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 25510
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.
61
votes
Is amateur research in mathematics viable?
This is possible. I have at least two friends who studied mathematics (in the graduate school), did not defend their PhD, and found some jobs not related to mathematics. Still they do research, and pu …
9
votes
Conic sections in high dimensions
The answer is no. A spherical cone is
$$x_0^2=x_1^2+\ldots+x_n^2.$$
Intersecting it with a hyperplane $x_0=c^Tx$, where $c$ is a (column) vector we obtain
a quadratic form with martix
$$I-cc^T,$$
that …
- 91.8k
8
votes
A search for theorems which appear to have very few, if any hypotheses
For every holomorphic map from the complex plane to the Riemann sphere,
and every $R<\arccos(1/3)$ there exists a disk of radius $R$ in the image in
which an inverse holomorphic branch exists.
(The co …
1
vote
A search for theorems which appear to have very few, if any hypotheses
Every bounded analytic function in the unit disk has radial limits almost everywhere.
12
votes
Proof or citation?
On my opinion, the main criterion for a reference is that it must be AVAILABLE.
Either on Internet or in most university libraries. An unpublished thesis in Ukrainian
which is not available on Interne …
23
votes
Fascinating moments: equivalent mathematical discoveries
An example which always puzzled me is J. Milnor's paper entitled
Eigenvalues of the Laplace operator on certain manifolds,
Proc. Nat. Acad. Sci. U.S.A. 51 1964, 542.
The whole paper occupies about ha …
16
votes
A search for theorems which appear to have very few, if any hypotheses
There are infinitely many prime numbers.
Every integer is a product of primes, in essentially unique way.
(Theorems with NO hypotheses:-)
16
votes
Can pure mathematics harness citizen science?
I have no proposal, but only want to mention a historical example of what can be called
"Citizen science" in mathematics. http://www.computer.org/portal/web/csdl/doi/10.1109/85.707573.
This is how th …
4
votes
Golden ratio in contemporary mathematics
Yes, it does:
Lyubich, Mikhail; Milnor, John The Fibonacci unimodal map. J. Amer. Math. Soc. 6 (1993), no. 2, 425–457.
and two more papers of the same authors studying what they call Fibonacci map.
16
votes
Special rational numbers that appear as answers to natural questions
Rational number 1/4 occurs as a universal constant in several problems of Analysis.
The most famous is the "Koebe 1/4 Theorem". Let $f(z)=z+\ldots$ be an injective holomorphic function in the unit dis …
12
votes
When is 2 qualitatively different from 3?
Complex numbers exist only in dimension 2. That is the only multiplication laws on $R^n$ which satisfy all field axioms exist for $n=1$ (real numbers) and $n=2$ (complex numbers).
0
votes
Idempotent solutions to the implict function theorem other than the identity?
Examples are abundant. If $x_0$ is a point such that $g(x_0,x_0)=0$ and
$g_y(x_0,x_0)\neq 0$ then $g_x(x_0,x_0)\neq 0$ the Implicit Function Theorem, there is a unique
function $y=\phi(x), \phi(x_0)=x …
- 91.8k
29
votes
Where can square roots come from when they are not distances?
$i=\sqrt{-1}$ has no apparent relation with any distance.
Also $\int_{-\infty}^\infty e^{-x^2}dx=\sqrt{\pi}.$
11
votes
Negative impact of wrong or non-rigorous proofs
There are several examples of wrong proofs which were believed to be correct for some time, but I would not say that they "did damage to mathematics".
One of the most famous examples is Dulac's proof …
9
votes
On similar concepts in mathematics whose similarity is a non-trivial fact.
In my example, the similarity did not require a hard proof but it was not seen for many years
for the reasons which I would call "social".
In 1928 Weil (and simultaneously Siegel) defined and studied …