In Nine Chapters on the Mathematical Art (Jiuzhang Suanshu),
negative numbers were used in the chapter on solving systems of simultaneous
equations. For instance, revenue numbers are considered positive, while expense
numbers are deemed negative; or surplus amounts are viewed as positive, while
deficit amounts are seen as negative. In a problem calculating grains, the
increased grains are considered positive, and the lost grains, negative.
At the time, calculation was done by the method of suan chou
(counting rods). Red rods were used to denote positive coefficients, and black
ones to denote negative ones. Or in another case, the normal position of
suan chou denoted positive, while an inclined position denoted
Rules for the calculation of signed numbers were also given in Jiuzhang
According to the book, the deduction (or subtraction) of two numbers with the
same sign (from another number) equals the deduction of the absolute values of
the two numbers, while the deduction of two numbers with different signs equals
the addition of the absolute values of the two numbers.
Also, a positive number subtracted from zero gives a negative number, whereas
a negative number subtracted from zero gives a positive number. Inversely, zero
plus a positive number is still a positive number, and zero plus a negative
number is still a negative number.
The addition of two numbers with different signs equals the deduction of
their absolute values, while the addition of two numbers with the same sign
equals the addition of their absolute values.
Jiuzhang Suanshu gave the most complete depiction on the rules for
adding and subtracting positive and negative numbers in the world until the 17th
In the thirteenth century, a diagonal stroke was drawn through the last
nonzero digit of a number to mark it as a negative number.
Negative numbers appeared very late in the West. Many noted mathematicians
did not admit negative numbers, because they consider zero as "nothing" and
could not understand that something could be even less than "nothing," and so
considered negative numbers "absurd." It was only in the 17th century when
Descartes invented the coordinate system, which gave a geometrical explanation
and an actual meaning for negative numbers, that negative numbers began to be
The introduction of negative numbers is an important contribution of Chinese
mathematicians to world mathematics. With the introduction of negative numbers,
the whole numbers and rational numbers became complete.