Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with gm.general-mathematics
Search options answers only
not deleted
user 2926
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.
34
votes
Is amateur research in mathematics viable?
As someone who has gone through a in-some-ways similar experience, I don't think you would be ostracized, and yes, you absolutely could still publish work. You might need people to endorse your work, …
- 53.3k
3
votes
Structures that turn out to exhibit a symmetry even though their definition doesn't
Some categories are self-dual in ways not obvious from their definitions.
One good example is Pontryagin duality, which states that the category of locally compact Hausdorff abelian groups is self-d …
- 53.3k
18
votes
17 camels trick
Evaluation of definite integrals via the method of differentiation under the integral sign has this character. This probably needs no introduction, but the idea is to view the integrand $f(x)$ of $\in …
- 53.3k
4
votes
Are there proofs that you feel you did not "understand" for a long time?
The recent answer by coudy reminds me that for a very long time I didn't really grok the proof of Minkowski's inequality from Hölder's inequality, even though it's fairly simple. It just looks like a …
- 53.3k
9
votes
Where can square roots come from when they are not distances?
Fixed points of fractional linear transformations $x \mapsto \frac{ax + b}{cx + d}$, where $a, b, c, d$ are integers, are usually quadratic surds. Equivalently, values of periodic regular continued fr …
- 53.3k
17
votes
Applications of Lawvere's fixed point theorem
It follows from Lawvere's theorem that for most spaces $X$ there is no space-filling curve for its path space, $\alpha: I \to X^I$, working here in the category of $k$-spaces. (Yes, that would also fo …
- 53.3k
21
votes
A search for theorems which appear to have very few, if any hypotheses
The theorem of Nash and Tognoli says that any compact smooth manifold is diffeomorphic to a nonsingular real algebraic set.
- 53.3k
14
votes
Sophisticated treatments of topics in school mathematics
Another categorical example: the laws of arithmetic, as applied to the arithmetic of finite integers, are ultimately explicable by the fact that the category of finite sets $\mathbf{Fin}$ is a cartesi …
- 53.3k
17
votes
Accepted
What is the term for combining functions $f_1,f_2,\dots,f_n$ into a tuple $(f_1,\dots,f_n)$?
I was encouraged to make my comment an answer:
In the case $n = 2$, I would call it the pairing. Similarly, one has "tripling", "quadrupling", and so in general one might call it the ($n$-)tupling o …
- 53.3k
2
votes
Examples of "Unusual" Classifications
In extensions of number fields $E/k$, you can look at primes in the ring of integers of $k$ that either (a) split in the integers of $E$, (b) remain prime in the integers of $E$, or (c) ramify. The ca …
- 53.3k
12
votes
Accepted
Is there any monoid in which the product of two non-invertible elements could be invertible?
Well, why not?
Let $\oplus_{n \in \mathbb{N}} k$ be a direct sum of countably many copies of a 1-dimensional space over a field $k$; the direct sum affords a standard basis $e_i = (0, \ldots, 0, 1, …
- 53.3k
6
votes
Are there proofs that you feel you did not "understand" for a long time?
I didn't feel I had really grokked Euler's magnificent identity
$$e^{ix} = \cos(x) + i \sin(x)$$
for a very long time. The first time I saw this formula, I think I was fourteen, and it was one of …
- 53.3k
19
votes
How to refer to a “theorem” that you have shown to be wrong
In my opinion, it would be a bad idea to label statements known to be false as theorems. If you really want to do this, maybe you could put inverted commas around the word "theorem", to indicate you e …
- 53.3k
12
votes
Proof synopsis collection
I don't know that I have a favorite proof-synopsis, but here's one I like which is a little different from the way most people prove it.
Proposition. Let $A$ be a real symmetric $n \times n$ matrix. …
- 53.3k
28
votes
Dimensional Analysis in Mathematics
This may be somewhat obliquely along the lines you are asking about, but I think it's interesting enough that it deserves to be made public.
My friend James Dolan has been developing with a number o …
CommunityBot
- 1