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.
Questions tagged [gm.general-mathematics]
344 questions
50
votes
13 answers
Is amateur research in mathematics viable?
After a long reflection, I've decided I won't go to graduate school and do a thesis, among other things. I personally can't cope with the pressure and uncertainty of an academic job.
I will therefore move towards a master's degree in engineering and…
Nilav
- 61
40
votes
14 answers
A set for which it is hard to determine whether or not it is countable.
I got thinking recently, while trying to come up with a problem, that I did not know of any sets which were reasonable to define but for which it was very difficult to determine whether or not they were countable or uncountable.
When one first…
Spencer
- 1,771
25
votes
14 answers
What are some examples of "chimeras" in mathematics?
The best example I can think of at the moment is Conway's surreal number system, which
combines 2-adic behavior in-the-small with $\infty$-adic behavior in the large. The surreally
simplest element of a subset of the positive (or negative)…
James Propp
- 19,363
18
votes
3 answers
Heat map of current mathematics
The recent article on Quanta
(by Natalie Wolchover)
concerning $\aleph_1$ vs. $\aleph_2$ suggests that there is
excitement within that community:
Juliette Kennedy: "It’s one of the most intellectually exciting, absolutely dramatic things that has…
Joseph O'Rourke
- 149,182
- 34
- 342
- 933
14
votes
4 answers
Applications of Zariski topology outside alg. geometry
Are there applications of the Zariski topology in mathematics that are not within the scope of algebraic geometry (including schemes and algebraic groups) ?
There is an older question with a similar title (What is the Zariski topology good/bad for?…
Todd Leason
- 1,999
10
votes
2 answers
What is the strategy for "all words valid" scrabble?
The rules for "all words valid" scrabble are exactly the same as ordinary scrabble, except that every single combination of letters is in the dictionary. To make the game deterministic, we will also assume that every letter is worth the same amount…
Phil
- 101
10
votes
1 answer
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 (Institution B) will soon expire since I will have to…
7-adic
- 3,764
9
votes
4 answers
Is there any monoid in which the product of two non-invertible elements could be invertible?
I think the title speaks for itself. Thus I just explain the story behind the question. Of course, you may want to skip the story.
Story: Currently, I teach a course in linear algebra and matrices with a mathematician colleague of mine. In preparing…
Amir Asghari
- 2,277
- 3
- 40
- 58
5
votes
0 answers
What's with the speaker's initial thing?
If you've ever been to a math talk (at least in pure maths in the UK) you've probably seen something like this written:
Theorem (E.--Johnson--Smith, 2022+) The XYZ conjecture is true.
At some point you probably realized that writing "E." is the…
Sean Eberhard
- 9,195
5
votes
1 answer
How the solve the equation $\frac{(a+b\ln(x))^2}{x}=c$
I need to solve the equation
$$\frac{(a+b\ln(x))^2}{x}=c$$
where $a$, $b$, and $c$ are given. It is known that $a$ and $b$ are fixed and satisfy some condition such that the left hand side is decreasing. So $x$ is uniquely determined by $c$ when $c$…
wyw
- 59
5
votes
1 answer
Is the solution to this trig function known to be algebraic or transcendental?
This largest solution to this gorgeous equation is the first local extremum on a function related to the Fibonacci sequence:
$$x^2 \cdot \sin \left(\frac{2\pi}{x+1} \right) \cdot \left(3+2 \cos \left(\frac{2\pi}{x} \right) \right) = (x+1)^2 \cdot…
Mitch
- 195
4
votes
0 answers
Is my equation for finding the length of a curve correct?
My son has been working on equations for finding length of the length of a curve without any resources (computers, calculators...) while in prison. He is wondering if he is on the right path. Sadly my understanding of mathematics is severely…
3
votes
0 answers
Reference request: name of a transform
Define a transform on polynomials which is linear and acts on each monomial as $$\widehat{z^k} = \frac{(1+z)(2+z)\ldots(k+z)}{k!}.$$ Does anyone know whether this has a name (and therefore has been studied)?
(Also, not sure what to tag this with...…
genneth
- 275
3
votes
0 answers
Where does Aphex Twin's "windowlicker" equation come from?
$\Delta M_i^{-1} = -\alpha \sum\limits_{n=1}^N D_i [n] \left[\sum\limits_{j \in C[i]} F_{ji} [n-1] + Fext_i [n^{-1}]\right]$
This is the name of the second song on Aphex Twin's album "Windowlicker". It comes with no variable descriptions or other…
James
- 31
3
votes
0 answers
Does this trig equation have a closed-form solution?
This equation came up when I was looking at the Fibonacci sequence; I adore its symmetry:
$$x^2 \cdot \sin \left(\frac{2\pi}{x-1} \right) \cdot \left(3+2 \cos \left(\frac{2\pi}{x} \right) \right) = (x-1)^2 \cdot \sin \left(\frac{2\pi}{x} \right)…
Mitch
- 195