Or search by topic
Published 2008 Revised 2009
Although the first set of rules for dealing with negative
numbers was stated in the 7th century by the Indian mathematician
Brahmagupta, it is surprising that in 1758 the British
mathematician Francis Maseres was claiming 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" .
Maseres and his contemporary, William Friend took the view
that negative numbers did not exist. However, other mathematicians
around the same time had decided that negative numbers could be
used as long as they had been eliminated during the calculations
where they appeared.

In 200 BCE the Chinese number rod system (see note1 below) 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. 
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.
