and its eventual evolution to the zero we know today.
Marcus du Sautoy, Professor of Mathematics at the University of Oxford explained in a YouTube video on the carbon dating discovery that the zero had been used as a “place holder” in many different cultures over the millennia, but it wasn’t until its use in India that it developed into the symbol of voidness and nothingness that it is today.
To understand the distinction in the historical uses of zero, consider zero as a placeholder in the number 100: In this case the 00s place the 1 in the correct position to let someone know that it’s not 1 of something, or 10 of something, or 12 of something, or 101 of something, rather it’s one hundred of something. In the placeholder use of zero, the 00s could be other sorts of marks, for example the “ “s that the Babylonians used as placeholders, or the dots used as placeholders in the Indian Bakhshali manuscript. Historically, the zero used in this way didn’t indicate the absence of something.
The understanding of zero as the absence of the thing being counted (Q. How many dots on a blank piece of paper? A. Zero) – and the understanding of how it functioned in relationship with other numbers (Q. What is the result of any number multiplied by zero? A. Zero) – were concepts that evolved over time. The first mathematical text that explored the zero as the absence of the thing being counted, and its relationship to other numbers, was another ancient Indian text, the Brahmasphutasiddhanta, written in 628CE, by the astronomer and mathematician Brahmagupta.
The dot, like the one that exists as a placeholder in the Bakhshali manuscript, has been thought to be the precursor of the zero (0) in ancient Indian mathematical theory for a long time. However, there was little textual evidence to support this progression. Based on writing style and content, the Bakhshali manuscript was originally placed between the 8th and 12th century CE by Japanese scholar Dr. Hayashi Takao who had done the most exhaustive study of the text as part of his doctoral thesis in 1985. Dr. Takao’s dating placed the manuscript after Brahmagupta’s Brahmasphutasiddhanta.
Complicating matters was the fact that the Bakhshali manuscript, written on seventy fragile leaves of birch bark, actually spans three different time periods, making it challenging to place the text in its appropriate century. The radiocarbon dating now definitively places the oldest sections of the Bakhshali manuscript between the 2nd and 4th centuries CE, prior to the Brahmasphutasiddhanta’s explorations of the zero as a symbol of voidness, nothingness and how it relates to other numbers.
Perhaps it is not surprising that the modern concept of zero – as the number that negates all other numbers when they are multiplied by it – originated in India. Indian philosophers, like Nagarjuna (ca 150-250 CE), had been working with the concept of voidness and negation for centuries prior to the evolution of the zero. This sort of voidness and negation were used in Indian philosophical systems in many ways, one of which applied to meditative states of realization. In Indian Sanskrit, the word śūnya (शून्य) is both the word for the number zero (0) and the basis for the concept of voidness or emptiness.
That the conceptualization of zero should take the leap from mere placeholder, to a number symbolizing this voidness and lack of existence of something, is a natural cultural evolution from philosophical thought, to symbolic thought, like what occurs in mathematics. That it takes layers of multinational scholarship, over centuries, to reconstruct the process of cultural and symbolic evolution speaks to how our methods of understanding continue to evolve.
A final thought: Much has been made of the dot in the Indian Bakhshali manuscript as the grandparent of the hollow symbol that we now recognize as zero (0), but if one looks at the rest of the numbering system in the Śāradā script, in which the manuscript is written, the symbol for one (1) is actually what we would now consider to be the symbol for zero (0). How this switch occurred may have to be the next mystery that the researchers at Oxford unravel.