Brahmagupta codifies zero and arithmetic of negatives (Brahmasphutasiddhanta)
- Date
- 628 CE
- Category
- Science, technology & invention
- Region
- South Asia (Bhillamala/Bhinmal, northwestern India)
- Era
- Post-Classical / Medieval
- Significance
In 628 CE the Indian mathematician and astronomer Brahmagupta completed the Brahmasphutasiddhanta ("Correctly Established Doctrine of Brahma") at Bhillamala (modern Bhinmal), then capital of the Gurjara realm in northwestern India.
The work gave the first systematic rules treating zero as a number in its own right, defining it as the result of subtracting a number from itself and stating that adding or subtracting zero leaves a quantity unchanged while multiplication by zero yields zero. Brahmagupta also laid out the arithmetic of positive and negative quantities, framed as "fortunes" and "debts," including the rule that the product of two negatives is positive. These operations were embedded in the decimal place-value system that India transmitted, via the Islamic world, to medieval Europe. Although his treatment of division by zero was flawed, the text is foundational to the formalisation of arithmetic and modern mathematics. It is distinct from the earlier dot-zero of the Bakhshali manuscript and Aryabhata's Aryabhatiya, marking the first place-value arithmetic to operate on zero and negatives as numbers.
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Empires active in 628 CE
- Tang Dynasty618 CE – 907 CE
- Sassanid Empire224 CE – 651 CE
- Byzantine Empire330 CE – 1453 CE
- Classic Maya Civilization250 CE – 900 CE
- Tibetan Empire618 CE – 842 CE
- Kingdom of Aksum100 CE – 940 CE
Related science, technology & invention events
- Construction of the Grand Canal under Emperor Yang605–609 CE
- First Islamic hospital (bimaristan) founded in Baghdadc. 805 CE
- Al-Khwarizmi composes Al-Jabr and founds algebrac. 820 CE
- The Diamond Sutra, the earliest dated printed book11 May 868 CE
- Ibn al-Haytham Completes the Book of Opticsc. 1021 CE
- Al-Zahrawi completes the Kitab al-Tasrif, foundational surgical encyclopediac. 1000 CE
Further reading
The wider story
A Little History of Science
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