Early History.
The history of negative numbers shows that they have not been widely accepted for long. Only positive rationals interested Euclid (300 BCE) as solutions.
They appeared in China during the Han dynasty (202 BCE to 220 CE) in the Nine Chapters on the Mathematical Art. They had a system of rods of different colours for positive and negative.
Diophantus lived circa 214 CE and although he did not consider negatives to be numbers, he used subtraction in his workings and did accept that multiplying two negative numbers together would yield a positive number. However in his Greek language work on mathematics, Arithmetica, he wrote that the equation 4 = 4x + 20 was absurd because he could not accept negative numbers.
India, Persia and Negative Numbers.
Brahmagupta was an Indian mathematician who lived between 598 and 668 CE. He wrote his work on mathematics, Brāhmasphuṭasiddhānta, in verse in the Sanskrit language and did not use any mathematical notation. In his work, he describes positives as ‘fortunes’ and negatives as ‘debt’. He said in one verse that “a fortune subtracted from zero is a debt”. He wrote in another that the “The sum of positive and negative, if they are equal, is zero”. It is quite inspirational that someone could write about mathematics in verse.
Muḥammad ibn Mūsā al-Khwārizmī (c.780 – c850), from Persia which is now Iran, wrote ‘The Compendious Book on the Calculation of Al-jabr and Muqabala’ in arabic. The word ‘Algebra’ comes from the Arabic word ‘al-jabr’, which translates as ‘reunion of broken parts’ or ‘bone setting’. The word muqabala translates as ‘balancing’ and together the words can be better understood as ‘restoring and balancing’. He classified quadratic equations into six classes that allowed him to avoid negative coefficients.
Another Persian, Omar Khayyam (1048-1141) wrote his work ‘On the Proofs of the Problems of Algebra and Muqabala’ in Persian. He deals with cubic equations in his work and only looks at positive solutions.
So, there was not much support for negative numbers at this stage of history. Part 2 outlines the development of negative numbers during the second millennium.
