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.

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3
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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 $...
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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 ...
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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 ...
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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....
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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
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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
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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
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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
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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 ...
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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 ...
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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
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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
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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 ...
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4answers
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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 ...
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3answers
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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
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6answers
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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
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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 ...
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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 ...
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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=...
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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
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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
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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})...
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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 $f,g$ ...
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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
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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 ...
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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 "...
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3answers
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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
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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
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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
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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 ...
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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 ...
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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
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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 ...
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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 $...
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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
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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 ...
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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 ...
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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
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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 ...
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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?
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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
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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?
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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
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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 ...
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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
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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
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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
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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
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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
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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 ...

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