I'm working on a project with a professor for my MS. It's computational, and I am currently stuck at a critical point. I can physically justify some assumptions and get the model to work, but I can't do so mathematically. They would be mathematically arbitrary. I'm working to resolve this problem through more research, but it doesn't seem anybody has solved this specific problem before. I show him what I've done, and he looks clueless. As if he doesn't know why I'm required to do what I have done, even though my premise is correct. So I don't know how to mathematically derive the arbitrary values I used, and he doesn't even know what I'm doing, and doesn't have any clue as to how to go about deriving such values. What am I supposed to do? I'll continue researching and/or hope for a breakthrough, but what if I don't have one? I can't defend my thesis by doing what I've done. Especially given one of the committee members is a math professor, and I just know he's going to grill me for the approximations I've used throughout this project anyway. I can't compound that by using mathematically arbitrary values. He's not going to be thrilled. The engineering members of the committee I can probably convince if the results are empirically verified, but not a mathematician. I don't have to defend for another 10 months, but I'm nervous about my status. I don't have much left to do after I can mathematically derive the values in question and get good results, but that's another issue. I need to give myself a lot of time to make sure my results are empirically verified, and make revision accordingly.