The concept of zero is so deeply engrained in our culture that it is hard to imagine not having it. Yet most ancient cultures never came up with the idea, greatly to the detriment of their mathematical development. We don't know exactly when the idea first appeared, but re-analysis of a nearly 2,000-year-old Indian manuscript has taken us closer to this crucial point.
The Bakhshali manuscript is written on pieces of birch bark and was found buried in a field outside the village of Bakhshali, Pakistan, in 1881. It has been housed in the Bodleian Library, Oxford, since 1902. It contains hundreds of zero symbols, and clearly represents one of the oldest surviving references to this concept. However, its age has been in doubt, with estimates based on writing style placing it around the year 800.
Testing of three samples in the Oxford Radiocarbon Accelerator Unit revealed that the manuscript, rather than having a single origin, was created in pieces centuries apart. The earliest measured section dates to somewhere between 224 and 383 AD, while additions were made in 680-779 and 885-993 AD. The last date roughly aligns with other examples we have of the dot symbol, which gradually evolved into our 0, being used to indicate absence. However, the earlier dates are well outside expectations.
The fact the manuscript remained in use for so long, and was expanded at least twice centuries later, indicates its status, probably as a training manual. It is filled with examples of practical arithmetic and algebra. Oxford's Professor Marcus du Sautoy told The Guardian: “There’s a lot of ‘If someone buys this and sells this how much have they got left?’”
“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. 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,” du Sautoy said in a statement. “We now know that it was as early as the 3rd 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.”
Both the Babylonians and Mayans had symbols for nothing, but it was only when the Indians developed the idea that its mathematical power was realized. Even then, the placeholding dot took centuries to evolve into the concept that zero could be a number.
Arab traders spread the idea from India, but it faced considerable resistance upon its arrival in Europe, even facing attempts to ban it as heresy.