Linked Questions

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 plan to use this list in ...

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

Open Problem Garden and Wikipedia are good resources for more or less famous open problems. But many mathematicians will be happy with more specialized problems. They may want to find a research theme,...

Most branches of mathematics have big, sexy famous open problems. Number theory has the Riemann hypothesis and the Langlands program, among many others. Geometry had the Poincaré conjecture for a long ...

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 seems to be quite a lot ...

What are some (research level) open problems in Euclidean geometry ? (Edit: I ask just out of curiosity, to understand how -and if- nowadays this is not a "dead" field yet) I should clarify a bit ...

What are the open big problems in algebraic geometry and vector bundles? More specifically, I would like to know what are interesting problems related to moduli spaces of vector bundles over ...

What are some major open problems in Riemannian Geometry? I tried googling it, but couldn't find any resources.

What are the examples of interesting combinatorial identities (e.g. bijection between two sets of combinatorial objects) that can be proved using representation theory, or has some representation ...

I propose to collect here open problems from the theory of continued fractions. Any types of continued fractions are welcome.

Question: What are current open conjectures about the representation theory of the symmetric group? I am interested mostly in the characteristic 0 case, but conjectures for the modular case can also ...

In light of the nice responses to this question, I wonder what are some open problems in the area of toric geometry? In particular, What are some open problems relating to the algebraic ...

Are there any results stating that a given family of convex polytopes have Ehrhart polynomials with non-negative coefficients? What methods are available for proving such a property for some family ...