96
votes
73answers
12k views
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 pl …
1
vote
2answers
211 views
A conjecture on closed discrete subset
I am struggling with this old problem, which is also posted here:
Let $X$ satisfy countable chain condition(abbreviated as CCC) and $X$ has a regular $G_\delta$-diagonal. Then …
13
votes
10answers
1k views
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 a …
33
votes
30answers
4k views
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 mentione …
41
votes
1answer
2k views
A function whose fixed points are the primes
If $a(n) = (\text{largest proper divisor of } n)$, let $f:\mathbb{N} \setminus \{ 0,1\} \to \mathbb{N}$ be defined by $f(n) = n+a(n)-1$. For instance, $f(100)=100+50-1=149$. Clearl …
28
votes
11answers
2k views
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."
…
10
votes
7answers
757 views
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 wi …
1
vote
0answers
255 views
Collatz conjecture— finite state machine transducer construction, origination?
wikipedia has an entry on the Collatz conjecture with a section on As an abstract machine that computes in base two. this apparently describes a construction of a FSM transducer co …
7
votes
0answers
281 views
Is it true that every f.g. infinite simple group has exponential growth?
Is it true that every finitely generated infinite simple group has
exponential (word-)growth?
Remark: As Mark Sapir has pointed out, the question whether
every finitely generated …
22
votes
4answers
878 views
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 mildl …
37
votes
19answers
8k views
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' att …
11
votes
1answer
419 views
Randomly switching street lights, in a square city
This is a combinatorics-probability question, best stated however in "recreational" terms. Imagine a $N\times N$ city, meaning that we have $N$ horizontal streets, and $N$ vertical …
0
votes
1answer
204 views
An interesting computation related to OPNs (Odd Perfect Numbers) [closed]
Let $\theta_1 = \sqrt[3]{2}$ and
$$\theta_2 = 2 + \sqrt[3]{4} + \sqrt[3]{2} = {\theta_1}\left(1 + \theta_1 + {\theta_1}^2\right).$$
Now, if $N = {q^k}{n^2}$ is an Odd Perfect Nu …
1
vote
1answer
409 views
An open problem on general topology
There is an open problem in this paper: Classes defined by stars and neighbourhood assignments by van Mill and others.
Problem 4.8. Is a regular (Tychonoff) star compact space met …
7
votes
3answers
532 views
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 …

