I'm a rising fourth year undergraduate in math, who reached out to a Professor of mine a few months ago to start a project for the summer. I happened to explain the problem to some friends, and one of them asked to join me on the project. I said yes, and ever since I've been sending this friend all of my notes, ideas, every bit of work that I've been doing to keep them updated. However, prior to yesterday, they gave me no indication that they were even working on the problem at all.

Yesterday, we had a meeting with our Professor, during which my friend said almost nothing except for one or two ideas they had, along with the fact that they had a notes document themselves that they were working on. I asked them to send it to me, and they did not. A few hours later, they give me a call, telling me that they've solved the problem (or at least, they have a mostly complete outline). They explain it to me, and the proposal starts with a small fact that I had demonstrated, before taking it in a completely different direction, and to say 90% of the proposed solution is their work may be an understatement.

I'm beyond upset that they hid their work from me. I gave them every bit of work that I had done, had previously asked them to send any work they did my way as well, only for them to effectively scoop me on a project I started. To be fair, my work is not completely hopeless, rather than working directly on the problem directly I built up some interesting machinery around it and demonstrated some connections to another area of math, with the aims of eventually putting this towards the problem, and this work may still be of interest (although they happened not to not need it anyways). Additionally, they tell me they are perfectly fine sharing credit.

I don't care about credit. I just don't. It seemed like they really didn't intend to hurt me or scoop me, supposedly they didn't want to show me their work because they knew it was my project and last opportunity to do research before grad apps, but this is incoherent, if this is true why work on the problem at all, let alone present a solution to me that is almost 100% their work? No, I wanted the satisfaction of being able to actually participate and put in effort on the first undergraduate math research project I have ever done. Even if it ended up being that the bulk of the good ideas were theirs, I just wanted to have something to do with the final product, and this was taken from me.

So, here are my questions.

1. As I said, they are perfectly fine splitting credit. Given that almost all of the actual solution was their work, I feel like it would be misleading to both our advisor and any grad schools I will be applying to treat it this way. Would it be ethical? Especially considering that I plan to ask this Professor for a letter of recommendation for grad school, and I would feel pretty strange about leading him to believe that the problem was suddenly solved in some flash of divine inspiration by the two of us.

2. Do I explain the situation to my Professor? If this ends up being a solution, I want to continue working on the other ideas I had with my I don't want to come across as conniving or going behind someone's back, even if they did the same to me, but I was worried that after this solution my advisor may not be so interested in continuing this direction of research, and I imagine he would be more interested if I explained what happened.

3. Just... what do I even make of this? I feel so betrayed I don't know what to do with myself. I am going into my fourth year, I switched to pure math from previously being a physics major with a math minor towards the end of my second year so my time in pure math has been short, and this was my first and only real opportunity to do research before grad school applications. I have been working so hard on building up lemmas, proving theorems about connections to different fields, and collecting facts, and even though that may be interesting for related problems, it's still not certain, and I still feel like my effort was totally wasted. I've found things that didn't pan out before, but at least that way you feel like you learned something for your next attempt. This was just a complete rug pull