Ancient Text Reveals New Clues to the Origin of Zero

One of the biggest mathematical achievements in human history has to do with the origin of nothing—or zero, to be more specific.

Researchers at the University of Oxford's Bodleian Library recently conducted carbon dating on an ancient Indian text known as the Bakshali manuscript. They found that some pages in the manuscript date to the third or fourth century, five hundred years older than previously thought. That pushes back the origin of what would eventually become the zero symbol, 0, we use today.

The manuscript shows a series of Sanskrit numerals. In it, zero is represented by a small dot.

“This zero in India is the seed from which the concept of zero as a number in its own right represented by the same dot or circle will emerge some centuries later, something many regard as one of the of the great moments in the history of mathematics,” said lead researcher Marcus du Sautoy.

In this close-up image of folio 16v, you can see the use of a dot as a placeholder in the bottom line. This dot evolved into the use of zero as a number in its own right.
In this close-up image of folio 16v, you can see the use of a dot as a placeholder in the bottom line. This dot evolved into the use of zero as a number in its own right.
Photograph by Bodleian Libraries, University of Oxford

For mathematicians and historians like du Sautoy, the manuscript represents one of the most important clues to understanding a mathematical concept that would help fields such as calculus and physics flourish centuries later.

## Origins of Zero

To understand the origin of zero and the debates that surround it, it’s important to first understand the distinction between what math historians refer to as a “placeholder zero” and what they refer to as zero as a numeral unto itself.

Placeholder zeros, or their equivalents, have been documented for thousands of years. Sumerians in Mesopotamia were the first to represent this concept 5,000 years ago, Harvard math professor Robert Kaplan wrote in Scientific American.

This concept of zero spread from ancient Mesopotamia into India and eventually China, Kaplan noted. Independently, the ancient Maya used placeholder zeros represented by turtle shells drawings.

The first documented use of zero came from the ancient astronomer and mathematician Brahmagupta, said Sautoy.

“Brahmagupta’s text Brahmasphutasiddhanta, written in 628 A.D., is the first text to talk of zero as a number in its own right and to include a discussion of the arithmetic of zero, including the dangerous act of dividing by zero,” he said.

Historians theorize that zero was spread from northern India by Arab traders along the Silk Road, an ancient trading route that connected Europe and Asia, and may have helped to develop more complex schools of mathematical thought.

## Origins of the Bakhshali

A farmer unearthed the Bakhshali manuscript from a field in what is now Pakistan in 1881. It consists of 70 pages of birch bark, a common writing material before the advent of paper. Translations indicate that it may have been used by Silk Road merchants practicing arithmetic. In 1902, the manuscript was acquired by the University of Oxford, where it has been housed ever since.

For the past century, the manuscript’s date has been the subject of debate. Based on the writing style and mathematical content, scholars argued that it was created sometime between the eighth and twelfth centuries.

The Oxford researchers’ analysis revealed that parts of the manuscript contain birch bark from three different time periods, ranging from the third century to the 10th century.

Previously, the oldest known example of a zero symbol in ancient India came from a temple in Gwalior that was constructed in 876 A.D. If the carbon dating is correct, the Bakhshali manuscript could knock the Gwalior temple text into second place.

## Why Does Zero Matter?

To conclusively prove evidence of zero as a number, Peter Gobets isn’t convinced unless he sees it used in an equation. Gobets is a leading member of ZerOrigIndia, or Project Zero, in the Netherlands, which partners with researchers in Mumbai to pinpoint the origin of zero.

He agreed with du Sautoy’s statement that Brahmagupta’s writings were the first to describe zero as a number in its own right, but the first use of zero in practical applications is unclear.

Gobets isn’t convinced that the Bakhshali manuscript itself could have led to the creation of zero—he and his team hope to independently study the document themselves—but he said it’s possible. Where and exactly how the number zero made the leap from a concept of nothingness to a circle factored into equations, he said, is still highly debated.

“Our biggest enemy is that there is very little evidence,” he said, with speculation but no documentation of exactly who began to use zero in equations and when.

What we do know, said Gobets, is that zero was crucial to the zero-to-nine decimal system upon which algebra developed in 9th century Persia and was essential for physics principles documented by scientist Blaise Pascal in the 17th century.