*A debt minus zero is a debt.*

*A fortune minus zero is a fortune.*

*Zero minus zero is a zero.*

*A debt subtracted from zero is a fortune.*

*A fortune subtracted from zero is a debt.*

*The product of zero multiplied by a debt or fortune is zero.*

*The product of zero multiplied by zero is zero.*

*The product or quotient of two fortunes is one fortune.*

*The product or quotient of two debts is one fortune.*

*The product or quotient of a debt and a fortune is a debt.*

*The product or quotient of a fortune and a debt is a debt.*

The above is from the works of the Indian mathematician Brahmagupta (598-670)

Six standard forms for linear or quadratic equations were offered by Al-Khwarizmi (c. 780–c. 850 CE). He generated solutions using geometrical diagrams and algebraic techniques. Acknowledging that he took ideas for his algebraic methods from Brahmagupta, he was content with the concept of negative numbers. But he was convinced by his mathematical models—which were based on the research of Greek mathematicians—that negative outcome had no significance (how can a square be negative?). Al-Khwarizmi depicts negative amounts as debts in a different treatise on inheritance rules.

In the 10th century Abul -Wafa (940-998 CE) used negative numbers to represent a debt in his work on ‘what is necessary from the science of arithmetic for scribes and businessmen’?. This seems to be the only place where negative numbers have been found in medieval Arabic mathematics. Abul-Wafa gives a general rule and gives a special case where subtraction of 5 from 3 gives a “debt” of 2. He then multiples this by 10 to obtain a “debt” of 20, which when added to a ‘fortune’ of 35 gives 15.

It is interesting that the word debt is used to convey idea of negative numbers from the early stages when such numbers was used.

However, there were reference to negative numbers far earlier. In 200 BCE the Chinese number rod system represented positive numbers in Red and Negative numbers in black. An article describing this system can be found here. These were used for commercial and tax calculations where the black cancelled out the red. The amount sold was positive (because of receiving money) and the amount spent in purchasing something was negative (because of paying out); so, a money balance was positive, and a deficit negative.

The idea of negative numbers had always been difficult to understand. The idea of subtracting something out of nothing or taking out something larger from something smaller is counter intuitive. It is a difficult to wrap our heads around it when the larger gets bigger and the mathematics goes beyond simple arithmetic.

The world monetary system functions the way it does based on the idea of subtracting something out of nothing.

Here is a simple example. You apply for a loan to purchase a car. Once your loan is approved, your car dealer sees the amount in his account. And you start servicing the loan. This loan amount appeared from thin air. The bank doesn’t have to have the amount it loaned out to you (they can do this – and this why we all should own a bank) but you need to have the money to your monthly payment. You see, the bank had just done a magic trick. Not only it created money out of nothing, but you now have to pay for that and a little extra called interest. Subtracting something out of nothing, a debt. Neat trick, yes?

This is just a little something to add to your knowledge, that is if you don’t already know this.