The example given by Wojowu in the comments seems worth posting as an answer.

In the NOVA special <a href="https://www.pbs.org/wgbh/nova/transcripts/2414proof.html">The Proof</a>, Ken Ribet says the following.

>I saw Barry Mazur on the campus, and I said, "Let's go for a cup of coffee." And we sat down for cappuccinos at this cafe, and I looked at Barry and I said, "You know, I'm trying to generalize what I've done so that we can prove the full strength of Serre's epsilon conjecture." And Barry looked at me and said, "But you've done it already. All you have to do is add on some extra $\Gamma_0(M)$ structure and run through your argument, and it still works, and that gives everything you need." And this had never occurred to me, as simple as it sounds. I looked at Barry, I looked at my cappuccino, I looked back at Barry, and I said, "My God. You're absolutely right."

He also talks about this story in [this Numberphile video](https://youtu.be/nUN4NDVIfVI?t=636).