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I recently finished my Phd in pure maths and I am looking for open problems in my research area, functional analysis. Without going into the details, I stumbled onto an interesting problem and I shared it with one of my collaborators who proved a nice result. After a google search, however, I found a 2013 paper on the archive where the author considered the same problem and basically solved it. At first, I was a bit perturbed about this but it seems to happens quite often; the prime number theorem is one example of this phenomena.

I would like to know if this has happened to anyone in the math overflow community and how they dealt with it.

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    $\begingroup$ I proved a result about Benford's Law and factorials and discovered, before sending it in for publication, that Persi Diaconis had recently published a paper which included what I had found and more. You just shrug it off, and try to prove something else. What else can you do? $\endgroup$
    – Gerry Myerson
    Commented Apr 17, 2014 at 1:35
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    $\begingroup$ Do you know anybody to whom it never happened? $\endgroup$
    – Włodzimierz Holsztyński
    Commented Apr 17, 2014 at 1:39
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    $\begingroup$ This is normal, and even a good sign. $\endgroup$
    – Joël
    Commented Apr 17, 2014 at 6:00
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    $\begingroup$ It is important to have many proofs, with different ideas, of the same result. It helps to build a bridge between those ideas. So if your proof of a result is different enough from any known proof, you still need to publish it. $\endgroup$
    – Ben McKay
    Commented Apr 17, 2014 at 9:32
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    $\begingroup$ I share Ben McKay's opinion, but once it happened to me that my collaborator and I re-found a theorem with exactly the very same proof found by a math physicist more than 30 years earlier. We discovered this by chance, googling for something different. At the end we decided to generalize his result taking advantage of some functional analytical notions that had appeared since then, but clearly we were much less motivated to work on it after this discovery. $\endgroup$
    – Delio Mugnolo
    Commented Apr 17, 2014 at 22:57

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