Example of widely accepted and later refuted proof [closed]

Question

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

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.