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Questions tagged [gm.general-mathematics]

Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.

-4
votes
0answers
35 views

What is the answer and steps? [on hold]

Find f^(55)*(x). f(x)=e^8x enter image description here
34
votes
2answers
2k views

Mathematical research in North Korea — reference request

Question: Where can one find information on which areas of mathematics are represented at which of the more than 20 universities in the Democratic People's Republic of Korea (DPRK), and on which ...
8
votes
2answers
174 views

Permanent archival of errata/corrigenda for published papers

(Note: This question might be off-topic for MO but the only other plausible alternative that comes to mind is Academia Stack Exchange, and there are some features of this question that are, to some ...
4
votes
1answer
212 views

Applications of De-Bruijn Sequences in “Pure Mathematics”

I know of a few applications of De-Bruijn Sequences and De Bruijn Graphs in combinatorics, applied mathematics, Engineering and computer science. But I have only found one application of De Bruijn ...
3
votes
1answer
331 views

Improvements to one's own theorems

What are some notable (famous?) instances where the following has occurred. A particular author proves: Every P which satisfies Q has property Z. A few years later (roughly speaking) the same ...
7
votes
0answers
200 views

List of modern points of view simplifying or clarifying classical topics

There are many modern mathematical achievements which greatly clarify or (and) simplify classical important topics. I believe a list of such achievements, among other benefits, would be a big help for ...
0
votes
1answer
370 views

“Mathematics is the science of the infinite” [closed]

The title is the first sentence of Hermann Weyl's 1930 essay, "Levels of Infinity." He focuses on "the distinction between actuality and potentiality, between Being and Possibility." He opines ...
7
votes
1answer
284 views

A variant of Cauchy-type functional equation conjecture

Let $f:\mathbb{C}\to \mathbb{C}$ be a complex function such that $$|f(x-y)|=|f(x)-f(y)|,\qquad x,y\in\mathbb{C}.$$ Is it true that $$f(x+y)=f(x)+f(y),\qquad x,y\in\mathbb{C}?$$ The answer is ...
2
votes
1answer
103 views

smallest square containing k non-overlapping equal rectangles at any orientation

This seems like something that should have a known answer, but I haven't found it after some time alternating between searching and generating multiple pages of algebra. I'm interested in $k=4$ and $...
-1
votes
2answers
333 views

Is this expression always irrational? [closed]

Is it right that $$\sqrt[a]{2^{2^n}+1}$$ for every $$a>1,n \in \mathbb N $$ is always irrational?
2
votes
2answers
88 views

Terminology: product on strict preorders corresponding to direct product of preorders?

I’ve had trouble finding a well-established term for the following very obvious and elementary construction on strict partial orders (i.e. transitive, irreflexive relations): Given two strict partial ...
62
votes
16answers
6k views

Short papers for undergraduate course on reading scholarly math

(I know this is perhaps only tangentially related to mathematics research, but I'm hoping it is worthy of consideration as a community wiki question.) Today, I was reminded of the existence of this ...
0
votes
1answer
833 views

What is special about 2 + $\sqrt{3}$?

Well, one thing is special about it, but it takes a while to explain. Please let me know, whether this number occurs in other special occasions as well. The explanation: Let $p$ be a complex ...
0
votes
1answer
46 views

The minimal value of k for making a inequality true [closed]

I was wondering... What is the minimal value of $k$ for making the following inequality true. $(\sum_{x=1}^k (n-x)*x) > nˆ2$. Is there a way to know that? And how can I prove it? I was ...
1
vote
0answers
72 views

Cardinality of sets of Cauchy sequences [closed]

What is the cardinality of the set of all Cauchy sequences made by rational numbers?And why would that be so?
1
vote
1answer
79 views

Dividing Two Functions [closed]

I asked this question in Math StackExchange originally but haven't received an answer. When dividing two functions: $$h(x)=\frac{f(x)}{g(x)},$$ how do we account for the points at which $g(x)=0$ ? ...
2
votes
0answers
118 views

Computing harmonic sum [closed]

I want to show the following equalities for harmonic sum $$\sum_{k=1}^{\infty}\frac{(-1)^k}{k^3}=\lim_{n\to\infty}\int_0^{2n}\frac{-3}{x^4}([x]-2[\frac{x}{2}])dx$$ Any idea?
3
votes
0answers
111 views

What is the name of this substructure/embedding?

I am interested in the following property, be it on an abstract or concrete category: $A$ is a substructure of $B$ such that every automorphism of $A$ extends uniquely to an automorphism of $B$. Or ...
0
votes
1answer
50 views

Equivalent linear inequalities system - Coefficients bound?

Just having some difficulties with this system of inequalities... We know E is a system of m linear inequalities of the form: a1,1x1+ ··· +a1,nxn ≤ b1 ... am,1x1+ ··· +am,nxn ≤ bm And E' an ...
25
votes
2answers
2k views

Why aren't proceedings from ICM 2014 on mathscinet?

Articles from the Proceedings of the International Congress of Mathematicians, Seoul, 2014 don't appear to be on Mathscinet. Why is this? (Someone pointed this out to me recently, and I was reminded ...
2
votes
1answer
147 views

Elementary question about linear algebra on a circle

Let $T = {\mathbb R}/{\mathbb Z}$ be the $1$-torus. Let $a_{ij}$ be integer numbers, $1 \leq i \leq m$, $1 \leq j \leq n$ and $A$ the $m \times n$ matrix whose $(i,j)$ entry is $a_{ij}$. Consider the ...
4
votes
1answer
103 views

Explicit generalizations of Mobius transformations?

Mobius transformations map circles to circles. Wiki says 'Möbius transformations can be more generally defined in spaces of dimension n>2 as the bijective conformal orientation-preserving maps from ...
37
votes
5answers
4k views

How to improve writing mathematics?

My first language is not English. How can I improve my mathematical writing. I feel like the only things I can write down are numbers and equations. Is there any good suggestion for improving writing, ...
1
vote
1answer
137 views

Has a quasi-polynomial $\mathbb N\to\mathbb N$ just rational coefficients? [closed]

If $f(x) = a_k(n)n^k + \dots + a_1(n)n + a_0(n)$ is a quasi-polynomial (i.e. with $a_0, \dots, a_k$ being periodic functions) from $\mathbb N$ to $\mathbb N$, does it follow that all the coefficient ...
128
votes
43answers
22k views

17 camels trick

The following popular mathematical parable is well known: A father left 17 camels to his three sons and, according to the will, the eldest son should be given a half of all camels, the middle son ...
54
votes
8answers
4k views

Fascinating moments: equivalent mathematical discoveries

One of the delights in mathematical research is that some (mostly deep) results in one area remain unknown to mathematicians in other areas, but later, these discoveries turn out to be equivalent! ...
67
votes
13answers
4k views

What computational problems would be good proof-of-work problems for cryptocurrency mining?

What computational mathematics problems that could be used as proof-of-work problems for cryptocurrencies? To make this question easier to answer, I want proof-of-work systems that work in ...
8
votes
1answer
215 views

Convention of Address in math journals?

The paper was written and submitted when I was in Institution A. After (many) years, the paper is accepted when I am in Institution B. Which address shall I put on the paper? The current address (...
30
votes
3answers
2k views

Frequency of papers showing academic misconduct among the articles indexed by MathSciNet and Zentralblatt MATH

Among the papers indexed by MathSciNet and Zentralblatt MATH, I occasionally have seen papers which consist essentially only of text copied from elsewhere without proper attribution and without adding ...
2
votes
1answer
214 views

Solving a transcendental equation, in closed form

There is a change of variable between two varibles $q$ and $Q$ as the following: $$q=Q\exp(2f(Q))\quad\quad \quad (*)$$ where $f(Q)$ is given by $$f(Q)=\sum_{d=1}^\infty \frac{(2d-1)!}{(d!)^2}Q^d$$ ...
5
votes
3answers
950 views

Solution to a Diophantine equation

Find all the non-trivial integer solutions to the equation $$\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=4.$$
2
votes
2answers
145 views

A general question on comparison of integrals and a specific problem

When working on an applied math topic, I have come across the following general problem. Let $f(x_1, x_2, ..., x_n)$ be a real function of $n$ real variables $x_1, x_2, ..., x_n$ which is ...
8
votes
4answers
946 views

Computationally challenging integer sequences

I wonder what are the examples of integer sequences, where only few elements are known and the researchers are still actively looking for the new terms. I think this discussion might be a good ...
66
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7answers
7k views

Books on music theory intended for mathematicians

Some time ago I attended a colloquium given by Princeton music theorist Dmitri Tymoczko, where he gave a fascinating talk on the connection between music composition and certain geometric objects (as ...
1
vote
0answers
153 views

R.H. equivalent statement condition

Is the inequality $\prod \limits_{p \leq \sqrt{x}} (1+\frac{1}{p^2-1}) \prod \limits_{p \leq x} (1+\frac{1}{p}) \leq e^\gamma \ln(\theta(\sqrt{x})+\theta(x))$ where $\theta(x)$ is the Chebyshev's ...
10
votes
8answers
3k views

Most important mathematical results in last 30 years [closed]

Which results from the last 30 years, in any area of mathematics, do you think are the most important ones? Specifically, which are the ones that will have more impact across all math and/or settle ...
17
votes
4answers
1k views

A seemingly simple inequality

Let $a_i,b_i\in\mathbb{R}$ and $n>1$, does the inequality $$ \left(\sum_{i=1}^n a_i^2\right)\left(\sum_{i=1}^n b_i^2\right)+\left(\sum_{i=1}^na_i b_i\right)^2\ge \sqrt{\left(\sum_{i=1}^n a_i^4\...
1
vote
0answers
116 views

repeated addition and square root of fixed number

pick any real number $x$ and integer $k$ and do the following recursive : 1) $x_0 =x $ 2) $x_{n+1} = x_n + \sqrt x_n$ using only $x$ and $k$ how to find the value of $x_k$ without going through ...
0
votes
1answer
120 views

Numerical Calculations

i have this numerical calculation problem : $$\prod \limits_{i=121443371}^{455052511} 1+\frac{1}{p(i)} \leq 1.06406506887043952285362856325019948 $$ such that $p(i)$ is the $i$-th prime number i ...
5
votes
1answer
412 views

What structure do you get if you adjoint a root of $z \bar{z} = -1$ to the complex numbers?

A pop-up is informing me that my question is likely to be closed. Still, recall that the complex numbers $\mathbb{C}$ was conceived by trying to adjoint a root of the equation $x^2 = - 1$ to the ...
14
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0answers
489 views

Decidable open problems

Are there any significant open problems in mathematics which are clearly decidable (in that it is easy to write a clearly corresponding program which will eventually output either Yes or No (or ...
3
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2answers
1k views

the math behind the sequence 0,1,153,370,371,407

i was researching the numbers that are equal to the sum of their digits raised to the third power . like $153=1^3 + 5^3+3^3$ and i have 3 questions. 1) from any starting number $n$ ,do we always ...
1
vote
1answer
201 views

inequality involving increasing functions

Let $a_k$ and $b_k$ be ascending positive numbers for $1\leq k \leq K+1$. If it is known that $$\frac{K\left(\exp\left(\frac{1}{K}\sum_{k=1}^K b_k\right)-1\right)}{\left(\sum_{k=1}^K \sqrt{a_k} \sqrt{\...
9
votes
1answer
442 views

Applications of Morley's Categoricity Theorem

I just attended a lecture by Rami Grossberg and he mentioned that he is not aware of any applications of Morley's Categoricity Theorem. This is exactly my question. Question: Do you know of any ...
16
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0answers
845 views

What to do with results you found but cannot prove(outside your research area)?

Not sure if MathOverflow is still a place to discuss such things, but I'll give it a try. Tell me an alternative site, in case it is wrong here. I translated a representation-theory/combinatorial ...
32
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1answer
3k views

How much mathematics has been formally verified?

That's a vague question so allow me to tighten it up a bit. I recently noticed that there is a formal machine verified proof of the Central Limit Theorem (CLT) implemented with Isabelle. This ...
-2
votes
1answer
286 views

Correction symbols used for mathematical texts [closed]

When proof reading and correcting a mathematical text, I sometimes see people use special notation symbols in the margin to indicate correction, deletion, replacement and so on. Is there any standard ...
7
votes
1answer
720 views

On the parity of $[x^n]$

I am trying to find a problem which appeared years ago in the American Mathematical Monthly. It went something like this: There was a Putnam Competition question which asked to show that there is a ...
28
votes
4answers
1k views

Expert, Intuitive, Organizing Analogies

In learning a new area it is very helpful to have high-level intuitive analogies that keep track of the various parts of an important argument or strategy. Experts have a store of such things, and ...
41
votes
25answers
7k views

Where can square roots come from when they are not distances?

In a recent survey "Supergeometry in Mathematics and Physics", Kapranov points out cases in which observable quantities of immediate interest are represented as bilinear combinations of more ...