Complementing this situation, there are also cases where a proof hinges on a critical corollary or theorem where "no importance, I made another one!" did not or

Complementing this situation, there are also cases where a proof hinges on a critical corollary or theorem where "no importance, I made another one!" did not or does not come as easily. One recent example is Corollary 3.12 in Mochizuki's series of papers on Inter-universal Teichmüller Theory. This single corollary is the main topic of "Why abc is is still a conjecture" by Peter Scholze and Jakob Stix: http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf Quoting from the paper: "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." An argument can be made that hence, this is no proof at all, and indeed that is the conclusion of the paper. However, mistakes in other suggested proofs were also found in the past, and they could sometimes be salvaged with significant new insights and additional work. An example for this is Andrew Wiles's proof of Fermat's Last Theorem. Quoting from https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_...: Wiles states that on the morning of 19 September 1994, he was on the verge of giving up and was almost resigned to accepting that he had failed, and to publishing his work so that others could build on it and find the error. He states that he was having a final look to try and understand the fundamental reasons why his approach could not be made to work, when he had a sudden insight that ...