# 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?"

**2**

**2**answers

### A possible dynamical approach to the “Invariant Subspace Problem”

**2**

**0**answers

### Open problems concerning Araujo's biseparating maps

**12**

**1**answer

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

**2**

**0**answers

### Open problems in the theory of manifolds relating to construction [closed]

**9**

**4**answers

### What is the smallest sphere whose surface includes 100 integer points?

**7**

**0**answers

### On a question of Coste & Roy from 1979

**3**

**0**answers

### If $a^3+b^3+c^3=N$, then $x^3+y^3+z^3+t^3 = N$ in infinitely many ways?

**3**

**1**answer

### Asymptotic form of pdf of Escape Time of arithmetic fBm

**1**

**1**answer

### Portability of Thompson theorem about solvability to Moufang loops

**11**

**3**answers

### Undecidable easy arithmetical statement

**7**

**1**answer

### On statistical bases in Banach spaces

**3**

**1**answer

### Can one find a Jordan curve which has exactly one inscribed rectangle?

**13**

**1**answer

### Equilaterally triangulated surfaces with prescribed boundary

**1**

**0**answers

### What is an umbilic point of a convex polyhedron?

**12**

**2**answers

### Intrinsic vs Extrinsic geometry of convex surfaces

**74**

**0**answers

### Converse to Euclid's fifth postulate

**8**

**0**answers

### Plank invariant measures on convex bodies

**32**

**0**answers

### Converse of the Archimedean property of the sphere

**16**

**2**answers

### Characterisation of bell-shaped functions

**1**

**0**answers

### Does this idea give an algorithm for constructing Hadamard matrices?

**15**

**1**answer

### Does the image of the exponential map generate the group?

**9**

**4**answers

### Is there always one integer between these two rational numbers?

**14**

**1**answer

### Who conjectured the Cartan determinant conjecture

**1**

**0**answers

### Modular which is metrizing but does not satisfy the $\Delta_2$ condition

**2**

**0**answers

### Splitting of ordinals of oscillation ranks of a Baire $1$ function

**2**

**0**answers

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

**7**

**0**answers

### Limit cycles as closed geodesics(2)

**4**

**0**answers

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

**13**

**3**answers

### Current state of the Komlos conjecture on vector balancing

**35**

**6**answers

### Open problems in mathematical physics

**13**

**3**answers

### Random N-body problem

**15**

**1**answer

### Open bilinear maps that are not uniformly open

**12**

**2**answers

### Is the fundamental group of any compact hyperbolic 3-manifold embeddable into a p-adic group?

**3**

**1**answer

### Hausdorff's question on $\omega_1$-gap

**4**

**1**answer

### Surface bundles over surfaces with(out) flat structure

**6**

**1**answer

### Every PD group is $\pi_1$ of an aspherical manifold

**14**

**3**answers

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

**1**

**0**answers

### The derivative of an integral function with indicator and max function as integrand

**15**

**0**answers

### Decidable open problems

**1**

**1**answer

### Expectation of changing the gift choice [closed]

**8**

**2**answers

### Current state of Straus's illumination problem

**16**

**2**answers

### Is the Gromov conjecture still open?

**3**

**1**answer

### What arguments do exist against defining completeness in NP using injective Karp reductions?

**4**

**0**answers

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

**4**

**0**answers

### Does every separable Banach space have a Markushevich–Auerbach basis?

**4**

**1**answer

### Can we solve the FGF problem by finding an appropriate action?

**2**

**0**answers

### Pro-V topology on a free group

**2**

**1**answer

### On attempting a proof for $r > 1$, if $M = {2^r}{b^2}$ is an even almost perfect number which is not a power of two

**31**

**1**answer

### A long-lasting conjecture of Pólya & Szegő

**1**

**0**answers