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Kepler's conjecture concerning sphere packing is famous for having a proof, where referees got persuaded only after formal verification. Are there any other proofs originally claimed in full on paper, which went through similar process from doubt to acceptance, not necessarily through formal verification, possibly just through time?

On the other hand Mochizuki's proof of abc conjecture seems to come up as an example of a proof too frustrating to verify or completely refute. Are there any other ongoing examples where the work is too complex and with doubted results, but neither finally disproved or proved? I consider Mochizuki's work exemplary as compared to other false/too complex proofs, in that there is ongoing work and relatively recent seminars dedicated to understanding the techniques. Another example of this phenomena might be Classification of finite simple groups, many people still prefer proofs of theorems not assuming CFSG, because the full proof is too complex. I haven't encountered another theorem used widely with this attitude towards the result.

Ilk
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    The most famous conjectures attract (probably due to the absurd high rewards) tons of flawed proofs or (rarely) disproofs. The abc-conjecture seems to be still open. I do not trust a mathematician that is apparently unable to explain his proof. I do not remember exactly Kepler's conjecture. Is it about packing ? Wasn't there a longstanding refuted conjecture in this topic as well ? – Peter Mar 10 '20 at 21:32
  • @Peter, all you have to do is google "Kepler's conjecture". – TonyK Mar 10 '20 at 21:41
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    @TonyK Maybe, but a little context in questions does not hurt the author. I nervertheless upvoted. – Peter Mar 10 '20 at 21:42
  • Another question concerning this topic just came in my mind : Which was the most surprising proven result in mathematics ? I mean a conjecture that was strong believed to be true, but turned out to be false or vice versa. The infinite many sign-changes of $\ \pi(x)-Li(x)\ $ is a striking example. – Peter Mar 10 '20 at 21:45
  • I agree with your points I am just curious about other examples of these 2 phenomena. I am not aware of a proof in case of Kelvin's conjecture on shaky standing for longer time, I think that's what you are referring to? If you have other suggestions for improvement, feel free to comment them, or suggest edits. – Ilk Mar 10 '20 at 21:46
  • @TonyK Maybe, in the case of the Kepler-conjecture googling would help because possibly there is only one (I don't know whether it is only one). In the case of, lets say, Erdoes's conjecture this would not help much since there are many. Anyway, a rough description of the conjecture is exactly that context that questions should have on this site. – Peter Mar 10 '20 at 21:58
  • @Nift Don't misunderstand my comment. The question is interesting. (+1 as already mentioned) – Peter Mar 10 '20 at 22:00
  • @Peter All good, I just want to make the question better :) – Ilk Mar 10 '20 at 22:01
  • @Peter: it takes longer to type "I do not remember exactly Kepler's conjecture. Is it about packing ?" than it does to google "Kepler's conjecture" :-) – TonyK Mar 10 '20 at 22:01
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    @TonyK Maybe displaying the sites. Depending on how good you want to understand the conjecture , googling might take a bit longer. Anyway, one of the spirits of this site is context. – Peter Mar 10 '20 at 22:06
  • @Tony it takes longer for a hundred users to google "Kepler's conjecture" than it takes for one user to type "I do not remember...." – Gerry Myerson Mar 10 '20 at 22:55
  • Perleman's proof of the the Poincare conjecture was a hard sell for quite some time. – lulu Mar 10 '20 at 23:10
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    @Peter non-euclidean geometry. The parallel postulate was believed a theorem for some 2000 years. Number theory being incomplete (Gödel). – vonbrand Mar 10 '20 at 23:54

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