>taking care to ensure that the experiments distinguish between the reality in which your theory holds, and the one where it doesn't. I get the impression that

>taking care to ensure that the experiments distinguish between the reality in which your theory holds, and the one where it doesn't. I get the impression that you're thinking of specific domains within science. Many theories are contextualized within something (e.g a theory of why there's lightning might be more domain specific than a theory of electromagnetism). I don't disagree that things are proved within mathematical systems and scientific claims / hypotheses are categorically different (and weaker, I suppose). But the author made a claim, discovered an error in their claim, and alerted the community to his mistake and signaled their intention to address it. That's not behavior that's exclusive to mathematics. Many scientists have made claims that they think the evidence supports, and then they realize that something wasn't correct, and they make the correction. Cartographers / mariners used to think that California was an island: https://en.wikipedia.org/wiki/Island_of_California https://en.wikipedia.org/wiki/Island_of_California They had solid evidence to think that's the case but then eventually they realized the mistake and they've corrected it.