Questions on problems that have yet to be completely solved by current mathematical methods.

learn more… | top users | synonyms

1
vote
2answers
141 views

A Problem on Time Complexity of Algorithms

I want no know if the following problem is solved or not, or how can I solve it? Problem: For every integer $t$, Is there any problem that can be verified in $O(n^{s})$ but its solution can be found ...
1
vote
0answers
58 views

Is the Hilbert-Smith conjecture still unsolved?

Conjecture Let $G$ be a locally compact topological group. If $G$ has a continuous faithful group action on an $n$-manifold, then $G$ is a Lie group. Is this conjecture still unsolved? Is ...
1
vote
0answers
48 views

Strict positivity on the diagonal of a particular integral kernel: A question from Simon's Schrödinger Semigroups

This is a question pertaining to a (formerly?) open question from Barry Simon's Schrödinger Semigroups. In Theorem C.5.2 (page 504) of that publication, the existence of a specific function ...
1
vote
0answers
177 views

Open problems with practical outcome in a visible future?

[Note] The question has been asked at Matheoverflow. But there is no answers. I believe that any non-trivial idea will sooner or later find application in real life. However "sooner" is better than ...
1
vote
0answers
127 views

Panel structure on epi F**

It is known that, generically, the convex hull of a hypersurface embedded in $\mathbb{R}^n$ has a panel structure of simplices. Of course one can construct embeddings where this is not the case, but ...
1
vote
0answers
212 views

Is there a ccc but not separable space $X$ with a zeroset-diagonal, that isn't submetrizable?

Is there a ccc but not separable space $X$ with a zeroset-diagonal, that isn't submetrizable? separable = $X$ has a countable dense subset. A space $X$ has a zeroset-diagonal when there is a ...
0
votes
2answers
2k views

What is the most important unsolved mathematical problem left? [closed]

Some time ago Andrew Wiles proved fermat's last theorem. The four colour theorem has been proved and Kepler's Conjecture has been proved. But what is the most important mathematical proof yet to be ...
0
votes
1answer
177 views

Proving that $\sum_{k=n}^{2n-2} \frac{|\sin k\ |}{k} < 0.7\ln 2$ for $n\ge2$

Prove that $$\sum_{k=n}^{2n-2} \frac{|\sin k|}{k} < 0.7 \ln 2, \qquad (n\ge2)$$ and $$\cot\left(\frac{\pi}{2n}\right) \le \sum_{k=1}^n \left|\sin\left(x+\frac{k\pi}{n}\right)\right| \le ...
0
votes
1answer
235 views

Waring's Inequality Solution

$$ \text{Waring's problem asks, "Is }\left\lfloor \left(\frac{3}{2}\right)^n\right\rfloor =\left\lfloor \frac{3^n-1}{2^n-1}\right\rfloor\text{ always true?"} $$ We craft an inequality, with $m,n ...
0
votes
1answer
126 views

Catch stochasticity of nature

Do you know of anything that comes close to topic 3 on http://www.darpa.mil/Our_Work/DSO/Programs/23_Mathematical_Challenges.aspx Capture and Harness Stochasticity in Nature Address Mumford’s ...
0
votes
1answer
286 views

symmetric difference of languages - both are in NP and coNP

I have this problem, Let $L_1,L_2$ be languages in $NP \cap co-NP$. I want to show that their symmetric difference is also in $NP \cap co-NP$. Like: $L_1 \oplus L_2 = \{x | x$ is in exactly one of ...
0
votes
1answer
70 views

How can I solve this problem without doing it by hand? [duplicate]

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
0
votes
0answers
5 views

Dominance Network Worded Problems

What are some methods to solve this? Normally for dominance I do as such: Write a matrix for one step dominance, then find total dominance by = D+D^2 - then sum each row of the matrix. Using this ...
0
votes
1answer
22 views

Problem Solving - Project Crashing Time

My working out: (EST,EFT) times for the activities: A: (0,0) B: (0,8) C: (3,3) D: (10,38) E: (10,18) F: (18,18) G: (25,33) H: (58,58) I: (25,33) J: (45,53) K: (118,118) Finish: (133,133) ...
0
votes
0answers
12 views

an idea about the relation between the residues at infinity and the infinity line?

i have a question about the following three concepts for infinity: The point at infinity, also called ideal point, of the real number line is a point which, when added to the number line yields a ...
0
votes
0answers
66 views

Conjecture related to the Erdős discrepancy problem

Conjecture: If $k \in \mathbb{N}$ and $S$ is an infinite set of primes, then the multiplicative $\pm$-sequence generated by $S$ contains $+^k$ as a substring infinitely often. (If $S$ is allowed to ...
0
votes
1answer
64 views

Perfect cuboid cube

Is there any proof that there is no cubic perfect cuboid? Here is a description of the problem: . I'm currently using trying to get an empty set to solve it... [ A "perfect cuboid" is one whose ...
0
votes
0answers
259 views

Possible proof for Frankl's Union-Closed Sets Conjecture?

Frankl's union-closed sets conjecture: if $F$ is a nonempty finite collection of nonempty finite sets, and if $X\cup Y\in F$ whenever $X,Y\in F$, must there be an element which is in more than half ...
0
votes
1answer
58 views

will $x_{n+1}=x_n/2$ if $x_n$ is even; otherwise $x_{n+1}=3*x_n+1$, will $x_n$ shrink to 1?

I was asked this question that, for any $x_1 \in \mathbb{N}$, define the sequence as $$x_{n+1}=\left\{ \begin{array}{l l} x_n/2 & \quad \text{if } x \text{ is even} \\ 3 x_n+1 & ...
0
votes
0answers
128 views

Can an odd perfect number be divisible by 101?

Preamble - This question is an offshoot from the following earlier questions here at MSE: Can an odd perfect number be divisible by 825? Can an odd perfect number be divisible by 165? Odd perfect ...
0
votes
0answers
52 views

Reference for the cardinality equal to continuum of space

Recently, I am considering an open problem, see here. Now, I want to prove the answer to the problem is true when the case that the cardinality of topological space is equal to continuum. However, I ...
0
votes
1answer
89 views

a Problem about Sequence [duplicate]

Let $a_1$ be an integer. Then we assume $$ a_{n+1} = \begin{cases} 3a_n+1,&\text{$a_n$ is odd}\\ \frac{a_n}{2},&\text{$a_n$ is even} \end{cases} $$ Now we prove that for any ...
-3
votes
2answers
132 views

Has the OPN Conjecture been finally proved? [closed]

Has the OPN Conjecture been finally proved? All perfect numbers are even, by Sanjit Singh Batra and Amitabha Tripathi
-5
votes
2answers
2k views

Is the Birch and Swinnerton-Dyer conjecture solved?

I read today that in 2010 Manjul Bhargava with Arul Shankar proved the conjecture basing upon the work of Kolyvagin. Is it right? Does it satisfy for all elliptic curves, or is it limited to some ...
-5
votes
1answer
479 views

Have 3n + 1 Problem Proof --But can't do the Mathspeak [closed]

I've come here as a last resort. When I first saw the Collatz conjecture I worked out pretty quickly what the dynamic was that drove the Collatz sequences. That was in 2009. Since then I've been ...