The open-problems-list tag has no wiki summary.

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

Most open problems, when formalized, naturally involve quantification over infinite sets, thereby obviating the possibility, even in principle, of "just putting it on a computer."
Some questions ...

**9**

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**6**answers

675 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.

**2**

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**1**answer

170 views

### Open problems books [closed]

As the title might indicate , I would like to look for recommendations for mathematical book that present open problems in depth with commentary.
The only book of this type that I've come across is ...

**4**

votes

**1**answer

181 views

### Open problems in Banach spaces, universality

I have gathered a list of universality problems in Banach spaces which have been solved:
1.The non existence of a separable reflexive space universal for the class of separable reflexive spaces.
...

**172**

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**93**answers

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### 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 ...

**26**

votes

**14**answers

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### 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 ...

**9**

votes

**2**answers

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### *The* open problem in General Relativity?

Q. Is there a single, clear mathematical question that has emerged as
the open problem in General Relativity?
I ask this on the ~100th anniversary of Einstein's (4-page!) 1915 paper,
"Die ...

**14**

votes

**2**answers

993 views

### Open problems in Berkovich geometry

I would like to know if there is a state of the art recent reference on non-archimedean analytic spaces mentioning/listing open problems, conjectures, unresolved questions in the theory (*). I have ...

**54**

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**23**answers

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### Open problems with monetary rewards

Since the old days, many mathematicians have been used to attaching monetary rewards to problems they admit are difficult. Their reasons could be to draw other mathematicians' attention, to express ...

**2**

votes

**0**answers

166 views

### Are there any interesting open questions having to do with submodularity, specially in the intersection of theoretical machine learning? [closed]

I was interested in knowing about open research topics related with sub modularity, specially within its intersection with theoretical machine learning (and related topics).
It seems to me that much ...

**41**

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**30**answers

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### Fundamental problems whose solution seems completely out of reach [closed]

In many areas of mathematics there are fundamental problems that are embarrasingly natural or simple to state, but whose solution seem so out of reach that they are barely mentioned in the literature ...

**2**

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**1**answer

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### Open problems in compressed sensing

What are the main open problems in compressed sensing?
I am interested in theoretical as well as in numerical point of view.

**4**

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**0**answers

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### Reduction argument from a general vertex set V(G) to a prime power in Prof. Keevash's proof on the Existence of Designs

The proof flow of the paper "On the Existence of Designs" by Prof. Keevash as I understand it is the following:
-- Reduction from the general case to $V = \mathbb{F}_{p^a}$ (Lemma 6.3)
-- Covering ...

**5**

votes

**1**answer

511 views

### List of open problems of formal languages [closed]

As we know, there are some open problems of formal languages. I am wondering if there is a somehow complete list of open problem of formal languages. If there isn't such a list, can we make it one as ...

**18**

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**2**answers

2k views

### Open Problems in Algebraic Topology and Homotopy Theory

Some time ago (I see it was initially written before 1999?) Mark Hovey assembled a list of open problems in algebraic topology. The list can be found here. Some of the problems I know about have been ...

**9**

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**4**answers

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### What are the major open problems in design theory nowaday?

I gather that the question whether the Bruck-Chowla-Ryser condition was sufficient used to top the list, but now that that's settled - what is considered the most interesting open question?

**7**

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**9**answers

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

This is a pair to
Not especially famous, long-open problems which anyone can understand
So this time I'm asking for open questions so easy to state for students of subjects such as undergraduate ...

**16**

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**9**answers

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### Open Questions in Riemannian Geometry

What are some major open problems in Riemannian Geometry? I tried googling it, but couldn't find any resources.

**10**

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**1**answer

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### List of Whitehead-like Problems

Whitehead problem is a rather well known problem:
Suppose that $G$ is an abelian group and $\mathrm{Ext}^1(G,\Bbb Z)=0$, is $G$ free?
It wasn't long before it was proved that if $G$ is ...

**39**

votes

**13**answers

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### 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 ...

**1**

vote

**3**answers

603 views

### Open problems in sub-Riemannian geometry

What are some open problems in sub-Riemannian geometry?
I am interested especially in problems concerning connections and curvature, but any contribution is welcomed.

**18**

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**10**answers

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### Open problems in PDEs, dynamical systems, mathematical physics

(This question might not be appropriate for this site. If so, I apologize in advance. I would have posted to mathstack, but I'm looking for advice from active researchers.)
I am an undergrad in math ...

**0**

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**0**answers

296 views

### Known and unknown about Ramanujan's tau function

What is a good reference for open problems relating to the Ramanujan tau function?
I know about Lehmer's conjecture. I know the following reductions of the problem: the smallest counterexample must ...

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**7**answers

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### Open problems in the theory of compact quantum groups

What are the important open problems in the theory of compact quantum groups? Or conjectures?
Here is an example from An De Rijdt's Ph.D. thesis: Is every compact quantum group with the fusion rules ...

**14**

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**3**answers

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### open problems in Seiberg-Witten Theory on 4-Manifolds

What are some of the open problems in Seiberg-Witten Theory on 4-Manifolds.I tried googling but couldn't any. I tried googling it, but couldn't find any resources.The places where I can a survey or ...

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**4**answers

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### Open problems in Birational Geometry, after BCHM

Rencently a breakthrough was made in the context of the Minimal Model Program by the work of Birkar-Cascini-Hacon-McKernan. They proved that the canonical ring of a smooth or mildly singular ...

**5**

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**1**answer

294 views

### Open problems about CMC hypersurfaces with symmetries?

Recently, Andrews and Li announced a complete classification of CMC ($H=const.$) tori in $S^3$, confirming a conjecture of Pinkall and Sterling. Their main result is that any such torus is ...

**9**

votes

**3**answers

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### Motivation and unsolved problems of TQFT

I have been studying topological quantum field theory by mainly reading the Turaev's book.
I'd like to know if there are unsolved problems that motivate mathematicians to study TQFT, like Riemann's ...

**24**

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**1**answer

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### Important open questions in the field of Tropical geometry

What are some of the important unanswered questions in the field of tropical geometry?