Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

-2
votes
0answers
81 views

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
0answers
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
1answer
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
0answers
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
0answers
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
1answer
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 ...
0
votes
0answers
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
0answers
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
4answers
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
1answer
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
2answers
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
0answers
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
8answers
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
1answer
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
1answer
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
0answers
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
1answer
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
1answer
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
4answers
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
1answer
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
1answer
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
2answers
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
43answers
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
4answers
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
0answers
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
11answers
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
0answers
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
5answers
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
1answer
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
0answers
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
5answers
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
1answer
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
2answers
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
3answers
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
1answer
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
0answers
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
votes
0answers
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
1answer
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
8answers
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
4answers
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
1answer
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
1answer
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
2answers
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
1answer
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
1answer
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
2answers
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
0answers
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
1answer
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
2answers
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
1answer
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 ...