Negative numbers
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Chinese mathematicians used negative numbers in calculations before India. Brahmagupta (628 CE) gave the first full set of rules, including that a debt times a debt is a fortune.
Earlier elsewhereMathematics & astronomy
Indian claim
Negative numbers were first used and understood in India by Brahmagupta.
Evidence for the Indian claim
- Brahmagupta (628 CE) calls positive numbers fortunes (dhana) and negative numbers debts (rina).
- He gives rules for adding, subtracting, multiplying and dividing them, including with zero: for example, the product of two debts is a fortune.
- He used them to give a single rule for quadratic equations.
Commonly credited to
The Chinese Nine Chapters on the Mathematical Art used red and black counting rods for positive and negative numbers several centuries earlier.
Evidence for the other claim
- The Nine Chapters (compiled by about the 1st century CE, with Liu Hui's commentary of 263 CE) use negative numbers in solving simultaneous equations, with rules for adding and subtracting them.
- In Europe, Diophantus called negative answers absurd, and negatives were widely accepted only in the 17th century.
What historians and scientists say
China used negative numbers first. Brahmagupta's rules were the first complete arithmetic of negative numbers and zero, a major step that Europe took much later.