# 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?"

**18**

**1**answer

### Is every projective space curve a set-theoretic intersection of two surfaces? What is known about this question?

**4**

**1**answer

### A question regarding Kadison-Kaplansky idempotent conjecture (A nearest group element $g$ to a nontrivial self adjoint unitary element u )

**51**

**9**answers

### What are some important but still unsolved problems in mathematical logic?

**103**

**1**answer

### What is the definition of the function T used in Atiyah's attempted proof of the Riemann Hypothesis?

**25**

**0**answers

### Milnor's cartography problem

**12**

**1**answer

### What is known about the relationship between Fermat's last theorem and Peano Arithmetic?

**32**

**11**answers

### Open questions about posets

**30**

**1**answer

### Updates to Stanley's 1999 survey of positivity problems in algebraic combinatorics?

**106**

**0**answers

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

**154**

**30**answers

### Proposals for polymath projects

**14**

**2**answers

### Is it known how the Sigma Algebra generated by Jordan measurable sets compares to universally measurable sets and analytic sets?

**7**

**0**answers

### When do two knots have isomorphic fundamental bikeis?

**2**

**0**answers

### A cubic system with two nested limit cycles with opposite orientations(2)

**6**

**4**answers

### Bounds on number of conjugacy classes in terms of number of elements of a group ?

**50**

**14**answers

### Open problems in Euclidean geometry?

**0**

**0**answers

### Area of Disc that Intersects Another under Smooth Flow

**8**

**3**answers

### Hamiltonian $S^1$ actions with isolated fixed points

**6**

**0**answers

### A cohomology associated to a (not necessarily integrable) distribution (Hilbert 16th problem and dynamical Lefschetz trace formula 2)

**27**

**7**answers

### Decision problems for which it is unknown whether they are decidable

**13**

**2**answers

### Is every finite-order unimodular matrix conjugate to a $0,1,-1$ matrix?

**11**

**0**answers

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

**8**

**3**answers

### Birkhoff conjecture about integrable billiards

**9**

**0**answers

### Is it an open problem whether fast-growing hierarchies can be defined without fundamental sequences?

**3**

**1**answer

### Is there any progress toward solving Gilbreath's conjecture?

**89**

**26**answers

### Open problems with monetary rewards

**305**

**105**answers

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

**12**

**1**answer

### Which knot invariants have no known diagram-independent descriptions?

**16**

**2**answers

### Characterisation of bell-shaped functions

**76**

**11**answers

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

**14**

**3**answers

### Can there be a polymath project for mathematical physics?

**8**

**1**answer

### What is the state of research on finding all Prime Knots with 17 Crossings?

**2**

**1**answer

### Any results towards the irrationality of the sum of reciprocals of perfect numbers? [closed]

**33**

**5**answers

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

**1**

**1**answer

### The Total Graph is similar to a line graph

**2**

**0**answers

### How many solutions of x^3 +y^3 = z^3+3 are known? [duplicate]

**58**

**1**answer

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

**4**

**0**answers

### Remaining models conjectured to converge to SLE(6) or CLE(6)

**68**

**16**answers

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

**52**

**10**answers

### The “sensitivity” of 2-colorings of the d-dimensional integer lattice

**7**

**1**answer

### Hyperbolic groups and spaces of negative curvature

**0**

**0**answers

### On the convergence of $\sum_{n\geq 1} \frac{\sin (2^n)}{n^s}$

**11**

**3**answers

### An integral related to the Euler gamma function

**12**

**2**answers

### Die-rolling Hamiltonian cycles

**460**

**2**answers

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

**5**

**0**answers

### Existence of infinitely many number fields with bounded class number

**0**

**0**answers

### Coloring a graph formed by cliques sharing at most one point

**24**

**7**answers

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

**0**

**0**answers

### Is the exact solution of the wave equation for the scattering of waves by a disk/cylinder an open problem?

**14**

**1**answer

### Minimizing the excursion of a sum of unit vectors

**7**

**1**answer