A small dot on an old piece of birch bark marks one of the biggest events in the history of mathematics. The birch bark is actually part of an ancient surviving Indian mathematical document known as the Bakhshali manuscript. It is written in Sanskrit with significant influence of local dialects. And the dot is the first known recorded use of the number zero. Although the Bakhshali manuscript is widely acknowledged as the oldest Indian mathematical text, the exact age of the manuscript has long been the subject of academic debate. The researchers from the University of Oxford recently discovered the document is 500 years older than was previously estimated, dating to the third or fourth century — a breakthrough discovery.

The origin of the symbol zero has long been one of the world’s greatest mathematical mysteries. New carbon dating research commissioned by the University of Oxford’s Bodleian Libraries into the ancient Indian Bakhshali manuscript, held at the Bodleian, has revealed it to be hundreds of years older than initially thought, making it the world’s oldest recorded origin of the zero symbols that we use today. New carbon dating provides insights on one of the most pivotal moments in the history of mathematics.

On a wall of Chaturbhuj temple in Gwalior Fort in Madhya Pradesh dedicated to Lord Vishnu, is a plaque, which dates back to c. 875 CE and has a circle, considered as the earliest representation of the number zero in the world. The plaque mentions a land grant of 270 hastas (a traditional Indian unit of length, measured from the elbow to the tip of the middle finger. 1 hasta roughly equals 18 inches or about 45 centimetres) for a flower garden as well as a daily grant of 50 flower garlands.

The surprising results of the first-ever radiocarbon dating conducted on the Bakhshali manuscript, a seminal mathematical text which contains hundreds of zeroes, reveal that it dates from as early as the 3rd or 4th century (224-383 CE) – approximately five centuries older than scholars previously believed. 

This means that the manuscript, in fact, predates the 9th-century inscription of zero on a wall of the Chaturbhuj temple, which was previously considered to be the oldest recorded example of a zero used as a placeholder in India. The findings are highly significant for the study of the early history of mathematics.

The Bakhshali manuscript was found in 1881, buried in a field in a village called Bakhshali, near Peshawar, in what is now a region of Pakistan. It was found by a local farmer and was acquired by the Indologist AFR Hoernle, who presented it to the Bodleian Library in 1902, where it has been kept since then. 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. A large part of the manuscript had been destroyed and only about 70 leaves of birch bark, of which a few were mere scraps, survived to the time of its discovery.

While the use of zero as a placeholder was seen in several different ancient cultures, such as among the ancient Mayans and Babylonians, the symbol in the Bakhshali manuscript is particularly significant for two reasons. Firstly, it is this dot that evolved to have a hollow centre and became the symbol that we use as zero today.

Secondly, it was only in India that this zero developed into a number in its own right, hence creating the concept and the number zero that we understand today – this happened in 628 CE, just a few centuries after the Bakhshali manuscript was produced, when the Indian astronomer and mathematician Brahmagupta wrote a text called Brahmasphutasiddhanta, which is the first document to discuss zero as a number.

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 subcontinent for centuries. Translations of the text, which is written in a form of Sanskrit, suggest it was a form of a training manual for merchants trading across the Silk Road, and it includes practical arithmetic exercises and something approaching algebra.

Determining the date of the Bakhshali manuscript is of vital importance to the history of mathematics and the study of early South Asian culture and these surprising research results testify to the subcontinent’s rich and longstanding scientific tradition. The project is an excellent example of the cutting-edge research conducted by the Bodleian’s Heritage Science team, together with colleagues across Oxford University, which uncovers new information about the treasures in our collections to help inform scholarship across disciplines.

Richard Ovenden, Bodley’s Librarian

Quoting from The Conversation, zero’s late arrival was partly a reflection of the negative views some cultures held for the concept of nothing. Western philosophy is plagued with grave misconceptions about nothingness and the mystical powers of language. The fifth century BCE Greek thinker Parmenides proclaimed that nothing can exist since to speak of something is to speak of something that exists. This Parmenidean approach kept prominent historical figures busy for a long while.

After the advent of Christianity, religious leaders in Europe argued that since God is in everything that exists, anything that represents nothing must be satanic. In an attempt to save humanity from the devil, they promptly banished zero from existence, though merchants continued secretly to use it.

Indian ideas of spiritual nothingness led to mathematical zero. The development of zero as a mathematical concept was inspired by India’s long philosophical tradition of contemplating the void and may explain why the concept took so long to catch on in Europe, which lacked the same cultural reference points.

So after zero finally emerged in ancient India, it took almost 1,000 years to set foot in Europe, much longer than in China or the Middle East. 

Historians theorise 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.

In 1200 CE, the Italian mathematician Fibonacci, who brought the decimal system to Europe, wrote that:

The method of the Indians surpasses any known method to compute. It’s a marvellous method. They do their computations using nine figures and the symbol zero.