Questions tagged [soft-question]
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
2,311 questions
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How long are you allowing yourself to be stuck on a problem? How you know when to stop?
I searched for this question on the site but couldn't find it, so I'm asking it.
As a researcher, how long do you allow yourself to be stuck on a problem before deciding to move on? And how do you ...
56
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12
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How might mathematics have been different?
I think most people believe that mathematical truths are logically necessary. The fact that $\sqrt{2}$ is irrational doesn't depend on who proved it, when they proved it, whether they liked it, or ...
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Useful applications of convergence algebras
This is a soft question motivated by reading of "Convergence Structures and Applications to Functional Analysis" by Beattie and Butzmann.
A convergence algebra is a generalization of a ...
0
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Rook polynomial in Algebraic Geometry
The rook polynomial of a polyomino $\mathcal{P}$ is
$$
r_\mathcal{P}(t) = \sum_{k=0}^{r} r_k(\mathcal{P})\ t^k,
$$
where:
$r_k(\mathcal{P})$ is the number of ways to place $k$ non-attacking rooks on $...
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Are there interesting finite groups which are not small?
I was playing around with finite groups recently, and a thesis (not really a conjecture, since it's rather informal) came to my mind that "all interesting behaviour of finite groups happens ...
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When did it become prevalent to only capitalize the first word (and names) in titles of journal articles? [closed]
Recently, I have noticed that it seems to be a relatively recent trend to only capitalize the first word (and names) in the title of a journal article. Some examples from the 21st century include:
...
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What determines which classes of functions can be naturally extended to a given ring? [closed]
We know that any real function can be extended to split-complex numbers, because this ring is isomorphic to $\mathbb{R}^2$.
But there is no obvious way of extending a non-analytic function to complex ...
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When does the Kodaira symbol determine the Tamagawa number?
Let $E/K$ be an elliptic curve over a local field. I understand that the Kodaira type of $E/K$ refers to the isomorphism class of the special fiber of the Néron minimal model of $E/K$ as a scheme over ...
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Compact function representation
One of my interest is 3D shape analysis, and there's a relatively recent framework called functional maps. In the framework of functional maps for shape analysis we represent shape features as a ...
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Naming categories beyond their objects
Can you provide a known instance where it becomes necessary or useful to introduce a different name for the objects of a category and for the category itself?
Specifically, I am interested in cases ...
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Note vs Notice in Mathematics [closed]
In common language there seems to be a difference between note and notice. However, I am discussing it with a co-author now and we are not sure about the usage in math. My feeling is that 'note' is ...
5
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Rigorous general treatment of degrees of freedom
My question is the following.
Is there an accepted mathematically rigorous and general treatment of the notion of "degrees of freedom" which at least accounts for its pervasive usages in ...
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How might fundamental mathematics differ for entities with intuitive comprehension of the continuum?
Dear MathOverflow Community,
I'd like to pose a speculative question, with apologies for its "soft" nature. My curiosity lies in how the day-to-day practice and the challenging frontiers of ...
- 479
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0
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Partitioning a cube into cuboids of different dimensions
This is how I have tried:
Initial stage: One triplet of the form $(n,n,n)$.
Second stage: Decompose original triplet into two triplets by splitting one of the elements of $(x,y,z)$ into two parts at ...
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Why not begin studying sets with Hierarchy Theory?
By $\sf HT^\psi$ I mean the Hierarchy Theory of $\psi$ height. This is a set theory written in mono-sorted first order logic with equality and membership, with the following axioms:
Specification: $\...
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