(I'm a math PhD student)
I'm writing a paper and part of my work relies on an old result of my advisor.
Recently, I started to become concerned that the old result does not have a proof (only a sketch) and I have a hunch that the proof is considerably harder (or possibly just much trickier) than the sketch makes it look. (It's possible I'm wrong; it concerns an area that I'm more of a novice in. However, I know enough that I couldn't cite this result without at least reading the sketch.)
Not only that, there are certain questions I have not been able to address as it pertains to my results, and the more I have thought about the missing proof of the old result, the more confident I have become that those questions could be addressed if I knew the missing proof. Therefore, not only does some of my work rely on this old result, but I may be able to substantially improve it if I figure out the old one. (To put it differently, in my own brain at least, the old result is an important open question.)
Further (and, ironically, this was brought to my attention by my advisor), there is a rather big theorem in our research area that relies on the old result. It's troubling to me that I don't know how to prove the big theorem without it, and it could be an issue for the larger community if, as I suspect is possible, no one knows how to fill out the sketch in the original paper. It may be that this is simply an open problem that has been overlooked.
I am discussing this with my advisor and I'm concerned that he won't be willing to show me how to fix the sketch or to make time for us to come up with our own proof. (We discussed it previously, before I had understood its importance, and his explanation followed the sketch in the paper. It looks possible that my advisor and his coauthor overlooked the difficulty in turning the sketch into a proof.)
What's worse is my advisor is starting to get a bit defensive about it (or that's my impression). I don't doubt that he will eventually hear my concerns, I'm simply worried that he will want to move on or will admit that he no longer knows how to fix it; and I don't want to sit around waiting until that happens.
Is now a bad time to reach out to a junior person in the field (who I know and trust) asking if they know how to turn the sketch into a proof? I would not phrase it as "I'm concerned the old result is wrong," but as "What am I missing? I'm new to this particular problem, is it known how to address this kind of issue? Have you read this part of the paper before?" I would ask that this person not discuss it with my advisor before we had come to a conclusion and have the entire conversation via Zoom rather than e-mail. At the end of the day, I don't want to bother my advisor with technical details from old papers, whereas the person I have in mind is someone I trust to listen to my questions and take the details seriously.
My concern is if my advisor hears about it, he could misunderstand my intentions and think I'm telling others his old result is wrong. However, this issue is pretty distracting right now and I just want to know I'm not missing something that really is obvious or understood by experts. If that's the case, then I can stop pressing my advisor about it and move on to other things.
I could wait until this takes its course with my advisor; it's just that he's busy. In retrospect, I wish that I had asked someone else first (before my advisor) so that I wouldn't be in the awkward position I'm in now.