# Questions tagged [open-problems]

If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"

494 questions
Filter by
Sorted by
Tagged with
180 views

### problems in algebraic geometry

In the section 6 Nonsingular Curves of the "Algebraic Geometry by Robin Hartshorne " I study : "In considering the problem of classification of algebraic varieties, we can formulate ...
196 views

### Dense sets in $\Bbb{R}^2$ with rational distance

We call a subset $S\subset \Bbb{R}^2$ rationally distanced if all $s_1,s_2 \in S$ have rational Euclidean distance. The Erdos-Ulam conjecture asks if there is a dense subset of $\Bbb{R}^2$ which is ...
255 views

### On RH in the Clay Institute list

As everybody knows, the Riemann Hypothesis is one of the problems of the millenium raised by the Clay Institute. Looking at the "official formulation" of various problems, say for instance ...
87 views

### How small the radical of $xyz(x+y+z)$ can be infinitely?

This is an open problem. Let $x,y,z$ be coprime integers (not necessarily pairwise coprime) and no proper subset sum of $\{x,y,z,-(x+y+z)\}$ is zero. For a quadruple $(x,y,z,-(x+y+z))$ define the ...
201 views

### Open problems in matroid theory

I read Oxley's book on matroid theory and found the theory fascinating. At the end, Oxley stated some open problems and conjectures in matroid theory. Are there any modern lists about such problems? ...
236 views

361 views

### What is the state of research on finding all Prime Knots with 17 Crossings?

In this 1998 journal paper, all the prime knots with 16 or fewer crossings are found (some of which were found earlier by others). There are over 1.7 million such knots. But the prime knots with 17 ...
376 views

### Which knot invariants have no known diagram-independent descriptions?

Many knot invariants in knot theory are discovered by finding a property of knot diagrams which is invariant under the three Reidemeister moves. Now in principle, any knot invariant can be described ...
7k views

### Why polynomials with coefficients $0,1$ like to have only factors with $0,1$ coefficients?

Conjecture. Let $P(x),Q(x) \in \mathbb{R}[x]$ be two monic polynomials with non-negative coefficients. If $R(x)=P(x)Q(x)$ is $0,1$ polynomial (coefficients only from $\{0,1\}$), then $P(x)$ and $Q(x)$ ...
63 views

### The Total Graph is similar to a line graph

Consider the total graph of a regular graph. From the structure, it seems that it has a similar structure to the line graph ( two different sub-cliques joining at a single point) except that, in ...
215 views

### How many solutions of x^3 +y^3 = z^3+3 are known? [duplicate]

I've been told that there is reason to think that the equation $x^3 + y^3 = z^3 + 3$ has solutions in positive integers other than $$4^3 + 4^3 = 5^3 +3.$$ Can someone tell me the current status of ...
457 views

136 views

735 views

### Is it known how the Sigma Algebra generated by Jordan measurable sets compares to universally measurable sets and analytic sets?

Unlike the collection $L$ of Lebesgue measurable sets, the collection $J$ of Jordan measurable sets do not form a Sigma algebra. (A set is Jordan measurable if and only if its characteristic function ...
1k views

### Is it still an open problem whether $\mathbb{R}^\omega$ is normal in the box topology?

On page 205 of his Topology textbook, James Munkres made an interesting remark: It is not known whether $\mathbb{R}^\omega$ is normal in the box topology. Mary-Ellen Rudin has shown that the answer ...
Computations suggest that $$\int_{0}^{\infty}\int_{0}^{\infty} \sqrt{x+y^2} \cdot e^{-\frac{1}{2}(\frac{x}{s}+s^2y^2)}dxdy=\frac{2}{s}+\frac{2s^2\arctan(\sqrt{s^3-1})}{\sqrt{s^3-1}}.$$ The question ...
In Michael Atiyah's paper purportedly proving the Riemann hypothesis, he relies heavily on the properties of a certain function $T(s)$, known as the Todd function. My question is, what is the ...