Two things called zero
“Who invented zero?” has no single answer because the question hides two different inventions. The first is a placeholder: a mark that says “this column is empty”, so that a positional notation can tell 25 from 205 from 250. The second is zero as a number: a quantity in its own right, which you can add to, subtract from, and multiply by, and which obeys stated arithmetical rules.
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These are genuinely separate achievements, and they appear centuries and continents apart. A culture can have the first without the second for a very long time. Most of the confusion in popular accounts comes from treating one claim as if it settled the other.
Graded by that distinction, the record is unusually clean: the placeholder is attested early in at least two unrelated civilisations, while zero-as-number has a single, datable, textual first appearance.
The Babylonian placeholder
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Babylonian scribes wrote in base 60 from the early second millennium BCE, at first leaving a blank space where a sexagesimal “digit” was empty. By the Seleucid period (from roughly the third century BCE) they used a definite sign — a pair of slanted wedges — to mark the empty place.
Two limits matter. The sign was used medially, between digits, and rarely at the end of a number, so 2 and 120 still had to be told apart from context. And it was never treated as a quantity: no Babylonian text adds to it or computes with it. It is a notation device, not a number. That is exactly the first invention and not the second.
The Maya placeholder
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Mesoamerican scribes independently developed a positional system — vigesimal, with one irregular place for the calendar — and a shell glyph to mark an empty position. It is securely attested in Long Count dates by the first century BCE, and the system is well understood because the Long Count can be correlated precisely with the Western calendar.
As in Babylon, this is a placeholder embedded in a counting notation, not a number manipulated in abstract arithmetic. Two civilisations with no contact reached the same device for the same reason: a place-value system has to be able to say that a place is empty. The Maya case is treated more fully under Maya numerics.
Brahmagupta makes zero a number
The decisive step is Indian and it is dated. In 628 CE the astronomer Brahmagupta completed the Brāhmasphuṭasiddhānta, which treats śūnya (“emptiness”) as a number alongside positive quantities (“fortunes”) and negative ones (“debts”), and states rules for operating with it.
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Brahmagupta gives, correctly: a number plus zero is unchanged; a number minus itself is zero; zero multiplied by anything is zero; and he handles signed arithmetic (a debt minus zero is a debt, and so on). This is the first known text anywhere to define zero as a number and legislate its arithmetic, rather than merely use a placeholder.
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His division rules are where he falls short by modern standards. He states that zero divided by zero is zero — which is wrong — and leaves a nonzero number divided by zero essentially undefined, writing it as a fraction with zero denominator without resolving it. Bhāskara II (twelfth century) later proposed treating n/0 as an infinite quantity. The point is graded disputed only in the sense that Brahmagupta’s own answer is defective; that the text contains these rules is not in doubt.
Notice what has changed. The Babylonian and Maya marks answer the scribe’s question “how do I write an empty column?” Brahmagupta answers the mathematician’s question “what happens when I calculate with nothing?” The second question is the one that turns zero into a number, and India is where it is first asked in writing.
The Bakhshali dot and its date
The Bakhshali manuscript — a birch-bark mathematical text found in 1881 near the village of Bakhshali, in the Peshawar region — uses a dot (bindu) as a zero symbol. In 2017 the Bodleian Library in Oxford radiocarbon-dated three of its folios and announced that the earliest contained “the oldest recorded origin of the zero symbol”, placing it in the third to fourth century CE.
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That the manuscript uses a dot for zero is not in question, and the radiocarbon measurements themselves are a laboratory fact.
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The headline date is disputed. The three dated folios returned three widely separated ranges — roughly 224–383 CE, 680–779 CE and 885–993 CE — yet the manuscript is, by its content and script, a single coherent work. A codex cannot have been written across three separate centuries, so dating the whole text, and the zero in it, to the earliest sample is not justified by the evidence. Plofker, Keller, Hayashi, Montelle and Wujastyk (2017) argued that the manuscript’s mathematical content and palaeography point instead to a composition several centuries later than the Bodleian’s announced date.
This is a useful case precisely because the laboratory result and the historical inference pull apart. The carbon dates are real; the claim “the world’s oldest zero” is an interpretation stacked on top of them, and it is the interpretation that scholarship contests. The securely dated first appearance of zero-as-a-number remains Brahmagupta’s text of 628 CE.
How the Indian zero reached the world
The transmission from this point is well documented. Indian decimal arithmetic, zero included, was taken up by mathematicians writing in Arabic — al-Khwārizmī in the ninth century among them — and from the Islamic world it entered Latin Europe, most influentially through Leonardo of Pisa’s Liber Abaci (1202). The English “zero” and “cipher” both descend from Arabic ṣifr, itself a translation of Sanskrit śūnya.
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The word carries its own history: a single Sanskrit term for “empty” travelled, in translation, across three language families to become the name of the number on which modern positional arithmetic depends. The route, unlike many cross-cultural claims on this site, has named texts and datable steps at every stage.
Sources
The works below are where each claim on this page can be checked. Primary texts are listed first, then the secondary scholarship.
- Brahmagupta, Brāhmasphuṭasiddhānta (628 CE), chapter on arithmetic with zero and signed quantities — the primary text.
- The Bakhshali manuscript, Bodleian Library, Oxford (MS. Sansk. d. 14); edited by Takao Hayashi, The Bakhshālī Manuscript: An Ancient Indian Mathematical Treatise (Groningen, 1995).
- Kim Plofker, Agathe Keller, Takao Hayashi, Clemency Montelle and Dominik Wujastyk, “The Bakhshālī Manuscript: A Response to the Bodleian Library’s Radiocarbon Dating”, History of Science in South Asia 5.1 (2017) — the critique of the 2017 dating.
- Kim Plofker, Mathematics in India (Princeton University Press, 2009).
- Robert Kaplan, The Nothing That Is: A Natural History of Zero (Oxford University Press, 1999).
- Charles Seife, Zero: The Biography of a Dangerous Idea (Viking, 2000).
Numeral Systems
Positional notation across traditions — the setting in which a placeholder becomes necessary.
Calendrical Mathematics
The Maya Long Count, where the placeholder zero does its work.
Maya Numerics
The shell glyph and the vigesimal count in detail.
Numerical Architecture
How written systems, not buildings, carry the best-evidenced number work.
Cite this page
Formatted references for this page. The evidence grade is part of the claim — when quoting a graded statement, carry the grade with it.