Gwalior is rightly famous for its majestic cliff-top fort, the awe-inspiring Jain monuments that have been hewn from the hillside, and for the ancient temples of Sas Bahu and Teli Ka Mandir. Tourists flock to Gwalior in their thousands to see these monuments, probably unaware that it is also the home to a simple carving that is the oldest of its type in India, and is arguably the greatest conceptual leap in the history of mathematics…the zero.
Recently installed signposts now help tourists find this historic location. Halfway up the cobbled pathway on the eastern approach to the fort is the small and unassuming Chaturbhuj Temple.
The temple has been completely carved out of the rock face, and thanks to an inscription in the sanctum we know that it was constructed in the year 876 AD. It is this inscription that also contains one of the earliest known uses of the mathematical zero.
India is where the decimal numbering system based on position was invented. The Romans had letters to represent numbers, the largest being M which represented 1,000. So if you wanted to indicate 10,000 in Roman numerals, you would write MMMMMMMMMM – a cumbersome system, prone to errors.
India created a system where the place of a number determined what its value is. Taking the number 111 as an example and reading from right to left, there’s a 1 in the unit position, a 1 in the 10s position, and a 1 in the 100s position. 1 + 10 + 100 = 111.
With a decimal number system based on position you can write really big numbers very easily, you only need seven digits to write all numbers up to a million. In the Roman numerals system, you’d need to write a thousand Ms in a long line to represent a million !
But a decimal number system based on position required a new mathematical concept to be created, a zero, for when there is nothing in that position. Taking the number 101 as an example this time and again reading from right to left, there’s a 1 in the unit position, a 0 (zero) in the 10s position, and a 1 in the 100s position. 1 + 0 + 100 = 101.
There are two examples of the use of zero on the inscription in the sanctum of the Chaturbhuj Temple, located to the left of a now damaged Vishnu idol. I was only able to successfully identify one of the zeros.
The inscription records the date as 876 AD, and documents the dimensions of a land grant to a neighbouring temple along with the size of a daily gift of flowers to be paid for from an endowment made to this temple.
“Om. Adoration to Vishnu! In the year 933 , on the second day of the bright half of the month of Magha the whole town gave to the temple which Alla, the son of Vaillabhatta, had caused to be built a piece of land 270 hastas in length and 187 hastas in breadth, for a flower garden the town gave in perpetual endowment for a daily gift of 50 garlands of flowers”
The hasta is a traditional Indian unit of length, measured from the elbow to the tip of the middle finger. It equals about 18 inches, or 45 centimetres.
The “270 hasters” and “50 garlands” is where we see that all important little circle, the zero.
I was a little surprised at how similar the numbers looked to how 270 is written today.
While there was an understanding of ‘nothingness’ in the ancient Babylonian and Chinese cultures, it was in India that mathematicians put a symbol, the circle, for it. The Babylonians used a marker to represent it, the Chinese used a space to represent ‘nothing’.
By 876 AD the concept of zero was already in common use in India. We know that approximately two centuries earlier the Indian mathematician Brahmagupta wrote down the rules for arithmetic; adding, subtracting, multiplication and division, and he brought forward the use of zero and its role in mathematics.
The Indian decimal number system that used position and a zero was far superior to all other systems because it made calculations so much easier. It came into wider international use through the writings of the leading Persian mathematician Mohammed ibn-Musa al-Khowarizmi. It was through their trade with India that Arabs picked up the zero, and it spread via the Middle East to Europe, reaching Spain 1,000 years ago.
By rights all the numbers we use today should be called Indian numerals rather than Arabic ones. It’s what the whole world now uses, and here in Gwalior is the oldest inscribed zero in India with a verifiable date.
Many Indian philosophical texts have the notion of Shunya, a word used to describe a void when nothing is present. The word came into common use around 300 BC, and was used by Buddhist, Jain and the early Vedic religions to describe a particular state when all your impressions have been wiped out, Shunya is effectively reaching the state of Nirvana. So ironically, the concept of nothing also means everything.
It’s curious to think if a spiritual idea of nothingness also inspired the mathematical idea of zero. The use of a circle to represent a zero may indeed have religious roots. The circle is symbolic of the sky, and many words used to verbally encode zero in Sanskrit mean sky or void. The sky was often represented by a circle of the heavens, and so an appropriate symbol for zero.
Until quite recently it was believed the Gwalior Zero was the oldest known inscription of zero in the world. Then in 1931 a French archaeologist, Georges Cœdès, deciphered a plaque (known as inscription K-127) found in the ruins of a 7th century temple at Sambor, Cambodia. The plaque was dated to 683 AD, predating the Gwalior zero by 193 years. The inscription was moved to the Cambodian National Museum from where it ‘disappeared’ during the Khmer Rouge regime. For a time the Gwalior Zero regained its title as the world’s oldest zero. Then in January 2017 it was announced that the Cambodian National Museum had found their lost artifact, and it was going to be put on public display. The Gwalior Zero was then relegated back to second place.
The earliest recorded use of zero on any medium in India can be found on the Bakhshali manuscript. The Bakhshali manuscript was discovered in 1881, buried in a field in what was then an Indian village called Bakhshali, now in Pakistan.
It was broadly recognised as the oldest Indian mathematical text, but it’s exact age had been widely contested. Written on 70 fragile leaves of birch bark, recent radiocarbon dating of the manuscript has placed its date to the 3rd century AD, predating the Gwalior zero inscription by 500 years.
However, in a further twist there are questions raised as to whether the text written on the bark is contemporary with the radiocarbon date for the bark itself. You can read much more about this development here.
The decimal numbering system features heavily in this document, as does the number zero written as a circle. The document is kept by University of Oxford’s Bodleian Library.
Access to the interior of the Chaturbhuj Temple below Gwalior Fort used to be by appointment only. These days it would appear that a guard is almost always nearby with keys to open the gate and allow you to take a look inside.
The many signposts to the temple rather uncharacteristically declare this to be the “The oldest Zero in the Gwalior region” – I’m so used to guides making extravagant claims about places but here it seems perhaps a little understated.
If you ever find yourself in Gwalior, I hope you too will come looking for nothing – India’s greatest gift to the world.
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