Definition:Negative/Number/Historical Note

Historical Note on Negative Number
The idea of a negative number was the cause of considerable philosophical difficulty.

Negative numbers made no sense to the ancient Greeks. A number expressed a magnitude and that was all.

recognised that certain equations yielded both a positive root and a negative root, but rejected the negative root as nonsensical. If an equation had no positive root, for example $x + 10 = 5$, then it was not a proper equation.

The early Hindu mathematicians recognised the existence of negative roots, but were still wary of them. As put it:
 * The second value is in this case not to be taken, for it is inadequate; people do not approve of negative roots.

The Chinese were using negative numbers by the $12$th century as a matter of course. However, they still did not recognise negative roots.

The general acceptance of negative numbers in calculations seems in fact to have started with merchants and accountants. The symbols $+$ and $-$ originated in $15$th century German warehouses for indicating whether a container was over or underweight.

referred to negative numbers as absurd or fictitious.

It was who was one of the first to accept negative numbers, and he even went as far as considering their square roots in his.

However, as late as the end of the $18$th century,, together with , published between them a number of works, most notably in $1796$, which rejected the concept of negative numbers as invalid.