When I write someone to tell them there’s a mistake in their paper, I usually get one of these five reactions, ordered from best to worst:
- “It’s not a mistake.” (and they’re right)
- “Indeed, that’s wrong, I’ll correct it.”
- “It’s not a mistake.” (and they’re wrong)
- “Indeed, that’s wrong, but I’ll not correct it.”
- “Indeed, that’s wrong, people already told me about it, but I’ll not correct it.”
The first two need no explanation. The third one is of course frustrating to hear, but sometimes people will just disagree about what is a mistake or not, and we need to live and let live. The fourth one is really annoying. Your paper is wrong, just fix it, how can you leave something wrong on the arXiv? It’s so easy to fix! But maybe it really doesn’t make a difference, perhaps I’m the only one that even read that part of the paper and got sidetracked by it. But the fifth one really drives me crazy: if several people told you about the mistake it shows that it does matter, it is actually causing problems.
Anyway, I’m ranting about this because I’ve recently updated several of my papers on the arXiv to fix some mistakes. Maybe all my papers are wrong, but at least I correct them when I’m told about the problem. I even get happy about it, it’s a proof that somebody actually reads them. And when the mistake is in Appendix C, wow, respect, you need some determination to reach all the way down there.
Luckily in all the cases the mistakes were only in the proofs, and didn’t change any of the actual results of the papers. In two of the cases, arXiv:1401.8127 and arXiv:1611.08535, it’s easy to understand why: we just had written down the result in a particular way in the first draft, then decided to change the presentation for clarity, did a sloppy job in the rewriting, and ended up with some inconsistent equations. Another case, arXiv:1706.09854, it’s a bit mysterious: we had a completely wrong derivation leading up to a correct quantum circuit. I guess what happened is that we had found the quantum circuit in a different way, and afterwards thought about a way to derive it that didn’t involve black magic, because you really can’t write that you got the answer by sacrificing a black chicken for Exu at some crossroads. We can’t remember what was the original derivation, if it ever existed, but now we managed to find another derivation without black magic that does work.
The last case, arXiv:1903.10526, was really just blind luck. I really had the wrong thing in mind when deriving the result, which does follow from the wrong argument. It’s just that, by chance, it was correct. Zombie Schrödinger guided my hands on this one.