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Negative numbers appear for the first time in history in the Nine Chapters on the Mathematical Art (Jiu zhang suan-shu), which in its present form dates from the period of the Han Dynasty (202 BC – 220 AD), but may well contain much older material.[1] The Nine Chapters used red counting rods to denote positive coefficients and black rods for negative.[2] (this system is the exact opposite of contemporary printing of positive and negative numbers in the fields of banking, accounting, and commerce, wherein red numbers denote negative values and black numbers signify positive values). The Chinese were also able to solve simultaneous equations involving negative numbers

For a long time, negative solutions to problems were considered "false". In Hellenistic Egypt, Diophantus in the third century A.D. referred to an equation that was equivalent to 4x + 20 = 0 (which has a negative solution) in Arithmetica, saying that the equation was absurd.

The use of negative numbers was known in early India, and their role in situations like mathematical problems of debt was understood.[3] Consistent and correct rules for working with these numbers were formulated.[4] The diffusion of this concept led the Arab intermediaries to pass it to Europe.[3]

The ancient Indian Bakhshali Manuscript, which Pearce Ian claimed was written some time between 200 B.C. and A.D. 300,[5] while George Gheverghese Joseph dates it to about 400 AD and Takao Hayashi to no later than the early 7th century, carried out calculations with negative numbers, using "+" as a negative sign.