Part of the problem is demonstrated by the comments by "Craig" to this item. He knows quite a bit, and writes well, but he seems to be wrong in a fundamental w

Part of the problem is demonstrated by the comments by "Craig" to this item. He knows quite a bit, and writes well, but he seems to be wrong in a fundamental way. Further, he can't see why, and so keeps pressing his point. If P=NP then it's plausible that a gifted, enthusiastic and persistent amateur can prove it, although they will most likely then have a difficult time convincing the establishment. If P!=NP then it seems very unlikely to me that an amateur will prove it, and be able to demonstrate to the establishment that they have done so. Even though it's the result most mathematician's expect, a proof is going to be difficult. Not knowing the standard language for talking about these things (which will almost certainly be the case of an amateur who proves it) will be an insuperable barrier. There are a lot of results floating around already showing that certain "obvious" approaches won't work. It may be that not knowing those results is a prerequisite for solving the problem, because then your mind isn't predisposed to think in a certain way. On the other hand, not knowing those results makes it likely those approaches will be used. I don't think an amateur will solve P?=NP. EDIT: changed some clumsy wording.