Concept of Zero Is Centuries Older Than Assumed, Analysis Suggests

Analysis of the Bakhshali manuscript shows that the concept of zero as a number in its own right may be centuries older than previously believed. Bodleian Libraries/University of Oxford

In mathematics, zero has two meanings. It can mean nothing, i.e., "I have zero dollars in my bank account," or it can serve as a placeholder that's part of a larger number, indicating that it is a multiple of 10.

As Robert Kaplan details in his 1999 book "The Nothing That Is: A Natural History of Zero," about 5,000 years ago, the ancient Sumerians who lived in what is now Iraq came up with the basic concept of zero as a placeholder. Instead of the 0 that we used today, though, they drew complicated combinations of wedges, lines and spaces in clay tablets to indicate it. As this short Scientific American essay by Kaplan explains, that concept was adopted by the Babylonians, who passed it along, by way of the ancient Greeks, to India, where Arab traders picked it up and eventually brought it back to medieval Europe.

Somewhere along the way, the wedges that signified zero the placeholder evolved into a solid dot, the precursor of the 0. For a long time, it was believed that the earliest example of that was an inscription on the wall of a temple in Gwalior, India, which dates back to the seventh century C.E.

But now, researchers have found evidence of an even earlier example. The Bakhshali manuscript, an Indian mathematical text written on 70 pieces of birch bark, was discovered back in 1881 by someone digging in the soil in the village of Bakhshali, in what is now Pakistan. The exact age of the manuscript has long been a subject of controversy, but the most authoritative answer to date — based on an analysis by Japanese scholar Takao Hayashi — seemed to place it between 700 and 1100 C.E. Recently, though, the University of Oxford's Bodleian Libraries, which has possessed the manuscript since 1902, commissioned a carbon dating study of it. The new study revealed that the manuscript actually may date as far back as 200 to 300 C.E., making it the oldest example of the dot that later evolved into zero.

"Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world," said University of Oxford mathematics professor Marcus du Sautoy in a press release. "But the creation of zero as a number in its own right, which evolved from the placeholder dot symbol found in the Bakhshali manuscript, was one of the greatest breakthroughs in the history of mathematics.

"We now know that it was as early as the third century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. The findings show how vibrant mathematics have been in the Indian sub-continent for centuries."