I was reading an article on Wikipedia and I came across a list of two problems which they asserted to be open, but without citation. I have looked through some literature but not all, as I am afraid I would not exhaust all literature in the field.
I'm wondering if there's some way I can be sure that it is open (or at least provide a source other than wikipedia to confirm that it is indeed open).
The question is not listed on sites like Open Problem Garden either, though I believe this is because it is not very well known.
Thank you!
It's impossible to be sure that a problem is open -- certainly it has happened to me that I've published a result only to much later learn part of it was already described in a seemingly unrelated paper in a different field.
Search Google, Google Scholar, the Arxiv, and other paper databases; look for recent survey papers on closely related areas and see if they assert the problem is open; ask a trusted and knowledgeable colleague... Those can all increase your confidence (but not prove) the problem is still open.