Linked Questions

297
votes
105answers
60k views

Not especially famous, long-open problems which anyone can understand

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 ...
84
votes
25answers
47k views

Open problems with monetary rewards

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 ...
73
votes
25answers
12k views

More open problems [closed]

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,...
95
votes
13answers
33k views

What are the big problems in probability theory?

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 ...
55
votes
14answers
9k views

What are some of the big open problems in 3-manifold theory?

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 ...
45
votes
14answers
13k views

Open problems in Euclidean geometry?

Which 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 ...
51
votes
11answers
14k views

What are some open problems in algebraic geometry?

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 ...
30
votes
11answers
11k views

Open Questions in Riemannian Geometry

What are some major open problems in Riemannian Geometry? I tried googling it, but couldn't find any resources.
18
votes
14answers
2k views

Applications of Representation Theory in Combinatorics

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 ...
16
votes
8answers
2k views

Open problems in continued fractions theory

I propose to collect here open problems from the theory of continued fractions. Any types of continued fractions are welcome.
15
votes
2answers
2k views

What are some open problems in toric varieties?

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 ...
8
votes
4answers
876 views

Positivity of Ehrhart polynomial coefficients

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 ...