Linked Questions
12 questions linked to/from Mathematical "urban legends"
185
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127
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Most memorable titles
Given the vast number of new papers / preprints that hit the internet everyday, one factor that may help papers stand out for a broader, though possibly more casual, audience is their title. This view ...
106
votes
83
answers
19k
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Elementary + short + useful
Imagine your-self in front of a class with very good undergraduates
who plan to do mathematics (professionally) in the future.
You have 30 minutes after that you do not see these students again.
You ...
170
votes
47
answers
34k
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Every mathematician has only a few tricks
In Gian-Carlo Rota's "Ten lessons I wish I had been taught" he has a section, "Every mathematician has only a few tricks", where he asserts that even mathematicians like Hilbert ...
175
votes
39
answers
31k
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Short exact sequences every mathematician should know
I'd like to have a big-list of "great" short exact sequences that capture some vital phenomena. I'm learning module theory, so I'd like to get a good stock of examples to think about. An ...
66
votes
20
answers
9k
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Do mathematical objects disappear?
I am asking this question starting from two orders of considerations.
Firstly, we can witness, considering the historical development of several sciences, that certain physical entities "disappeared"...
86
votes
19
answers
15k
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Each mathematician has only a few tricks
The question "Every mathematician has only a few tricks" originally had approximately the title of my question here, but originally admitted an interpretation asking for a small collection ...
47
votes
11
answers
5k
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Reference request: Examples of research on a set with interesting properties which turned out to be the empty set
I've seen internet jokes (at least more than 1) between mathematicians like this one here about someone studying a set with interesting properties. And then, after a lot of research (presumably after ...
9
votes
2
answers
674
views
Powers of finite simple groups
I have heard about the following result: for each finite simple non-abelian group $S$ and each natural number $r\ge 2$ there exists a number $n=n(r,S)$ such that the power $S^n$ is $r$-generator but $...
- 331
22
votes
1
answer
2k
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What is known about the common knowledge of mathematicians outside their field?
When giving a talk or writing a paper intended for non-specialist (i.e., mathematicians not specializing in the topic being discussed), the question inevitably occurs of what one can assume to be "...
2
votes
2
answers
291
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If either $A$ is exact or $B$ is nuclear then every closed ideal of $A\otimes_{min}B$ is of the form $A \otimes _{min}J$ for some ideal $J$ of $B$
From one of the talks I attended long back, I vaguely seem to remember the following fact:
Let $A$ and $B$ be $C^{\ast}$-algebras. If either $A$ is exact or $B$ is nuclear then every closed ideal of $...
- 1,115
3
votes
0
answers
895
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Is the Kolmogorov-Arnold representation theorem an example of the Yoneda lemma?
From Wikipedia:
https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Arnold_representation_theorem
In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or ...
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0
votes
0
answers
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Is the equivalence $\mathrm{CRing}^{\mathrm{op}}\simeq \mathrm{AffSch}$ related to the homotopy hypothesis?
At the heart of algebraic geometry lies the op-equivalence between commutative rings and affine schemes, i.e.,
$$\mathrm{CRing}^{\mathrm{op}}\simeq \mathrm{Aff\,Sch}.$$
At the heart of homotopy theory ...
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