Negative Number - History

History

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 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. 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, the Greek mathematician 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. Consistent and correct rules for working with these numbers were formulated. The diffusion of this concept led the Arab intermediaries to pass it to Europe.

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

During the 7th century AD, negative numbers were used in India to represent debts. The Indian mathematician Brahmagupta, in Brahma-Sphuta-Siddhanta (written in A.D. 628), discussed the use of negative numbers to produce the general form quadratic formula that remains in use today. He also found negative solutions of quadratic equations and gave rules regarding operations involving negative numbers and zero, such as "A debt cut off from nothingness becomes a credit; a credit cut off from nothingness becomes a debt. " He called positive numbers "fortunes," zero "a cipher," and negative numbers "debts."

During the 8th century AD, the Islamic world learned about negative numbers from Arabic translations of Brahmagupta's works, and by the 10th century Islamic mathematicians were using negative numbers for debts. The earliest known Islamic text that uses negative numbers is A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen by Abū al-Wafā' al-Būzjānī.

In the 12th century AD in India, Bhāskara II also gave negative roots for quadratic equations but rejected them because they were inappropriate in the context of the problem. He stated that a negative value is "in this case not to be taken, for it is inadequate; people do not approve of negative roots."

Knowledge of negative numbers eventually reached Europe through Latin translations of Arabic and Indian works.

European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted as debits (chapter 13 of Liber Abaci, AD 1202) and later as losses (in Flos).

In the 15th century, Nicolas Chuquet, a Frenchman, used negative numbers as exponents and referred to them as “absurd numbers.”

In A.D. 1759, Francis Maseres, an English mathematician, wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". He came to the conclusion that negative numbers were nonsensical.

In the 18th century it was common practice to ignore any negative results derived from equations, on the assumption that they were meaningless.