# 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. In other words, questions that can be answered without making computations or applying theorems and axioms.

1,616 questions

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### Mathematics blogs

I was wondering if there are similar blogs such as:
1)http://noncommutativegeometry.blogspot.com/
2)http://cvgmt.sns.it/
3)https://gecogedi.dimai.unifi.it/
in any area.
If one knows one more, I ...

**5**

votes

**0**answers

178 views

### How should one approach reading Higher Algebra by Lurie?

A question posed at the nForum asked for a roadmap to learn Lurie's Higher Topos Theory, including helpful sources other than HTT itself (to read along it) and information about which parts of HTT ...

**5**

votes

**1**answer

74 views

### Sum of squared nearest-neighbor distances between points in a square

Let $\square_2=\{(x,y): 0\leq x, y\leq1\}$ be the unit square in $\mathbb{R}^2$. Take $n>1$ points $P_1, \dots, P_n\in\square_2$.
Denote the distances $d_j=\min\{\Vert P_k-P_j\Vert: k\neq j\}$, ...

**6**

votes

**0**answers

160 views

### Does anyone use non-sober topological spaces?

Recall that a sober space is a topological space such that every irreducible closed subset is the closure of exactly one point.
Is there any area of mathematics outside of general topology where non-...

**-1**

votes

**0**answers

115 views

### Balance teaching and multiple research projects as a graduate student: how to organize an effective schedule [closed]

In your experience, what tools turned out to be the most useful to organize an effective schedule to manage multiple research projects and teaching duties?
I'm interested both in tools for personal ...

**2**

votes

**1**answer

206 views

### Thematic programs for collaborative research (similar to the one in Bonn) [closed]

The Hausdorff Institute in Bonn periodically organizes thematic junior trimester programs, which "give young mathematicians (postdocs, junior faculty) the opportunity to carry out collaborative ...

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votes

**0**answers

83 views

### (Semi-)Riemannian geometry for working PDE analysts

What is a good reference on (semi-)Riemannian geometry written for PDE analysts (that is, with main focus on analytical problems and approaches)?
The closest thing I know to this, are two books by ...

**0**

votes

**0**answers

46 views

+50

### Critical growth and geodesic connectedness in Lorentz manifold

What is the deep ("heuristic") reason why the quadratic growth of $\beta$ is critical for the study of geodesic connectedness in standard static Lorentz spacetime $\mathcal M = \mathcal M_0 \times \...

**5**

votes

**4**answers

430 views

### How to organize collaborations? Managing communication within the team [closed]

What is an effective tool for managing the communication within a small team of coauthors working on a paper (when face-to-face interaction is not possible)?
I've previously used back-and-forth email ...

**25**

votes

**1**answer

425 views

### “Matchmaking website” for project-specific mathematical collaborations [closed]

It seems that even in the age of Internet, most mathematical collaborations are born (and pursued) off-line.
However, I wonder if there exists a "matchmaking website" for mathematical ...

**8**

votes

**2**answers

620 views

### How to organize collaborations? Managing shared library and LaTeX document

What is an effective way to organize collaborations with several people on the same paper? How do you arrange the $\LaTeX$ document, the shared (digital) papers library, and other aspects?
More in ...

**1**

vote

**0**answers

133 views

### MathJobs: Should I update submitted material after deadline?

I am using MathJobs to apply for research postdocs in mathematics and I have a doubt.
Suppose I have applied for a postdoc at University X by submitting all requested material (CV, research statement,...

**45**

votes

**8**answers

3k views

### Your professional $\LaTeX$ experiences that saves your time in typesetting

In $\LaTeX$ typesetting, when we repeat a long and complex formula in long documents, it is appropriate to create a new command that just by calling this new command we get the desired output. For ...

**4**

votes

**1**answer

126 views

### Compilation of representations of holomorphic functions

Holomorphic functions are my muse. As my muse, I love drawing them different ways. Allow me to frame this as though an artist talking about his muse.
A holomorphic function $f$ on the unit disk $\...

**3**

votes

**1**answer

109 views

### Interpretation of free energy for Ising models

In thermodynamics, the physical meaning of free energy is the maximum amount of work that can be extracted from a system. Now if we take an Ising model on a graph, with interaction weights on each ...

**0**

votes

**0**answers

41 views

### Elliptic Dirichlet problems with measure boundary data

Can you point out any references on the Dirichlet problem for divergence-type elliptic operators with a Radon measure as boundary data?

**2**

votes

**1**answer

80 views

### Boundary condition for elliptic problems and domain decomposition

This question is motivated by one that has been previously asked on this website: Elliptic problem on a domain split in two subdomains
Consider an open domain $U$ split in two non-overlapping ...

**3**

votes

**1**answer

181 views

### Elliptic problem on a domain split in two subdomains

Consider the following elliptic problem in a split domain:
$$ (\ast) \quad\begin{cases} -\Delta u=f_1 \quad &\text{ in } U_1\\
-\Delta u =f_2 & \text{ in }
U_2\\
u=g & \text{ on } \...

**7**

votes

**4**answers

656 views

### Different derivations of the value of $\prod_{0\leq j<k<n}(\eta^k-\eta^j)$

Let $\eta=e^{\frac{2\pi i}n}$, an $n$-th root of unity. For pedagogical reasons and inspiration, I ask to see different proofs (be it elementary, sophisticated, theoretical, etc) for the following ...

**3**

votes

**1**answer

170 views

### Heuristics for boundary Harnack inequality

What is the heuristic idea of the proof of the boundary Harnack inequality presented in the appendix of Caffarelli's 1998 lectures on the obstacle problem (page 38 here)?

**14**

votes

**1**answer

555 views

### “Gauss trick” vs Karatsuba multiplication

This question is inspired by article Alexander Shen "Gauss multiplication trick?" (submitted to "Mathematical Enlightenment").
Dasgupta, Papadimitriou, Vazirani, Algorithms (2008) Ch. 2:
The ...

**15**

votes

**2**answers

1k views

### Integrating over a hypercube, not a hypersphere

Denote $\square_m=\{\pmb{x}=(x_1,\dots,x_m)\in\mathbb{R}^m: 0\leq x_i\leq1,\,\,\forall i\}$ be an $m$-dimensional cube.
It is all too familiar that $\int_{\square_1}\frac{dx}{1+x^2}=\frac{\pi}4$.
...

**109**

votes

**43**answers

14k views

### Old books you would like to have reprinted with high-quality typesetting

There are some questions on mathoverflow such as
What out-of-print books would you like to see re-printed?
Old books still used
with answers that tell us things such as:
Mathematicians prefer to ...

**48**

votes

**4**answers

5k views

### What to do if you notice a substantial improvement to a result in a paper whilst refereeing it?

What would you do/have you done in such a situation?
Hand out the improvement for free in your report
Wait until the result is published and then submit elsewhere
Inform the editor about the ...

**4**

votes

**0**answers

187 views

### Is there a theory behind these puzzles? (communicating by modifying data)

Consider the following puzzles:
Problem 1: Alice is given two data by Zora: a binary string $w$ of length $2^r$, and a position $p$ in the string (which we can view as an integer $0\leq p<2^r$). ...

**46**

votes

**11**answers

5k views

### What definitions were crucial to further understanding?

Often the most difficult part of venturing into a field as a researcher is to come up with an appropriate definition. Sometimes definitions suggest themselves very naturally, as when you solve a ...

**6**

votes

**0**answers

208 views

### Best software to do big number calculations quickly [closed]

I am trying to do some work on some math conjecture. I am testing the conjecture numbers using very large math numbers (100+ digits ). I am currently using python to test these numbers.
In the ...

**28**

votes

**5**answers

3k views

### Should computer code be included within publications that present numerical results?

Many research papers include numerical results obtained through computation. Most of the time such computations are performed using software that is used by many mathematicians, i.e., Maple, ...

**8**

votes

**1**answer

288 views

### Polymath type websites for specialized areas

This question is inspired by the success and more importantly, the democratizing affect of the polymath projects and Mathoverflow. I put the idea in my NSF proposals a few times, but the panels don't ...

**7**

votes

**0**answers

99 views

### A generalization of matrix minors to non-integer values

I am interested to know if there exist a notion of $k$-minors of a real square matrix, for non-integer positive values of $k$
One approach I thought of was to use the fact that the $k$-minors are (...

**-1**

votes

**5**answers

552 views

### Mathematical phantoms, specifically but not exclusively in applied mathematics [duplicate]

A while ago over at our sister site, there was an interesting question [not by me] with next to no answers which I feel is, fleshed out in a more precise fashion, appropriate for MathOverflow.
The ...

**36**

votes

**1**answer

2k views

### On proof-verification using Coq

So i recently learnt that there is now a certain software called ''Coq'' by which one can check the validity of mathematical proofs. My questions are:
Are there limitations on the kinds of proofs ...

**11**

votes

**2**answers

345 views

### What are the 'wonderful consequences' following from the existence of a minimal dense subspace?

In Peddechio & Tholens Categorical Foundations they quote PT Johnstone in their chapter on Frames & Locales:
...the single most important fact which distinguishes locales from spaces: the ...

**32**

votes

**3**answers

3k views

### Publishing a Simple Paper as an Undergraduate

First off I apologize if this question does not belong here, I would be happy to hear about any better locations to post this on.
I am a (first year) undergraduate mathematics student, and I recently ...

**-5**

votes

**1**answer

275 views

### Big list of “outstanding paper awards” [closed]

What are the prizes awarded for significant papers published in mathematical journals?
One of them is the SIAM Outstanding Paper Prize.
I'd be particularly interested in hearing about prizes ...

**2**

votes

**0**answers

59 views

### Reference on elliptic obstacle problem that covers the material in the lecture notes by Caffarelli

Can you recommend a modern, self-contained, readable reference that covers (approximately) the results on elliptic obstacle problem that are covered in the lecture notes by L. Caffarelli (Scuola ...

**5**

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**0**answers

277 views

### Theorems conditional on false conjectures

What is an example of a theorem that was conditional on a conjecture that later turned out to be false?

**5**

votes

**1**answer

255 views

### Progress towards a computational interpretation of the univalence axiom?

I will preface this by saying that I am not an expert on type theory. I am just a curious outsider slowly making my way through the HoTT book when I (rarely) have some spare time.
I am just curious ...

**26**

votes

**8**answers

5k views

### How to explain to an engineer what algebraic geometry is?

This question is similar to this one in that I'm asking about how to introduce a mathematical research topic or activity to a non-mathematician: in this case algebraic geometry, intended as the most ...

**5**

votes

**4**answers

512 views

### mixing theorem with definition (definition with proof)

I often find myself writing a definition which requires a proof. You are defining a term and, contextually, need to prove that the definition makes sense.
How can you express that? What about a ...

**3**

votes

**1**answer

208 views

### Generating function for 3 -core partitions: Part II

Let $\lambda$ be an integer partition: $\lambda=(\lambda_1\geq\lambda_2\geq\dots\geq0)$. Further, let $h_u$ denote the hook-length of the cell $u$.
We call $\lambda$ a $t$-core partition if none of ...

**5**

votes

**1**answer

121 views

### Generating function for $3$-core partitions

Let $\lambda$ be an integer partition: $\lambda=(\lambda_1\geq\lambda_2\geq\dots\geq0)$. Further, let $h_u$ denote the hook-length of the cell $u$.
We call $\lambda$ a $t$-core partition if none of ...

**14**

votes

**2**answers

665 views

### How to handle results from an unpublished paper?

I am writing a paper right now, and part of the paper makes use of a (trivial) generalization of a number of really nice theorems and constructions from a paper that was never made public. The author ...

**6**

votes

**1**answer

233 views

### How to visualize local complete intersection morphisms?

As the question title asks for, how do others visualize local complete intersection morphisms? My experiment in asking people in real life didn't pan out, so I'm consulting the MO algebraic geometry ...

**4**

votes

**1**answer

338 views

### Question on academic affiliation when submitting paper

I just finished grad school, earning a Phd in mathematics. Currently I do not know if I want to continue my academic career or not, but in the meantime I have written an article containing some of the ...

**21**

votes

**2**answers

2k views

### Should I inform the editor about a generalized result of a result in a paper under review?

Hoping that my question is appropriate for MO, I would like to ask the following question: I have sent one of the editors of a very good math journal a paper of mine which contains a main result, call ...

**4**

votes

**0**answers

97 views

### Is there a simple algebraic setup to accomodate fibres and cofibres at the same time?

If I understand it correctly, there are two mutually dual "leading principles" in homotopy theory:
never perform quotients, add structure instead;
never require subobjects, take fibres instead.
...

**10**

votes

**1**answer

662 views

### Research semester in math

Admittedly, this is a soft question.
My own experience in mathematical research has been of long periods of research, mostly characterized in long "blocks" and sporadic breakthrough.
How does this ...

**8**

votes

**2**answers

661 views

### How Much Flesh to the Bones does an Initial Online Publication need?

Background of my question is the following: I have found a solution for my question Smoothness Conditions for Planar “Mock-parametric” Spline Interpolation and while developing the solution, I ...

**3**

votes

**1**answer

519 views

### CMI at 20 conference [closed]

Just recently (September 24 - 26) there was a conference at Oxford dedicated to 20th anniversary of CMI. (https://www.claymath.org/events/cmi-20) The program looks interesting. Does anyone know if ...