I'm looking for an example of the following situation:

  • Proof of some statement that was widely accepted for a noticeable amount of time (say, at least 10 years).
  • The proof was later refuted (i.e. the proof turned out to be incorrect), and the refutation was similarly widely accepted.
  • The error in the proof was due to incorrect reasoning, not due to wrong assumptions. E.g. I'm not interested in a case when some proof relied on the laws of Newton's mechanics but is incorrect in the settings of special relativity.
  • This happened in the last, say, 150 years.

I'm also not interested in the case when some result had an error that was quickly found and fixed in the follow-up work.

Somewhat related to Is there a single example of an outsider considered a "crank" publishing a ground-breaking result that was found to be correct (in the last 30 years)?

@CrimsonDark gives a good reference to a question with some good (as far as I can tell) examples: https://math.stackexchange.com/questions/139503/in-the-history-of-mathematics-has-there-ever-been-a-mistake

  • 2
    I suggest to ask this question on another SE, for example, History of Science & Mathematics, Maths Over Flow.
    – Neuchâtel
    Commented Dec 20, 2022 at 16:45
  • @Pikachu피카츄, right when I was going to delete the question, it was answered. What should I do?
    – Dmitry
    Commented Dec 20, 2022 at 16:53
  • 2
    Have a look at math.stackexchange.com/questions/139503/… Commented Dec 20, 2022 at 16:53
  • 1
    @Dmitry Then just leave it here.
    – Neuchâtel
    Commented Dec 20, 2022 at 16:54
  • 2
    Looks like a duplicate of mathoverflow.net/q/35468/78525
    – Dan Romik
    Commented Dec 21, 2022 at 0:22

1 Answer 1


I don't have an example at hand, so this isn't technically an answer, but yes it happens in math. I once worked in a field (classical analysis) that had the reputation of all proofs being wrong, but the results still accepted. Lots of proofs in analysis are of the ε, δ variety as is, say, the definition of the derivative. The problem is that such proofs can be layered with several levels. Once you go beyond about three levels the proofs are devilishly difficult to keep straight in your mind and you can get it wrong. (See the magic number seven, plus or minus two for a possible underlying reason.)

This has been done by celebrated mathematicians. A vaguely remembered example was from around the 1920's, corrected maybe by the 70's.

  • Thank you for the answer. "reputation of all proofs being wrong, but the results still accepted" sounds very weird to me (and, in particular, probably means that "accepted" means something different), but I guess it makes more sense to people in the field. It would be great if you could remember the example.
    – Dmitry
    Commented Dec 20, 2022 at 17:01
  • I think that the reason was the people believed that the errors were "merely" technical and "obviously" overcome-able. In many cases that was true, but who can say. The original IIRC was (perhaps) published in Analytic Functions by Zygmund and Saks. Too long ago to remember, but I was the one that found the error. Both of those folks were giants.
    – Buffy
    Commented Dec 20, 2022 at 17:11
  • Note that the theorem was older than the book and (faulty memory here) was by another person.
    – Buffy
    Commented Dec 20, 2022 at 17:16

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