Zero was not invented all at once. The Babylonians used a placeholder mark by about 400 BC, and the Maya had a zero by 665 AD. In India, the placeholder dot became a real number: the Bakhshali manuscript has zeroes dating from AD 224 to 383, and Brahmagupta wrote rules for calculating with zero in 628. Fibonacci brought these numbers to Europe in 1202.
the history of zero quick facts
- The Babylonians used a placeholder for zero by about 400 BC.
- The Maya used a shell symbol for zero.
- The oldest recorded zero symbol is a dot in India’s Bakhshali manuscript.
- Brahmagupta wrote rules for calculating with zero in 628.
- The word zero comes from the Arabic word sifr.
When was zero created?
Zero was not created on one day by one person. It grew slowly, in different places, over more than a thousand years.
The MacTutor History of Mathematics archive, run by the University of St Andrews, says the Babylonians were using a mark for an empty place by about 400 BC. The Maya of Central America had a zero by 665 AD, and probably earlier.
But zero as a real number came from India. The University of Oxford says the oldest recorded zero symbol is a dot in an ancient Indian book called the Bakhshali manuscript, whose oldest pages date from AD 224 to 383. In 628, the Indian mathematician Brahmagupta wrote the first rules for doing sums with zero.
| When | What happened |
|---|---|
| About 700 BC | Babylonian tablets use hooks to mark empty places |
| About 400 BC | Babylonians use two wedge marks as a placeholder |
| AD 224 to 383 | the oldest pages of India’s Bakhshali manuscript, with zeroes as dots |
| 628 | Brahmagupta writes rules for calculating with zero |
| By 665 | the Maya use a place-value system with a zero |
| 876 | an inscription in Gwalior, India, writes 270 and 50 with a zero |
| 1202 | Fibonacci brings the numbers 0 to 9 to Europe |
The two jobs of zero
Zero does two different jobs. MacTutor explains that it is a placeholder, showing an empty place in a number like 205, and it is also a number of its own.
The placeholder job matters a lot. MacTutor says it is what tells numbers like 2106 and 216 apart. Without a zero, it is easy to mix them up.
Making zero a number was a giant step. The University of Oxford quotes the mathematician Marcus du Sautoy, who said it “was one of the greatest breakthroughs in the history of mathematics”.
Babylon: the first placeholder
The Babylonians lived in what is now Iraq. MacTutor says they counted in 60s, not in tens like us, and needed only two symbols to write every number from 1 to 59 in each place.
At first they had no zero at all. MacTutor says an empty place was simply left out, so the Babylonians wrote 1 and 60 in the same way, and readers had to guess which was meant.
Over time, they found a fix. MacTutor says clay tablets from the city of Kish, from around 700 BC, used hook marks to show an empty place. By around 400 BC, Babylonians were putting two wedge-shaped marks where we would put a zero.
But their placeholder was never written at the end of a number, MacTutor says, so it was not yet a full zero like ours.
Greece
The ancient Greeks were brilliant mathematicians, but MacTutor says their maths was mostly about geometry, shapes and lines, so they did not use place-value numbers.
A few Greek astronomers did use a symbol like O in their records. MacTutor says the astronomer Ptolemy used it both between digits and at the end of a number, but few people copied him.
The Maya zero
On the other side of the world, the Maya of Central America invented a zero of their own. MacTutor says they counted in twenties, perhaps because people have 20 fingers and toes.
Maya numbers used just three symbols: a dot for one, a bar for five and a shell for zero. MacTutor says the Maya used a place-value system with a symbol for zero by 665 AD, and probably earlier.
The Maya used their numbers for a very long calendar. The Smithsonian’s National Museum of the American Indian says the Maya Long Count counts days from a creation date in 3114 BCE, and it finished a great cycle on 21 December 2012.
India: the dot becomes a number
India is where zero grew up. The University of Oxford says that only in India did the placeholder dot develop into a number in its own right.
MacTutor says numerals called Brahmi numerals appeared in India around the 3rd century BC, but did not yet use place value. Around 500 AD, the mathematician Aryabhata used a place-value idea, and his word “kha” for a place later became a name for zero.
The Bakhshali manuscript
The oldest recorded zero symbol comes from a fragile book called the Bakhshali manuscript. The University of Oxford says a farmer found it in 1881, buried in a field near Peshawar, in what is now Pakistan.
It is made of 70 leaves of birch bark, and it contains hundreds of zeroes, written as dots. It has been kept at Oxford’s Bodleian Libraries since 1902.
In 2017, the Bodleian Libraries had the manuscript carbon-dated. Smithsonian Magazine says its oldest pages were written between AD 224 and 383, about 500 years older than scholars had thought.
The University of Oxford says the dot in the manuscript later developed into the round 0 that we use today.
Brahmagupta’s rules
The first person to write down rules for using zero as a number was Brahmagupta. MacTutor says he was born in 598, possibly in Ujjain, India, and in 628, aged 30, he wrote a book called the Brahmasphutasiddhanta.
He described zero as what you get when you subtract a number from itself. He wrote that adding zero to a number, or taking zero away, leaves the number unchanged.
Brahmagupta even worked with negative numbers. MacTutor says he called positive numbers “fortunes” and negative numbers “debts”, with rules such as “A debt minus zero is a debt”.
He did get one thing wrong. He said zero divided by zero is zero. MacTutor says this was incorrect, but still a brilliant attempt at a very hard problem.
The zero at Gwalior
A stone inscription at a temple in Gwalior, India, shows zero being used in everyday life. MacTutor says it is dated 876 AD, and records a garden measuring 187 by 270 hastas, an old unit of length.
The same inscription says the garden produced 50 garlands of flowers a day. MacTutor says the numbers 270 and 50 are written almost as we write them today, although the 0 is smaller and a little raised.
How zero travelled to Europe
Zero travelled west through the Arab world. MacTutor says that in 776, an Indian scholar came to the court of Caliph al-Mansur in Baghdad, and an Indian astronomy book was translated into Arabic.
A scholar called al-Khwarizmi, who worked at the House of Wisdom in Baghdad, wrote a book explaining the Indian numerals 1 to 9 and 0. MacTutor says the word “algorithm” comes from his name.
MacTutor says the word “zero” comes from the Arabic word sifr, which also gave English the word “cipher”.
The first European document with these numerals, the Codex Vigilanus, was copied by a monk in Spain in 976, MacTutor says.
Fibonacci
The man who made the numbers famous in Europe was Leonardo of Pisa, known as Fibonacci. MacTutor says he learned mathematics in North Africa, where his father worked for merchants from Pisa.
In 1202, Fibonacci published a book called Liber abaci, which brought the Indian place-value numbers to Europe. MacTutor says he wrote about “the nine Indian symbols together with the sign 0”.
Europe was slow to switch, MacTutor says. For a long time, many people kept using older systems. See one of them in our Roman numerals facts.
Why you cannot divide by zero
Even Brahmagupta found dividing by zero tricky. Imagine sharing 6 sweets among 0 friends. How many does each friend get? The question does not make sense, because there is nobody to share with.
That is why, in maths today, dividing by zero is not allowed. MacTutor says later Indian mathematicians, such as Mahavira and Bhaskara, also struggled with it.
More about the story of zero
The Maya counted in a clever way. MacTutor and the Smithsonian’s National Museum of the American Indian say the third place in Maya numbers stood for 18 times 20, or 360, instead of 400. That is close to the number of days in a year, which helped with their calendar.
Much of what we know about Maya numbers comes from one book. MacTutor says the Dresden Codex was copied in the 11th century from an original made in the 7th or 8th century.
The Bakhshali manuscript was not all written at once. The University of Oxford says carbon dating showed its leaves come from at least three different periods.
In India, MacTutor says the oldest dated document using place value is a legal record from 594 AD, although that date is disputed.
New ways of doing sums followed. MacTutor says that in the 10th century, a scholar called al-Uqlidisi showed how to calculate with Indian numerals using pen and paper, instead of drawing in dust on a board.
MacTutor says Fibonacci’s real name was Leonardo Pisano. He published a second version of Liber abaci in 1228.
Three things people get wrong
No single person invented zero. The Babylonians, the Maya and mathematicians in India all developed zero-like signs.
“Arabic numerals” were not invented by Arabs. They came from India, and Arab scholars passed them on.
Fibonacci did not invent zero. He learned it in North Africa and introduced it to Europe.
Did you know? The Bakhshali manuscript, with the oldest recorded zeroes, was found buried in a field by a farmer in 1881.
Try it
Write the number 305 without using a zero. Can you think of a way to show the empty tens place, like the Babylonians had to?
Knowledge check
What are the two jobs of zero?
Show answer
A placeholder and a number of its own.
Who first wrote rules for calculating with zero?
Show answer
Brahmagupta, in 628.
Frequently asked questions
Who invented zero?
No single person. The Babylonians and Maya made zero-like signs, and mathematicians in India turned zero into a real number.
When was zero first used?
The Babylonians used a placeholder by about 400 BC. The oldest recorded zero symbol, in the Bakhshali manuscript, dates from AD 224 to 383.
What is the Bakhshali manuscript?
An ancient Indian maths book on birch bark, found in 1881 near Peshawar. It has hundreds of zeroes written as dots.
Who was Brahmagupta?
An Indian mathematician who, in 628, wrote the first rules for adding, subtracting and multiplying with zero.
How did zero get to Europe?
Indian numbers passed through Arab scholars in Baghdad, and Fibonacci’s 1202 book Liber abaci brought them to Europe.
Why can’t you divide by zero?
Sharing something among zero people makes no sense, so dividing by zero has no answer. Even Brahmagupta got this rule wrong.
Sources
- MacTutor History of Mathematics (University of St Andrews): a history of zero — Babylon, Greece, the Maya, India and Gwalior; MacTutor’s pages on Babylonian, Mayan, Indian and Arabic numerals were also used
- MacTutor: Brahmagupta — Brahmagupta’s life and his rules for zero; MacTutor’s page on al-Khwarizmi was also used
- MacTutor: Fibonacci — Fibonacci and Liber abaci
- University of Oxford: carbon dating of the Bakhshali manuscript (2017) — the manuscript, its dating and zero becoming a number
- Smithsonian Magazine: zero is 500 years older than thought (2017) — the manuscript’s oldest dates; its article on the Gwalior temple was also used
- Smithsonian National Museum of the American Indian: the Maya calendar system — the Maya Long Count and counting in twenties
