Questions on problems that have yet to be completely solved by current mathematical methods.
11
votes
0answers
159 views
Any proof to $\pi^{e}$'s irrationality?
I've searched for this for a while but get nothing...
There are plenty of proofs to irrationality of $e$,$\pi$,$e^{\pi}$. However, I can't find a proof for $\pi^e$. More, when searching for this I ...
1
vote
2answers
114 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
111 views
Is “P vs NP” problem solved?
Many people have tried to solve the very famous problem "P vs NP" and a lot of solutions are proposed. (e.g. A. D. Plotnikov, On the Relationship between Classes P and NP). But I couldn't find any ...
11
votes
2answers
380 views
Has anyone found a “pattern” in prime numbers?
Yesterday I was having some fun trying to look for some patterns in primes; and I think I found something interesting (to me at least). I still have not found any lists of patterns already found, ...
0
votes
1answer
123 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 ...
-5
votes
1answer
204 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 ...
2
votes
0answers
40 views
What relationship(s) [if any] exist between primorial primes and palindromic primes?
Information on primorial primes are in the following hyperlinks:
MathWorld - Primorial Prime
Wikipedia - Primorial Prime
On the other hand, we have the following hyperlinks providing information on ...
0
votes
0answers
41 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 ...
7
votes
1answer
90 views
Independence results that cannot be established by forcing.
I read the Wikipedia article on Absoluteness recently and found mention of Shoenfield’s Absoluteness Theorem, which states that if $ \phi $ is any $ \Sigma^{1}_{2} $- or $ \Pi^{1}_{2} $-sentence of ...
5
votes
1answer
138 views
A question on Paul Erdős's research on Egyptian fractions
A good day to everyone!
I have a (somewhat) intriguing question regarding Paul Erdős's papers on Egyptian fractions (e.g., his 2nd paper during his mathematical career was about this topic).
My ...
12
votes
2answers
130 views
Status of the classification of non-finitely generated abelian groups.
From the Wikipedia on abelian groups:
By contrast, classification of general infinitely-generated abelian groups is far from complete.
How far are we from a classification exactly? It seems ...
4
votes
1answer
136 views
Some contradiction in an open problem
Recently, I'm considerring an open problem from the paper by Ofelia T.Alas and others':On the extent of star countable spaces. It easily can be downloaded by google. The open Problem is this:
...
1
vote
0answers
48 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 ...
7
votes
0answers
97 views
What turmite runs the longest before becoming predictable?
When looking at 2D Turing machines, many of them eventually become predictable. For example, Langton's Ant, the champion 2-color 1-state turmite, develops a highway after 10,000 steps. Predictable ...
3
votes
0answers
122 views
An open problem on general topology
There is an open problem in this paper: Classesdefined by starsand neighbourhood assignments by van Mill and others.
Problem 4.8. Is a regular star compact space metrizable if it has a ...
5
votes
1answer
117 views
Hausdorff Dimension of Arbitrary Julia Set
I am looking to find an exact solution to the Hausdorff dimension of a Julia set $J(f)$ for a polynomial $f: z \mapsto z^2 +c$ given an arbitrary $c$.
I know this question is known for a number of ...
3
votes
0answers
66 views
Polyonimo Tiling
I came up with the following conjecture the other day, and was wondering if the result was well-known or even true:
Define $f(P)$ for a polyomino $P$ (without holes) to be the least number of total ...
6
votes
2answers
119 views
How many partial order on a n-set?
Let $A$ be a set has $n$ element, my question is how many partial order on it?
For $n=0,1$, $N_P(n)=1$
Case $n=2$, $N_P(n)=3$
Case $n=3$, $N_P(n)=19$
Is there a general formula?
Update:
It seems ...
3
votes
1answer
241 views
Which side has winning strategy in Go?
Go is actually a finite two-person game of perfect information and cannot end in a draw. Then by Zermelo's theorem, it is exactly one of the two has winning strategy, either Black or White.
So my ...
7
votes
2answers
363 views
When is $\left\lfloor \frac {7^n}{2^n} \right\rfloor \bmod {2^n} \ne 0\;$?
Is
$$\left\lfloor \frac {7^n}{2^n} \right\rfloor \bmod{2^n} \ne 0\;$$
always true when $n \ge 3$.
Baker's theorem on transcendental numbers that provide bounds for diophantine equations may be ...
3
votes
0answers
427 views
Lists of open problems in set theory
Are there any publicly available lists of open problems in set theory besides the following ones? (And if so, what are they?)
http://www.math.wisc.edu/~miller/res/problem.pdf
...
0
votes
2answers
593 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 ...
21
votes
5answers
1k views
Can someone explain the ABC conjecture to me?
I am an undergrad and I know that the conjecture may have been proven recently. But in reading about it, I am entirely confused as to what it means and why it is important. I was hoping some of you ...
2
votes
0answers
39 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 ...
8
votes
1answer
345 views
What are possibilities to disprove the Collatz Conjecture?
I was thinking about the Collatz Conjecture yesterday, and as opposed to trying to prove it, I was considering what would make the conjecture false. There were only two cases I could think of:
We ...
10
votes
3answers
468 views
Solving P vs NP with computer
Is it possible to build a computer program that would (eventually) bring a solution to the P vs. NP question?
21
votes
14answers
2k views
How can we produce another geek clock with a different pair of numbers?
So I found this geek clock and I think that it's pretty cool.
I'm just wondering if it is possible to achieve the same but with another number.
So here is the problem:
We want to find a number ...
10
votes
2answers
493 views
Why is Hodge more difficult than Tate?
There are strong connections between the Hodge and the Tate conjectures, mainly at the level of similarities and analogies. To quote from an answer of Matthew Emerton on MathOverflow:
"[...] we ...
8
votes
1answer
352 views
Thoughts on the Collatz conjecture; integers added to powers of 2
I've had a thought about the Collatz conjecture (the 3n+1 problem).
Suppose some number, C, diverges under the iteration. We first note that C must be odd because if C were even it would be halved ...
4
votes
3answers
267 views
If a graph of $2n$ vertices contains a Hamiltonian cycle, then can we reach every other vertex in $n$ steps?
Problem: Given a graph $G,$ with $2n$ vertices and at least one triangle. Is it possible to show that you can reach every other vertex in $n$ steps if $G$ contains a Hamilton cycle (HC)?
EDIT: ...
2
votes
2answers
207 views
Triplets based equation
Let $p \ge 7$ be a prime number. Find the triples $(x, y, z)$ in $\mathbb{Z}$ such as $xyz$ is not equal to zero, $\gcd (x, y, z) = 1$ and $x^p + 2y^p = z^2$. I want triplets and proof/generalization. ...
0
votes
1answer
95 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 ...
7
votes
3answers
710 views
What does proving the Collatz Conjecture entail?
From the get go: i'm not trying to prove the Collatz Conjecture where hundreds of smarter people have failed. I'm just curious.
I'm wondering where one would have to start in proving the Collatz ...
3
votes
2answers
115 views
Variation of the inscribed square problem
The inscribed square problem (summary here) is currently open:
Does every Jordan curve admit an inscribed square?
(It is not required that the vertices of the square appear along the curve in ...
0
votes
1answer
174 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 ...
8
votes
2answers
541 views
What does the Hodge conjecture mean?
I read from the Internet that according to the Hodge conjecture, a certain harmonic differential form in a projective, non-singular algebraic variety is a rational linear combination of the cohomology ...
1
vote
0answers
108 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 ...
-2
votes
1answer
360 views
Most famous Mathematical open problems? [closed]
I wanted to get a list of the most famous open problems in Mathematics.
Like in Number theory RH is the most famous open question. In Topology the smooth 4th dimension generalization of the Poincare ...
5
votes
1answer
214 views
Open problems in Mathematical Tomography?
Since I feel that Tomography can be applied to a wide range of sciences, I was wondering what the current open problems in Tomographic Reconstruction are.
Furthermore, I am curious as to how these ...
1
vote
1answer
152 views
Cube nets hexomino tilings.
I am looking for an ~12x12 rectangle (small holes and small obtrusions are okay) made entirely of cube net hexominos.
It is my understanding that perfect rectangles, in general, are not possible ...
0
votes
3answers
299 views
Tiling with polyominos
How to prove or disprove that if a polyomino tiles the plane, it must also be able to perfectly tile some larger polyomino, which also tiles the plane?
A polyomino is finite set of unit squares ...
3
votes
2answers
305 views
Are there infinitely many primes of the form $6^{2n}+1$ or only finitely many?
Does anyone know whether there are only finitely many of primes of the form $6^{2n}+1$, where $n$ zero or any natural number?
7
votes
1answer
310 views
Any serious work on Lychrel numbers/$196$-Algorithm?
I've been googling around a little lately and have stumbled across the so called Lychrel problem. For a natural number $x$, let $Rx$ denote the number obtained by reversing the base-$10$ digits of $x$ ...
4
votes
2answers
516 views
Undergraduate Research Problems
I'm a third year undergrad with this summer off so would appreciate some material to look at.
I took courses in Galois theory, Topology, Complex analysis, ...
My main interest is in Analysis / ...
1
vote
0answers
113 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 ...
7
votes
1answer
202 views
What is the importance of 3n in the Collatz Conjecture?
I'm not mathematician, so forgive me if I make wrong assumptions. I was wondering what the importance of the $3n$ is in the Collatz Conjuncture.
If you just do $n + 1$, it seems you'll end up at $1$ ...
2
votes
0answers
198 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 ...
2
votes
1answer
101 views
Can 7 Hoffman-Singleton graphs cover $K_{50}$?
Three copies of the Clebsch Graph can cover $K_{16}$, the complete graph on 16 vertices. This is part of the demonstration that $\mathrm{Ramsey}(3,3,3) > 16$.
The Hoffman–Singleton graph is a ...
2
votes
0answers
287 views
Social Golfer Problem - Quintets
I wrote an article on the Social Golfer Problem, which has questions like:
Each day, 16 people play Munchkin in foursomes simultaneously. How many days can they play with no two people playing with ...
4
votes
0answers
110 views
Is the maximal temperature of the curlicue fractal acheived by $e\times\gamma$?
The Curlicue Fractal is defined as follows:
Choose an irrational number $s$ and a horizontal unit segment with angle $\phi_0 = 0$. Define $\theta_{n+1} = \theta_{n} + 2 \pi s \pmod{2 \pi}$, with ...
