The Bakhshali Manuscript: the World's Oldest ‘True’ Zero?

The Bakhshali Manuscript: the World's Oldest ‘True’ Zero?

It may be elementary maths, but the concept of zero has given rise to many an existential, intellectual debate over the history of zero, with much musing over nothing.

An international group of academics, including a mathematician from the University of Canterbury (UC) in Christchurch, is challenging Oxford University’s recent findings about the use of zero in an ancient Indian manuscript.

The Bodleian Library at Oxford University last month issued a press release and YouTube video announcing that a Sanskrit manuscript housed in the library for the last century had been dated using radiocarbon techniques. Contrary to existing proposals, which dated the manuscript to sometime between the eighth and twelfth centuries, Oxford's radiocarbon dating laboratory announced that three of the birch-bark folios of the Bakhshali Manuscript could be dated to roughly 300 CE, 700 CE and 900 CE. Oxford's announcement was widely reported in the international media.

The key result, the Bodleian Library said, was that because of this early date of 300 CE, one of the manuscript's leaves contained the oldest known written zero.

The Library also announced that the zero in the manuscript was not a “true” zero, in the sense that it functioned only as a marker showing an empty decimal place, and not as a fully-fledged number that participates in calculations.

However, an international group of historians of Indian mathematics is challenging Oxford's findings, stating the zero in the Bakhshali treatise is younger, but more important than Oxford claims.

The team, which includes scholars from universities in New Zealand, the United States, France, Japan and Canada, has published a peer-reviewed article that refutes several of the Library's key assertions.

The scholars, including University of Canterbury Associate Professor Clemency Montelle, Mathematics and Statistics, argue that the work written on the leaves of the Bakhshali manuscript is a unified treatise on arithmetic that must have been written at the time of the latest of the manuscript’s leaves, not the earliest.

Contrary to the different dates the radio carbon dating suggests, the treatise shows no signs of being a jumble of fragments from different periods, the academics say. Both the handwriting and the topic being discussed are continuous across the boundary of the first two dated leaves. It looks very much as if the scribe, who may have lived at the end of the eighth century, wrote out his treatise on a group of leaves that had been manufactured at very different times.

But of greater significance for the history of mathematics is the authors’ evidence showing that the Bakhshali treatise does indeed know the “true” zero, and contains calculations like long multiplication that would have necessitated using zero as an arithmetical number.

From various other features of the manuscript's style and content, the team concludes that Oxford’s claims are implausible and do not fit with what has previously been discovered about the Bakhshali Manuscript. They urge further study of the radiocarbon dating procedures and the textual tradition of mathematics in South Asia to integrate the new findings with existing information in a way that will be historically consistent.

UC’s Dr Clemency Montelle says, “Radio carbon dating offers exciting new insight into historical documents, however the results must be carefully integrated into the other information that we know about the manuscript; that is, science can’t trump all.”

Source: Kim Plofker, Agathe Keller, Takao Hayashi, Clemency Montelle and Dominik Wujastyk. “The Bakhshālī Manuscript: A Response to the Bodleian Library's Radiocarbon Dating” in History of Science in South Asia [Online], Volume 5 Number 1 (6 October 2017). DOI: http://dx.doi.org/10.18732/H2XT07

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