Negation in Mathematics

-1*-1 = 1  Right? I don't think so!

Why does -1*-1 = 1?  I have searched and searched the internet for an answer, but nothing has come up with a satisfactory answer; they're all based on how English operates or they just say "math will break without it."  Why would math break without it?

I think it is just based on English, or to sum it up, a linguistic translation into a mathematical operation.

Negation in math fails, particularly in economics.  Let us say I owe a company $100 so my current balance would be $-100.  If I tell them I'll pay them $-100, would that mean that they would pay me $-100?  I think not; I would still owe them $100.  Another example would be in electronics; a negative charge with a negative charge just repels each other, it doesn't combine into a positive charge.

A mathematical translation from a linguistic operation indeed.