As we know ,there are some open problems of formal languages,I am wandering if there is a somehow complete list of open problem of formal languages,or if there is no somehow comple …

Question: I'm asking for a big list of not especially famous, long open problems that anyone can understand. Community wiki, so one problem per answer, please. Motivation: I pl …

(This question might not be appropriate for this site. If so, I apologize in advance. I would have posted to mathstack, but I'm looking for advice from active researchers.) I am a …

In many areas of mathematics there are fundamental problems that are embarrasingly natural or simple to state, but whose solution seem so out of reach that they are barely mentione …

Most open problems, when formalized, naturally involve quantification over infinite sets, thereby obviating the possibility, even in principle, of "just putting it on a computer." …

What are the important open problems in the theory of compact quantum groups? Or conjectures? Here is an example from An De Rijdt's Ph.D. thesis: Is every compact quantum group wi …

What are some of the open problems in Seiberg-Witten Theory on 4-Manifolds.I tried googling but couldn't any. I tried googling it, but couldn't find any resources.The places where …

Since the old days, many mathematicians have been used to attaching monetary rewards to problems they admit are difficult. Their reasons could be to draw other mathematicians' att …

What is a good reference for open problems relating to the Ramanujan tau function? I know about Lehmer's conjecture. I know the following reductions of the problem: the smallest …

Rencently a breakthrough was made in the context of the Minimal Model Program by the work of Birkar-Cascini-Hacon-McKernan. They proved that the canonical ring of a smooth or mildl …

I gather that the question whether the Bruck-Chowla-Ryser condition was sufficient used to top the list, but now that that's settled - what is considered the most interesting open …

From what I understand, the geometrization theorem and its proof helped to settle a lot of outstanding questions about the geometry and topology of 3-manifolds, but there still see …

Whitehead problem is a rather well known problem: Suppose that $G$ is an abelian group and $\mathrm{Ext}^1(G,\Bbb Z)=0$, is $G$ free? It wasn't long before it was proved tha …

This is a pair to http://mathoverflow.net/questions/100265/not-especially-famous-long-open-problems-which-anyone-can-understand So this time I'm asking for open questions so easy …

What are some open problems in sub-Riemannian geometry? I am interested especially in problems concerning connections and curvature, but any contribution is welcomed.