# 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?"

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### Places where one can post open problems

(This must have been asked before and exist somewhere in Community Wiki, but I can't find it...) Where can you post open (math) problems? And what are the advantages and disadvantages? Example: This ...
394 views

### Landau's century-old problems: Anything comparable?

Landau's four problems are now over a century old (1912), and each still unsolved. This seems remarkable, even though he was not the originating author all four (maybe only the 4th?). Still, he ...
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### Traveling salesperson problem algorithm [closed]

I was wondering something, let's say in a symmetric distance matrix of a sample of TSP, there was a sure algorithm that could remove between 30% to 80% of the values (distances) that wouldn't ...
1 vote
153 views

### Infinitely many $k \in \mathbb{N}$ such that the closed interval $[k, k+99]$ contains from $2$ to $23$ prime numbers

Let $k \in \mathbb{Z}^+$. Is it possible to prove that, for some given $m \in \{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23\}$, there are only finitely many $k$ such that the closed ...
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### What will be the set of non-Wieferich numbers if the set of non-Wieferich primes is finite?

Integer $n$ is Wieferich number if $2^{\phi(n)}-1 \equiv 0 \pmod {n^2}$. Wieferich prime is Wieferich number with $n$ prime. It is an open problem if there are infinitely many Wieferich primes and ...
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### Is it still not known whether the construction of shortest nonzero vector of a lattice w.r.t. $l^2$-norm is NP-hard?

It was shown in P. van Emde Boas, Another NP-complete partition problem and the complexity of computing short vectors in a lattice that the construction of a shortest nonzero vector of a Euclidean ...
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1 vote
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### Finding an optimal covering trail for the set $\{0,1,2,3\}\times\{0,1,2,3\}\times\{0,1,2,3\}$

Here is a key question (i.e., Question 2 below) that, if correctly answered, would let me support a very general conjecture on a wide class of related problems, a conjecture that I have never shared ...
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1 vote
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### Approximating spectra of (finite rank pertubations of) Laurent operators by spectra of (pertubations of) periodic finite operators

A tridiagonal matrix is a matrix which only has elements on three diagonals. So for $\alpha, \beta, \gamma \in \mathbb{C}$ consider the bi-infinite tridiagonal Laurent operator $T$ with $\beta$ on ...
314 views

### Open problems in type theory

I am only a beginner in the field of type theory, and I'm wondering if the community could point me out a few open problems in the field. I have a good background in logic, in particular, proof theory ...
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### Are there any open sourced or crowd source math research projects?

I’m looking for open source math research projects as I know computer science students can easily have access to material they can contribute to but this is not the case with math as far as I’m aware. ...
281 views

### What is the current status on bad tangent cones at isolated singularities?

Let $M^8 \subset B^9 \setminus \{ 0 \} \subset \mathbf{R}^9$ be a properly embedded, stable minimal hypersurface. Suppose that $0 \in \overline{M}$ is an isolated singularity of the surface. Question. ...
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### Resources where one can find open problems in Analytic Number Theory

Edit: I have asked this question separately because I am in need of some resources which focus on analytic number theory only.So, this question is not a duplicate of:Resources where I can find open ...
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### The "Smallest" open Diophantine Equation, a potential approach

In this question, Bogdan Grechuk found the "Smallest" open Diophantine equation, where size is determined by taking absolute values of all coefficients, then substituting 2 into all ...
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### Convex polygon shadows: Shortest equivalent segments

Let $P$ be a convex polygon. Q1. What is the shortest collection of line segments $S$ inside $P$ with the property that both $P$ and $S$ have the same sequence of orthogonal shadows as $P$ and $S$ ...
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### Mark Hovey's open problems in the theory of model categories

Mark Hovey maintains a list of open problems in model category theory. I think this list is quite old, and I don't know if Hovey is still updating it or not. My question is: i) which of the 13 ...
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1 vote
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### Source for conjectures in commutative algebra

Do you know some books/survey papers/ websites on conjectures or open problems in commutative ring theory? I want to see if there are very famous open problems or conjectures in commutative ring ...
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### Examples of a more general proof being easier to find than the proof itself? [duplicate]

Studying an open problem, it has become apparent that generalising and proving a more extensive theorem likely makes the problem simpler. Are there any well-known theorems where the author's ...