<P> For a long time, negative solutions to problems were considered "false". In Hellenistic Egypt, the Greek mathematician Diophantus in the 3rd century AD referred to an equation that was equivalent to 4x + 20 = 4 (which has a negative solution) in Arithmetica, saying that the equation was absurd . </P> <P> 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--AD 220), but may well contain much older material . The mathematician Liu Hui (c. 3rd century) established rules for the addition and subtraction of negative numbers . The historian Jean - Claude Martzloff theorized that the importance of duality in Chinese natural philosophy made it easier for the Chinese to accept the idea of negative numbers . The Chinese were able to solve simultaneous equations involving negative numbers . The Nine Chapters used red counting rods to denote positive coefficients and black rods for negative . 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 . Liu Hui writes: </P> <P> Now there are two opposite kinds of counting rods for gains and losses, let them be called positive and negative . Red counting rods are positive, black counting rods are negative . </P> <P> The ancient Indian Bakhshali Manuscript carried out calculations with negative numbers, using "+" as a negative sign . The date of the manuscript is uncertain . LV Gurjar dates it no later than the 4th century, Hoernle dates it between the third and fourth centuries, Ayyangar and Pingree dates it to the 8th or 9th centuries, and George Gheverghese Joseph dates it to about AD 400 and no later than the early 7th century, </P>

When do we use negative numbers in real life