Main result unpublished at the end of the PhD Before giving the context of my situation, I sum up my questions:

- As a 3rd year PhD student, what would you do if you have a nice result but cannot publish it because your advisor is too busy and doesn't help?

- If the main result of your PhD is not published by the time you apply to postdocs, can you still talk about it in the research statement? Will it have much less impact than if it was published?

I am currently a third year PhD student in the field of mathematical physics in a small unknown university. I will graduate before June 2019, but I will apply for postdocs this year. 

For the last 1.5 years, I mostly worked alone on a theory A, and I found out that there was a correspondence between this theory A and a theory B. Each of them have raised a lot of research in their own direction since 30 years, but I never found anything on the literature about a possible connection. So I guess it's interesting. 

The problem is that I got kinda far from my advisor research interests: he is a specialist of the theory A, but B sounds esoteric for him. The first time I asked his opinion, he was suspicious "no no, it has nothing to do". When I came back with more "proofs" (one year ago), he got much more enthusiastic. He wanted to publish a paper by the end of summer 2017, and  sent me an outline for the paper. He even discussed with the "boss" of the theory B (who knows almost nothing about A), and he seemed really surprised and intrigued.

Since one year, NOTHING happened. I did further and more precise computations, but he is very active in his own fruitful research and travels a lot. Since last summer, I sent him several versions of my notes and asked about discussion, but every time we discussed a little about it (maybe 3 times in one year?), I realize that he didn't read anything. Several weeks ago, he said it would be nice to publish the paper before I apply for postdocs, but that maybe he is too optimistic...

Today, I feel kinda discouraged and powerless. I am in a weird situation where I think I have nice unexpected results which raise many new questions, but I have on the bottom of the bottom of the list of my advisor priorities. Besides him, scientifically I am completely isolated in my university. I am supposed to apply for postdoc in September/October, and I put a lot of hopes in those results. I have 2 other papers but I find them way less interesting. I don't know what to do.

I would be interested to know if someone have been in a similar situation, and how was it during the postdoc process.
You should publish it, independent of your future carreer plans. But of course, journal papers help for postdoc positions!

I would recomment to write a first draft and send it to your supervisor. If you feel about it, ask him, if you should contact the big boss of theory B as potential co-author to strengthen the paper. If he agrees, you could at least get one feedback. 

Usually supervisors are becoming more active if their name is on a paper - they don't want it to be low quality. But maybe this is the problem of your supervisor: Since he is not into the topic, he might not be able to judge whether the paper is good or not. Therefore you could offer to publish the paper as single author and just mention your discussions in the acknowledgements if he prefers this. But I would leave this open as a last ressort.