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Results tagged with big-list
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user 1162
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
31
votes
Blackbox Theorems
I think the Uniformization theorem is an example of blackbox theorem : any simply connected Riemann surface is conformally equivalent to either the open unit disk, the complex plane or the Riemann sph …
2
votes
German mathematical terms like "Nullstellensatz"
There is Ahlfor's scheibensatz in complex function theory, which is a generalization of Ahlfors five islands theorem
28
votes
Examples of common false beliefs in mathematics
As a teaching assistant in an elementary number theory course, I've seen the following quite often :
If $a$ divides $bc$ and $a$ does not divide $b$, then $a$ divides $c$.
That's of course true if $ …
9
votes
Examples of common false beliefs in mathematics
I have heard the following a few times :
"If $f$ is holomorphic on a region $\Omega$ and not one-to-one, then $f'$ must vanish somewhere in $\Omega$."
$f(z)=e^z$ of course is a counterexample.
13
votes
12
answers
5k
views
On proving that a certain set is not empty by proving that it is actually large
It happens occasionally that one can prove that a given set is not empty by proving that it is actually large. The word "large" here may refer to different properties.
For example, one can prove that …
24
votes
Do you know important theorems that remain unknown?
I am not sure whether the following satisfies the OP's high standards for a good answer, but I thought the result was very interesting when I first learned about it a few years ago.
Theorem. Let $ …
78
votes
Not especially famous, long-open problems which anyone can understand
I always enjoyed telling people about the Inscribed square problem :
Does every (Jordan) curve in the plane contain all four vertices of
some square?
Update: Here is a variation due to Helge Tverbe …
112
votes
Famous mathematical quotes
"The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" — Jerry Bona
55
votes
Accepted
Math puzzles for dinner
I really like the following puzzle, called the blue-eyed islanders problem, taken from Professor Tao's blog :
"There is an island upon which a tribe resides. The tribe consists of 1000 people, with v …