I'm a bachelor student in mathematics writing my thesis at a small university in the US. A PhD student that has the same supervisor has spent a very significant amount of time working exclusively on a theorem which he hasn't been able to prove, so the supervisor offered me a thesis on the topic. No one was really expecting me to make any real progress, but everyone was very nice and enthusiastic.
It turned out that I was able to prove the theorem essentially straight away using a different approach to what they've tried. After this happened I've felt a distinct change in attitude towards me. There is no excitement, there is no discussion on how to strengthen or generalize the result and I generally get the feeling that they are pretty embarrassed about the whole situation.
The PhD student has a severe lack of publications and is probably feeling quite stressed because further progress on this problem seems unlikely. So what is my best plan of action here? Keep in mind that stepping on toes is the last thing I want to do given that I was hoping to pursue a PhD in this very department. How do I act diplomatically while at the same time making sure I get due credit for my achievements? Is it possible they will try to bully me out of first-authorship to protect the reputation of the PhD student?
I'd suggest you offer to go out for a couple of beers (you pay) - And after a few beers just be honest about your concerns. Be sure to give the PhD student a wealthy round of thanks for the "great" work that he has already done, as it certainly played a part in the solution you were able to come up with. Above all, be humble!