# Questions tagged [open-problems]

If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"

**308**

**105**answers

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

**44**

**1**answer

### improving known bounds for Pierce expansions; cash prize

**7**

**0**answers

### Limit cycles as closed geodesics(2)

**76**

**11**answers

### Is there a complex structure on the 6-sphere?

**73**

**6**answers

### Can we cover the unit square by these rectangles?

**33**

**5**answers

### Are nontrivial integer solutions known for $x^3+y^3+z^3=3$?

**14**

**2**answers

### Is a smooth closed surface in Euclidean 3-space rigid?

**11**

**0**answers

### Hilbert 16th problem and dynamical Lefschetz trace formula

**460**

**2**answers

### Polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$?

**154**

**30**answers

### Proposals for polymath projects

**18**

**2**answers

### Integer-distance sets

**4**

**0**answers

### Limit cycles of quadratic systems and closed geodesics(Finitness of $H(2)$)

**50**

**14**answers

### Open problems in Euclidean geometry?

**67**

**1**answer

### Nontrivial finite group with trivial group homologies?

**40**

**12**answers

### Can a discrete set of the plane of uniform density intersect all large triangles?

**24**

**7**answers

### Convex hull in CAT(0)

**37**

**5**answers

### Surfaces filled densely by a geodesic

**30**

**4**answers

### Are most cubic plane curves over the rationals elliptic?

**37**

**3**answers

### Is the fixed point property for posets preserved by products?

**22**

**0**answers

### Given a lattice L with n elements, are there finite groups H < G such that L $\cong$ the lattice of subgroups between H and G?

**16**

**2**answers

### Minimal graphs with a prescribed number of spanning trees

**2**

**2**answers

### If all real conjugacy classes are strongly real, then all real irreps are “strongly real”(symmetric), true?

**12**

**1**answer

### A maximal element, where Schur gives a minimal element

**5**

**0**answers

### Forcing with c.c.c forcing notions, Cohen reals and Random reals

**180**

**8**answers

### Two commuting mappings in the disk

**96**

**13**answers

### What are the big problems in probability theory?

**52**

**11**answers

### What are some open problems in algebraic geometry?

**119**

**4**answers

### If $2^x $and $3^x$ are integers, must $x$ be as well?

**113**

**0**answers

### Why polynomials with coefficients $0,1$ like to have only factors with $0,1$ coefficients?

**40**

**2**answers

### Open problems/questions in representation theory and around?

**68**

**16**answers

### Important open problems that have already been reduced to a finite but infeasible amount of computation

**44**

**3**answers

### Shortest closed curve to inspect a sphere

**43**

**5**answers

### Is Lebesgue's “universal covering” problem still open?

**23**

**2**answers

### Are there Ricci-flat riemannian manifolds with generic holonomy?

**58**

**1**answer

### Which region in the plane with a given area has the most domino tilings?

**36**

**4**answers

### Does there exist a comprehensive compilation of Erdos's open problems?

**15**

**10**answers

### Not especially famous, long-open problems which higher mathematics beginners can understand

**26**

**3**answers

### Work on independence of pi and e

**46**

**2**answers

### Local structure of rational varieties

**21**

**2**answers

### unboundedness of number of integral points on elliptic curves?

**24**

**7**answers

### Solving NP problems in (usually) Polynomial time?

**21**

**3**answers

### Periodic Automorphism Towers

**10**

**1**answer

### Transcendentality of all irrationals in the Cantor set

**32**

**0**answers

### Converse of the Archimedean property of the sphere

**13**

**1**answer

### Is $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$ correct, where $n$ is an integer?

**11**

**2**answers

### Is the Steiner ratio Gilbert–Pollak conjecture still open?

**14**

**3**answers

### Kaplansky's 6th conjecture: dim(Irrep) | dim(algebra) - for semi-simple Hopf algebras

**13**

**0**answers

### 3-piece dissection of square to equilateral triangle?

**15**

**1**answer

### Open bilinear maps that are not uniformly open

**5**

**3**answers