Have there been any examples in the past where a large proof is claimed but nobody takes the time to check and that has been proved/disproved after a long time? I am not interested in proofs that were never taken seriously because they were unreadable (not even wrong).
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3$\begingroup$ Your description of the Mochizuki situation seems inaccurate. Scholze and Stix found an alleged flaw in 2018, but Mochizuki disagreed. Neither side has changed their mind since. As far as I know most mathematicians with an opinion think Scholze and Stix are right. That a non-mathematician is now offering $1 million, awarded at his sole discretion, for something that most mathematicians think was accomplished years ago suggests that it's not a good-faith offer, or at least not a well-informed one. $\endgroup$– benrgSep 10 at 23:11
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2$\begingroup$ Further to benrg's comment, refer to the paper "Why abc is still a conjecture" [PDF]: "We, the authors of this note, came to the conclusion that there is no proof. We are going to explain where, in our opinion, the suggested proof has a problem, a problem so severe that in our opinion small modifications will not rescue the proof strategy. " $\endgroup$– AlexisSep 11 at 0:56
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1$\begingroup$ The latest on this is here: mathoverflow.net/questions/435110/… $\endgroup$– Mikhail KatzSep 11 at 12:51
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2$\begingroup$ The problem is not so much the length of the purported proof as the existence of a conceptual gap that has not been addressed. $\endgroup$– Mikhail KatzSep 11 at 12:53
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2$\begingroup$ I am not sure how long a time you have in mind, but an error in Kempe's verbose "proof" of the 4-color theorem went unnoticed for 11 years, see Bray. Classification of finite simple groups had tens of thousands of pages by 100 authors with gaps found and filled over half a century. $\endgroup$– ConifoldSep 14 at 9:17
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Maybe classification of finite simple groups qualifies ("The proof consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004.")?
1983 Gorenstein announces the proof of the classification is complete, somewhat prematurely as the proof of the quasithin case was incomplete.
2004 Aschbacher and Smith publish their work on quasithin groups (which are mostly groups of Lie type of rank at most 2 over fields of even characteristic), filling the last gap in the classification known at that time.
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1$\begingroup$ Personally, I don't understand in what sense that theorem qualifies as a "proof that nobody wants to check", seeing as it's been contiuously revised since 1985. $\endgroup$– Gae. S.Sep 21 at 14:13
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$\begingroup$ I agree with @Gae.S. If several hundred articles exist (in peer-reviewed journals), each covering a part of the proof, it can hardly be completely unchecked. $\endgroup$– mdeweySep 21 at 15:36
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$\begingroup$ @mdewey But also there's a group of people who have been writing it down for 30 years with the specific purpose of having it all in one place. $\endgroup$– Gae. S.Sep 21 at 17:21
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$\begingroup$ @Gae.S. : Maybe the theorem does not qualify as a "proof that nobody wants to check", as in OP's title, but it probably qualifies as "a large proof is claimed but nobody takes the time to check and that has been proved/disproved after a long time", as in OP's body. A more serious drawback of my answer is that the theorem was mentioned previously in Conifold's comment. I am sorry I missed it. $\endgroup$ Sep 22 at 7:35
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$\begingroup$ @akhmeteli Personally I don't believe that comments should have any claim to priority, since by design they are temporary and they need not abide to the same standards of quality as answers do. $\endgroup$– Gae. S.Sep 23 at 11:28