"You cannot prove a negative" basically means that you cannot prove that some claim or statement is, was, and always will be false (without perfect knowledge of

"You cannot prove a negative" basically means that you cannot prove that some claim or statement is, was, and always will be false (without perfect knowledge of the past, present, and future). That parenthetical is an important and almost always unstated axiom. The general inability to prove a false statement does not mean you cannot prove that the answer to some equation is a number below zero. I am not really aware of the phrase being used in the context of math, but rather more often with examinations or experiments that are susceptible to evidence. To be sure, "you cannot prove a negative" is itself unproven. It more a rule of thumb to remind you not to assume that though some statement is false now that it always was false and always will be false. It's not perfect, but it's also not a law of logic or anything. It's just a guideline.