The most absurd assertion on the planet is frequently seen, for example here:
Stop fucking saying that. Yes, dammit, one CAN prove a negative. And sometimes, it’s trivially easy. For example, one can prove that an equilateral triangle has no right angles. Or, one can prove that 1 + 1 is not equal to 3. In fact, one of the most common methods of proof, reductio ad absurdum, requires proving the negative of your premise.
How the stupid assertion got started is unclear. As best I can tell, it originated on Usenet sometime in the 90s. Certainly, it appears nowhere in classical or modern logic or philosophy. I’ve never even heard of a logical system in which a negative cannot be proved, and there are a boatload of weird-ass logical systems out there.
If one cannot prove a negative, then one cannot prove that one cannot prove a negative, so why assert it? Here’s an excellent article on the topic from Infidels Dot Org.
So please, in the interest of Straight Dope’s mission to stamp out ignorance, stop spreading that ridiculous myth.
Thank you.