Zero as a number (India)
Cero como número y símbolo (India)
- Date
- 628 · confidence medium
- Place
- Bhinmal, Rajasthan (Brahmagupta); Gwalior, Madhya Pradesh, India
- Credited to
- Indian mathematicians: positional system with zero in the Lokavibhaga (458); rules for zero as a number in Brahmagupta's Brahmasphutasiddhanta (628); zero written in the Gwalior inscription (876)
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What it is
A sign (a dot, later a circle) marking the absence of quantity in a position, treated as a number that can be operated on. It closes the decimal positional system and makes universal written calculation possible.
The Maya used an independent positional zero (c. 36 BCE) and Babylon a placeholder marker; only India turned it into an operative number. The radiocarbon dating of the Bakhshali manuscript (3rd-4th century) is disputed. Merged with 'Zero as a number and arithmetic rules (Brahmagupta)', 'Zero as a number and the rules of negative numbers' (duplicate, 23-09-2026).
What it led to
- Simple written arithmetic that replaced the abacus and Roman numerals
- Algebra with negative solutions and equations set equal to zero
- Transmission to the Islamic world (al-Khwarizmi) and Europe (Fibonacci)
- The conceptual basis of modern mathematics and digital computation
- adoption of the Indian system in Baghdad (translation of the Sindhind, 773) and the work of al-Khwarizmi
- Hindu-Arabic numerals and zero in Europe (Fibonacci)
- algebra of negatives and modern mathematics
- Arab algebra
- negative numbers in Europe (17th century)
- rings and fields
Built on
- Early counting board / abacusc. 2400 BCE
- Nine Chapters on the Mathematical Artc. 150 BCE - 100 CE
- Indian decimal place-value system and Aryabhata sine499
- Earth's daily rotation and shadow theory of eclipses (Aryabhata)499
- Babylonian positional zero
- Brahmi numerals
- Brahmi numerals
- Aryabhata (499)
- Babylonian zero as a placeholder
- The Nine Chapters (negative numbers)
Made possible
- Indian decimal place-value numeralsc. 450 CE
- Khmer inscription K-127 zero683
- Algebra and algorithm (al-Khwarizmi)c. 820
- Bakhshali square-root methodc. siglos VIII-XI
- Hindu-Arabic numerals in Europe976
- Al-Samaw'al's polynomial algebrac. 1144
- Zero and positional notation in Europe (Fibonacci)1202
- Brahmagupta's algebra
- Arabic numerals
- Algebra and algorithm (al-Khwarizmi)
- Hindu-Arabic numerals in Europe
- Zero and positional notation in Europe (Fibonacci)
- commercial arithmetic