I am doing my Ph.D. in maths and working on something. However, I was wondering what would happen if someone publishes similar results to the ones I am obtaining while I am working on that. I have no control over that because it may happen that the result is totally new and therefore I couldn't check before starting to work. Will all the time spent being lost? Are my results valid for defending my dissertation?
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As I understand it, in the math community, the method of proof is more important. If you have a different approach to proving the same result that is useful, then there is no worry. I think it's quite rare to have exactly the same approach unless you are looking over another person's shoulder. – Prof. Santa Claus Nov 30 '17 at 19:46