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.
230
questions
3
votes
0answers
119 views
Algebraic applications of an order-theoretic idiom of recursion
Many algebraic constructions must surely use the following observation, probably disguised as one of its proofs:
Lemma Let $s:X\to X$ be an endofunction of a poset such that
$X$ has a least element $...
0
votes
0answers
36 views
“Anti-Leibniz order”
It seems that some people use the term "anti-Leibniz order" for what I'd call the "diagrammatic order" of composition: writing $f;g$ for the composition of $f$ and $g$ instead of $g\circ f$.
(I have ...
0
votes
0answers
188 views
When can a co-author be trusted? [closed]
Suppose that you are writing a paper in collaboration with a co-author from a different mathematics area, each author writing a part. Can you trust your co-author about the details of his/her part or ...
-3
votes
0answers
31 views
RPM Calculation [closed]
How can I determine the RPM needed to make an object travel 120in on a conveyor belt in 1min?
I know 3 things:
1.) the length of the conveyor belt (distance between first and last wheel) is 120in
2....
17
votes
3answers
734 views
Examples of improved notation that impacted your research?
The intention of this question is to find practical examples of improved mathematical notation that enabled actual progress in someone's research work.
I am aware that there is a related post ...
2
votes
0answers
119 views
Studying the vast world of Number Theory [closed]
I'm a high school student, interested in mathematics, especially in number theory.
While preparing for the IMO test, and thinking about generalizations or the root of many olympiad problems led me to ...
34
votes
5answers
3k views
The origin(s) of the word “elliptic”
The word elliptic appears quite often in mathematics; I will list a few occurrences below. For some of these, it is clear to me how they are related; for instance, elliptic functions (named after ...
12
votes
2answers
385 views
Number triangle
This question arose just out of curiosity. Note the triangle of 0-1's below, whose construction is as follows. Choose any number, say 53 as done here. The first line of the triangle is the binary ...
8
votes
1answer
630 views
Recreational mathematical papers [closed]
Sometimes it is nice to get a less technical paper on mathematics to read and learn something different for a change. These papers often make us discover some new curiosity, to think about the process ...
1
vote
0answers
138 views
Advice for graphic tablet for math [closed]
With the current Coronavirus disease (COVID-19), many of us had to switch all our activity to full online mode.
I am wondering whether some of you had the chance to use graphic tablets. I am looking ...
-4
votes
1answer
241 views
PCP theorem to check hard proofs [closed]
Is it technically possible to check formidable proofs like Mochizuki's using PCP theorem before mathematicians spend time in understanding the mechanics of the proof? If so why have mathematicians not ...
0
votes
1answer
46 views
Rule to determine rotationally invariant orders of the points of arbitrary 2d splines
I would like to find a rule to determine the order of the points of arbitrary 2d splines, which should be invariant with respect to rotation (as far as possible).
To illustrate the problem, let us ...
3
votes
1answer
304 views
Journey into a strange wilderness [closed]
W. S. Anglin wrote
Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the ...
11
votes
4answers
1k views
Quirky, non-rigorous, yet inspiring, literature in mathematics
In contrast with such lucid, pedagogical, inspiring books such as Visualizing Complex Analysis by Needham and Introduction to Applied Mathematics by Strang, I've had the pleasure of coming across the ...
11
votes
3answers
1k views
How can I simplify this sum any further?
Recently I was playing around with some numbers and I stumbled across the following formal power series:
$$\sum_{k=0}^\infty\frac{x^{ak}}{(ak)!}\biggl(\sum_{l=0}^k\binom{ak}{al}\biggr)$$
I was able ...
69
votes
6answers
9k views
Is data science mathematically interesting?
I have seen a plethora of job advertisements in the last few years on mathjobs.org for academic positions in data science. Now I understand why economic pressures would cause this to happen, but from ...
0
votes
1answer
161 views
What exactly does it mean for a definition/example to be informal in Math? [closed]
Came across "(Informal)" while reading Analysis I by Tao . What exactly constitutes an example or a definition that is formal ?
Definition 3.1.1. (Informal) We define a set A to be any unordered ...
1
vote
5answers
602 views
Famous conjectures named after a mathematician that were resolved in their lifetimes [closed]
This is a question that I thought about recently, and I thought would be interesting to the MO community.
What are some famous conjectures, more specifically those that attracted a lot of attention ...
0
votes
2answers
557 views
Why does $\sqrt 5$ occur in manageable situations of these scenarios?
Banach-Mazur distance between $P_5$ and $P_3$ is $d(P_5,P_3)=1+\frac{\sqrt5}2$ where $P_n$ is regular polygon in $n$ sides https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7968198&tag=...
25
votes
5answers
4k views
Is the field of q-series 'dead'? [closed]
I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead ...
5
votes
5answers
223 views
Peculiarities in low dimensions or low order or etc
I have been pondering about certain conjectures and theorems viewed as either low vs high dimensions, or smaller vs larger primes, or anything of the sort "low vs high order". Let me mention a couple ...
2
votes
0answers
72 views
How can I prove that the following function is increasing according to x1?
Suppose that
$0 \le {X_1} < {X_2} < {X_3}$
.
How is it possible to prove the following function is increasing based on
${X_1}$
in the range of
$0 \le {X_1} < {X_2}$ ?
$f({X_1},{X_2},{X_3})...
0
votes
1answer
287 views
Integrals I am curious about [closed]
Let $C_n(x) = \frac{n!}{\Gamma(x)\cdot \Gamma(n-x)}$
Is the following true: $\int_{0}^{n} [C_n(x)\cdot y^x \cdot (1-y)^{n-x}dx] = 1$??
just wondering
In generality for continuous functions $f,g$ ...
4
votes
0answers
391 views
What solutions to useful computational problems could be rewarded through cryptocurrency smart contracts?
What kinds of cryptocurrency smart contracts could be used to reward people for solving specific kinds of useful computational problems?
Background
In this question, I asked for proposals for useful ...
4
votes
0answers
212 views
Looking for U.K. problem column (?) from 1980s
While digging through some dusty corners of my file cabinet, I found a photocopied sheet of eight (handwritten) problems from 1985 that I recall receiving from my secondary school mathematics teacher ...
20
votes
1answer
1k views
What is known about the common knowledge of mathematicians outside their field?
When giving a talk or writing a paper intended for non-specialist (i.e., mathematicians not specializing in the topic being discussed), the question inevitably occurs of what one can assume to be "...
41
votes
3answers
3k 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 ...
14
votes
2answers
421 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
234 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
395 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
240 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
454 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
296 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
2answers
167 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
341 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
103 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 ...
75
votes
16answers
7k 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
854 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
47 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
88 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
83 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
126 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
118 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
150 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 ...
5
votes
1answer
151 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 ...
148
votes
9answers
22k views
Endless controversy about the correctness of significant papers
In principle, a mathematical paper should be complete and correct. New statements should be supported by appropriate proofs. But this is only theory. Because we often cannot enter into the smallest ...
38
votes
5answers
5k 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
140 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 ...
