How can we determine if a question is an open question?

In mathematics, an open question is a question that no one has been able to answer. There are incomplete lists of open questions, for example here.

Suppose I think of a question and cannot answer it. I search for it but cannot find it. I post it (here) and receive no answer. I wonder if it is an open question. How can I determine if it is an open question?

Solution 1:

There is no way of knowing with absolute certainty that a given mathematical problem is still 'open' i.e. to confirm that no-one else has already solved it, since no method of searching for pre-existing solutions is completely foolproof. However, if the problem is now 'closed', then there are number of ways of finding out about it that are likely to succeed.

The first place to look would be MathSciNet, an online database of research papers in the mathematical sciences that is rather exhaustive and contains over 4 million papers to date. You can do very detailed searches here using subject classification codes and even search formatted LaTeX terms. You do need a membership of some kind to access this though, which will usually be through your university.

The second place to check would probably be the arXiv (pronounced 'archive'), where mathematicians can upload preprints of papers prior to publication, and also their own notes. This is all freely available, yet there is no requirement that work submitted there is peer reviewed, so in theory anyone could upload their work and some of what is on there is of questionable quality.

Google might throw up something obscure, like an old set of notes from a conference or various blog posts. MathOverflow is of course a good place to ask for references to literature on open problems or anything to do with research-level mathematics. There is a lot in mathematicians' heads that has not been committed to writing and therefore is not publicly available.