sourced story
628 CEReputable source · 2 sourcesWell documented

Brahmagupta Defines Zero as a Number

An Indian astronomer gives rules for arithmetic with zero, turning a placeholder into a full member of the number system

On the timeline · around 628 CE · Medieval and Islamic MathematicsGreek and Hellenistic MathematicsMedieval and Islamic MathematicsBrahmagupta Defines Zero as a Number300 CE400 CE500 CE600 CE700 CE800 CE900 CE

Quick facts

Brahmagupta's dates
598 CE to 670 CE
Treatise and date
Brahmasphutasiddhanta, 628 CE
Base of operations
Ujjain astronomical observatory, India
Older placeholder zero (disputed)
Bakhshali manuscript, radiocarbon dated to 3rd-4th century CE

What happened

Zero had two distinct roles to fill: as an empty-place indicator in a positional number system, a use with earlier precedents, and as a number in its own right that could be added, subtracted, and multiplied like any other. Brahmagupta, born in 598 CE and head of the astronomical observatory at Ujjain, then India's foremost mathematical center, closed the second gap in his 628 CE treatise the Brahmasphutasiddhanta. He defined zero as the result of subtracting a number from itself and gave explicit rules: when zero is added to a number or subtracted from a number, the number remains unchanged, and a number multiplied by zero becomes zero. He phrased other rules in terms of fortunes, positive numbers, and debts, negative numbers, stating that a debt minus zero is a debt and a fortune minus zero is a fortune. He also attempted rules for dividing by zero, though this was the one operation his framework could not correctly resolve.

Why it matters

Brahmagupta's rules mark the first time zero is treated as a full number with defined arithmetic behavior rather than only a placeholder marking an empty column, a conceptual step that later Islamic and European mathematics would inherit largely intact. Radiocarbon dating published by the University of Oxford's Bodleian Libraries in 2017 has shown the zero placeholder symbol itself, in the Bakhshali manuscript, may go back further still, to the 3rd or 4th century CE, though that earlier zero functioned only as a placeholder and not as a number that could be calculated with.

How we know

The Brahmasphutasiddhanta survives as a complete Sanskrit astronomical and mathematical text, and its date and authorship are corroborated by later Indian and Islamic scholars who cited and translated Brahmagupta's work; the Bakhshali manuscript's age has been independently tested through radiocarbon analysis of its birch-bark folios.

Sources

See something wrong? . Corrections with a source get fixed fastest.

Part of a timelineHistory of Mathematics26 events · A number system built for taxes, a theorem older than the man it's named for, a proof too long for a margin, and an infinity too big to countView all →