# 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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### Is spherical trigonometry a dead research area?

When I was an undergrad, the field of spherical trigonometry was cited as a once-popular area of math that has since died. Is this true? Are the results from spherical trigonometry relevant for ...
9k views

### 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 ...
59 views

### Computation involving Gauss integer function

I have used mathematica to test following equation is true \begin{equation} \sum_{a,b=0}^{m-1} \left[\frac{a+b n}{m}\right] = \frac{n m^2}{2} -\frac{nm}{2} \end{equation} where $[x]$ is the floor ...
536 views

### What is the most "informative" Yes/No math question you know? [closed]

Imagine that alien civilization contacted you and offered to answer one math question. This should be a Yes/No question (so, you cannot ask for a million-digit binary string encoding the answers to a ...
1 vote
38 views

### The exact distribution of the conditional distribution of the OLS estimator

This is the problem that I have tried figuring it out for a while, and I still need some advice because there is no explicit derivation in the textbook that I have seen so far. The problem looks easy ...
99 views

### What is the meaning of PUP in remarks?

I see the remarks in Gowers’s The Princeton Companion to Mathematics. What is the meaning of the abbreviation ‘PUP’? Never seen before…
277 views

### Can you get any natural number from 4 by performing given operations?

You can perform the following operations on numbers: divide the number by 2, add 0 or 4 at the end of the number. Can you get any natural number from 4 by performing only these operations? So far I ...
1k views

### Surprising applications of the theory of games?

I am currently studying the applications of games in quantum information theory and related fields and I am aware of its uses in places like model theory and set theory. So I was curious, what are ...
67 views

### How to eliminate angle in a Glissette equation of carried point of a line sliding along two lines not at right angles

Glissettes are the curves trances out by a point carried by a curve, which is made to slide between given points or curves. My problem specifically include a line which slides between two fixed lines (...
10k views

### Conceptual reason why the sign of a permutation is well-defined?

Teaching group theory this semester, I found myself laboring through a proof that the sign of a permutation is a well-defined homomorphism $\operatorname{sgn} : \Sigma_n \to \Sigma_2$. An insightful ...
488 views

### How far away can we get by multiple rounding and unit change?

This question is inspired by xkcd #2585 (Rounding): Let $u_0,\ldots,u_n$ be positive real numbers (we can assume w.l.o.g. that $u_0=1$) or “units”. Consider the following directed graph: its vertices ...
47 views

### How can C2 double-helices, produce C3 rotational symmetry?

I am trying to solve the structure of a helical protein complex using a software for maximum a posteriori refinement of (multiple) 3D reconstructions (Relion). When searching for helical symmetry, the ...
99 views

### Algorithm for compact polynomial expressions

Sometimes an ugly polynomial (perhaps in several variables) can be expressed as a small sum of much simpler polynomials. Can this be done algorithmically? More precisely: Is there a reasonable ...
218 views

### Récoltes et Semailles for the non (algebraic-) geometer

With the recent publication of Grothendieck's Récoltes et Semailles, I've been umm-ing and ah-ing about whether to get a copy, if only for the "soaking nuts" story. My French reading is ...
801 views

### Progress in robustifying mathematics - i.e. making mathematical theorems robust to small changes in hypotheses

The idea of making a mathematical theorem robust to small changes in its hypotheses has been known for some time. In areas such as group theory reasonable progress has been made leading to the theory ...
663 views

6k views

### Is pure mathematics useful outside of mathematics itself? [closed]

From time to time Mathoverflow allows soft questions because they are arguably best answered by active mathematicians and they can benefit other mathematicians/PhD students/math undergraduates. I ...
196 views

### 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 ...
1 vote
193 views

439 views

### how to prove this high degree inequality

Let $x$,$y$,$z$ be positive real numbers which satisfy $xyz=1$. Prove that: $(x^{10}+y^{10}+z^{10})^2 \geq 3(x^{13}+y^{13}+z^{13})$. And there is a similar question: Let $x$,$y$,$z$ be positive real ...
94 views

### Existence of functions satisfying a homogeneity condition

Do there exist a (non-trivial) globally Lipschitz continuous function $g:\mathbf{R}\to\mathbf{R}$ and a non-decreasing function $f:\mathbf{R}_+\to\mathbf{R}_+$ such that the identity \begin{equation} ...
269 views