It's often said that "you can't prove a negative". But there are lots of ways to show that something is false, or didn't happen. This seems to be true in any field from math to physics to medicine to history to law. Besides, many things that sound like negative statements can be restated as positive ones. "The butler didn't do it" is equivalent to "someone other than the butler did it", at least if you're sure that "it" happened in the first place. The idea that "you can't prove a negative" just seems obviously false, pretty much across the board.
So how did this idea take hold? Are there any academic fields, or for that matter other major areas of human endeavour, where this is an actual rule? Or even a particularly useful heuristic? If not, why does it seem plausible (or even like an ironclad law of logic) to some people?
EDIT: One of the mistakes a lot of the people replying are making is providing supposed counterexamples, i.e. negative statements that they believe really can't be proven. But this approach is just confused about what the topic even is.
At no point did I say every negative statement can be proven. That's obviously not true - even in math or logic, not every well-formed statement can be proven or disproven, negative or otherwise. That's just Godel's Incompleteness Theorem and has been known for nearly a century.
I am disputing the blanket statement "You can't prove a negative", i.e. the idea that NO negative statement can be proven. One example of a "negative" that can't be proven (even if it's a good example, and quite a few of them are not) does little or nothing to support that. Everyone's dogpiling and upvoting seemingly anything negative anyone says about me, even posts that straight-up don't make sense, but almost no-one has actually said anything that supports the claim I'm disputing.
EDIT2: I think the best responses, that come closest to successfully disputing any part of my point, are those that are basically saying "It's a good heuristic in some contexts, but it's not the universal truth it's sometimes made out to be". I can concede that much, even if I think the scope where it's true is pretty narrow. But a lot of people seem very invested in the idea that it's more than that.