All Questions
Tagged with open-problems big-list
36 questions
10
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Open problems in complete theories
It is well-known that every complete recursively enumerable first-order theory is decidable. Does that mean that such theories are "trivial", or are there still interesting open problems ...
user507115
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vote
3
answers
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No starter "accessible" well known open problems
We all know very famous open problems. Usually the ones that become famous are well studied and lots of progress was achieved and conjectures, partial results, reductions and so on exist. This is one ...
23
votes
4
answers
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Brute force open problems in graph theory
Usually, a graph theoretic problem asks whether some class of graphs $C$ possesses a quality $P$. For example, $C$ is the class of all graphs and $P$ is the reconstructability property in Kelly-Ulam ...
3
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0
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What are some of the big open problems in $4$-manifold theory?
I've recently been studying some Manifold Theory and got very interested in their topological as well as geometric properties. From my understanding of the current literature, most the big and ...
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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 ...
8
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0
answers
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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 ...
14
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2
answers
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Open problems in symbolic dynamics
I would like to know which are some noticeable open problems in symbolic dynamics, including substitution dynamics. I'm especially interested in connections with topological chaos of various forms. ...
43
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10
answers
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List of long open, elementary problems which are computational in nature
I would like to ask a question of a similar vein to this question.
Question: I'm asking for a list of long open problems which are computational in nature which a beginning graduate student can ...
34
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9
answers
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Decision problems for which it is unknown whether they are decidable
In computability theory, what are examples of decision problems of which it is not known whether they are decidable?
10
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1
answer
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Open problems concerning all the finite groups
What are the open problems concerning all the finite groups?
The references will be appreciated. Here are two examples:
Aschbacher-Guralnick conjecture (AG1984 p.447): the number of conjugacy ...
124
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40
answers
21k
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Noteworthy, but not so famous conjectures resolved recent years
Conjectures play important role in development of mathematics.
Mathoverflow gives an interaction platform for mathematicians from various fields, while in general it is not always easy to get in touch ...
0
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2
answers
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What are some of the unsolved mathematical problems that we generally agree were posed before the beginning of the XX.-th century?
Because mathematics has been extremely well-developed in XX.-th and continues to do so in XXI.-th century and because there is an enormous number of open problems and conjectures and hypotheses posed ...
7
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1
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What are some open problems in moduli spaces and moduli stacks?
I would like to know what are the open big and interesting problems related to moduli spaces and moduli stacks ?
Thanks in advance for your help.
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24
answers
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PhD dissertations that solve an established open problem
I search for a big list of open problems which have been solved in a PhD thesis by the Author of the thesis (or with collaboration of her/his supervisor).
In my question I search for every possible ...
36
votes
6
answers
11k
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Open problems in mathematical physics
What are good, still unsolved problems in mathematical physics that are in vogue? I always get the same answers: reference to Millennium Problems by the Clay Institute, or "there's still a lot to do ...
14
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3
answers
1k
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Can there be a polymath project for mathematical physics?
My hunch is that it might be possible to create something like https://polymathprojects.org/ for mathematical physics and I'd like to know whether MathOverflow users can recommend some appropriate ...
21
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3
answers
2k
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Open problems in Hopf algebras
I couldn't find a list of open problems in Hopf algebras. So my question is the following:
In the theory of Hopf algebras, what are the (big) open problems?
Any kind of problem/question will be ...
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73
votes
9
answers
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What are some important but still unsolved problems in mathematical logic?
In the past, first-order logic and its completeness and whether arithmetic is complete was a major unsolved issues in logic . All of these problems were solved by Godel. Later on, independence of ...
172
votes
36
answers
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Proposals for polymath projects
Background
Polymath projects are a form of open Internet collaboration aimed towards a major mathematical goal, usually to settle a major mathematical problem. This is a concept introduced in 2009 by ...
19
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8
answers
3k
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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.
7
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4
answers
2k
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Interactions of number theoretic conjectures and other fields of mathematics
There are many interesting open conjectures in number theory. My question is not about partial results or possible ways to prove them. It is about their interactions with the other fields of ...
36
votes
12
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 ...
11
votes
4
answers
2k
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problems from the scottish book
Which of the problems from the Scottish Book (pdf of English version) by Stefan Banach are still open? I know that one of the problems was solved by Per Enflo for which he got a live goose from ...
90
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17
answers
6k
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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 (e.g....
11
votes
1
answer
637
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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 countable (...
21
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10
answers
6k
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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 ...
54
votes
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 ...
394
votes
115
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 in ...
46
votes
2
answers
10k
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Open problems/questions in representation theory and around?
What are open problems in representation theory?
What are the sources (books/papers/sites) discussing this?
Any kinds of problems/questions are welcome - big/small, vague/concrete.
Some estimation ...
58
votes
14
answers
19k
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Open problems in Euclidean geometry?
What 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 bit ...
43
votes
11
answers
15k
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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.
61
votes
11
answers
21k
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What are some open problems in algebraic geometry?
What are the open big problems in algebraic geometry and vector bundles?
More specifically, I would like to know what are interesting problems related to moduli spaces of vector bundles over ...
113
votes
13
answers
46k
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What are the big problems in probability theory?
Most branches of mathematics have big, sexy famous open problems. Number theory has the Riemann hypothesis and the Langlands program, among many others. Geometry had the Poincaré conjecture for a long ...
62
votes
14
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 ...
8
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6
answers
6k
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List of recently solved mathematical problems
I'm looking for a news site for Mathematics which particularly covers recently solved mathematical problems together with the unsolved ones. Is there a good site MO users can suggest me or is my only ...
10
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10
answers
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Statements reliant on conjectures
There are lots of statements that have been conditionally proved on the assumption that the Riemann Hypothesis is true.
What other conjectures have a large number of proven consequences?