Who invented zero? How nothing became a number

No one person invented zero: the people who gave it to us worked over more than a thousand years. It was invented at least twice as a placeholder, a mark for an empty place in a number, by Babylonian scribes and in Maya Mesoamerica, and once as a true number, in India. The first known rules for calculating with zero were written by the Indian mathematician Brahmagupta in 628. From India, zero and the digits that go with it spread through the Arab world to Europe.

In short

• There are two zeros: a placeholder that tells 205 from 25, and a number in its own right that you can add, subtract and multiply.
• The placeholder appeared in Babylonia by about 400 BCE and in Maya and other Mesoamerican dates by the 3rd century CE; the number came from India, set out by Brahmagupta in 628 CE.
• Zero reached Europe through Arabic texts, and Fibonacci's book of 1202 made it known there; it took centuries more to replace Roman numerals.

Why is zero two different ideas?

The first zero is a placeholder. In a place-value system, where a digit's position says what it is worth, you need a way to show that a position is empty. Write the digits 2 and 5 with no zero and you can't tell 25 from 205, 250 or 2,005. A gap between the digits can stand in, but gaps are easy to misread or miss when a text is copied.

The second zero is a number. It answers the question "how many?" when the answer is none, and it obeys rules: any number plus zero is that number, any number minus itself is zero, any number times zero is zero. Treating "nothing" as a quantity you can calculate with is the harder step, and the one that changed mathematics. Many cultures had the placeholder; only one is known to have made zero a number first.

Who used zero first?

Here is the record, with the evidence for each step:

When	Where	What	How we know
About 700 BCE	Babylonia (Iraq)	Hook marks for an empty place on a tablet from Kish	The tablet survives
About 400 BCE	Babylonia	A double-wedge sign used as a placeholder inside numbers	Clay tablets
2nd century CE	Alexandria, Roman Egypt	Ptolemy's Almagest uses a small circle for empty places in astronomical tables	His text, copied ever since
From the 3rd century CE	Mesoamerica, best known from the Maya	A zero sign in Long Count calendar dates, in base 20	Dated stone monuments
628 CE	India	Brahmagupta gives rules for arithmetic with zero and negative numbers	His book, the Brahmasphutasiddhanta
683 CE	Cambodia	The year 605 carved with a dot for zero at Sambor	The oldest firmly dated zero in a decimal number
About 825 CE	Baghdad	Al-Khwarizmi writes a book on the Indian numerals, including zero	Later Latin translations
876 CE	Gwalior, India	A temple inscription writes 270 with a small circle	The earliest Indian zero all historians accept as genuine
1202 CE	Pisa, Italy	Fibonacci's Liber Abaci teaches the Hindu-Arabic numerals in Europe	His book

The dates for the Babylonian, Greek, Gwalior and Arabic steps come from the MacTutor history of zero at the University of St Andrews; the Maya and Cambodian dates from Wikipedia's history of 0. The Babylonians used base 60, and for more than a thousand years they managed without any placeholder, relying on context. Mesoamerica's zero was invented independently, on the other side of the world, for counting days. Long Count dates from as early as 36 BCE, found outside the Maya homeland, already need a placeholder, so it may be older than the Maya, though no surviving date shows the zero sign itself before the 3rd century CE.

What did Brahmagupta do?

In 628, in Bhillamala in what is now Rajasthan, Brahmagupta finished a book on astronomy and mathematics, the Brahmasphutasiddhanta. One chapter sets out rules for "fortunes", positive numbers, "debts", negative ones, and zero, which he defines as a number subtracted from itself. MacTutor's biography calls him the first person known to have tried to extend arithmetic to negative numbers and zero.

Brahmagupta's rule	In modern terms	Right today?
A number minus itself is zero	7 − 7 = 0	Yes
Zero added to a debt is a debt; to a fortune, a fortune	−3 + 0 = −3; 3 + 0 = 3	Yes
Any number times zero is zero	5 × 0 = 0	Yes
Zero divided by zero is zero	0 ÷ 0 = 0	No: modern mathematics leaves it undefined

He got division by zero wrong, and so did later Indian mathematicians. Mahavira wrote around 830 that a number divided by zero stays unchanged, and Bhaskara in the 12th century suggested it gives infinity. Mathematicians today leave division by zero undefined: no number times zero gives 5, so 5 ÷ 0 has no answer. That the hardest question took centuries to settle shows how strange a number zero is.

How did zero travel to Europe?

Indian astronomy reached the court of the caliph in Baghdad in the 8th century, and Brahmagupta's work was translated into Arabic. Around 825, the Persian mathematician al-Khwarizmi wrote a book explaining the Indian numerals, zero included. His name gave us the word "algorithm". The Sanskrit word for zero, shunya, meaning empty, was translated into Arabic as sifr, which became "cipher" in English and, by way of Fibonacci's Latin zephirum and Italian, "zero".

Leonardo of Pisa, known as Fibonacci, learned the numerals as a boy in North Africa, where his father was a trade official. His Liber Abaci of 1202 showed European merchants how to calculate with them, the same book that gave the world the Fibonacci sequence. Europe still used Roman numerals, a system inherited from the Roman Empire with no zero at all, and they took centuries to give way. Merchants and bankers, who needed fast and checkable arithmetic, adopted the new digits first; MacTutor's historians note that zero came into wide use only in the 1600s.

Why was zero such a big idea?

Try multiplying MCMXLIV by XXVII in Roman numerals and the point makes itself. With place value and zero, 1,944 × 27 is a few lines of routine steps a child can learn; without them, calculation needed an abacus, and the written number was only a record of the answer. Zero made written arithmetic, algebra and later the decimal fractions behind measurement possible. It is the reason pi can be written to trillions of decimal places at all. Computers run on just two digits, 0 and 1, so every piece of digital information depends on a symbol for nothing.

Still argued

When India first wrote zero is still argued. The Bakhshali manuscript, a birch-bark mathematics text found in 1881 near Mardan, in what is now Pakistan, that uses a dot for zero, was radiocarbon dated for Oxford's Bodleian Library in 2017, which reported that one folio came from as early as 224–383 CE and called it the oldest recorded zero. Specialists including Kim Plofker and Dominik Wujastyk disputed that reading, arguing that the earliest folio is unlikely to date the whole text and that the latest date best fixes when it was copied. Then, in a report published on 14 October 2024, Oxford's radiocarbon unit and the Bodleian gave new dates for five folios, including folio 16, the one first put at 224–383 CE, now at 901–1032 CE; their model places the making of the manuscript between about 799 and 1102 CE. Whether the text copies a much older original remains open.

The story of zero is a good case of how knowledge builds: no single inventor, but many people over many centuries, each adding a piece and each piece checked by use.

Check yourself

• What is the difference between zero as a placeholder and zero as a number?
• Without looking back, trace zero's route from India to Europe, naming two people along the way.
• Why can't any number be divided by zero?

Sources

• A history of Zero — J J O'Connor and E F Robertson, MacTutor History of Mathematics, University of St Andrews
• 0 — Wikipedia
• Brahmagupta — J J O'Connor and E F Robertson, MacTutor History of Mathematics, University of St Andrews
• The Bakhshālī Manuscript: A Response to the Bodleian Library's Radiocarbon Dating — Plofker, Keller, Hayashi, Montelle and Wujastyk, History of Science in South Asia, 2017
• Radiocarbon dating of the Bakhshālī manuscript — Chivall, Lladó-Buisán, Howell and Evison, University of Oxford, 2024