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.

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What is the best journal to publish in? [closed]

I have prepared three articles on probability theory for publication. One is a very serious work on a fairly relevant topic. The previous work on this topic has been accepted and will soon be ...
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3 votes
0 answers
76 views

Formal and informal proofs: Is there any "bilingual corpus"?

There are extensive libraries of formalized mathematics like those of Lean, Coq or Isabelle/HOL. What I am interested in is documents of formalized mathematics that closely follow certain informal ...
37 votes
11 answers
4k views

Topology in non-mathematical literature

A great piece of knowledge that I heard from a talk of Robert Ghrist, is that one of the earliest instances of non-trivial manifolds (i.e. of dimension higher than 2) appears in Dante's Paradise, ...
1 vote
0 answers
71 views

Advice on constructing a Non-structural Flood Mitigation Model [closed]

I am not sure if this is the right site to post this. But I seek some valuable suggestions, and I believe I can get them here. At present, I am in the final semester of my BSMS Mathematics course. I ...
15 votes
2 answers
2k views

What should one do before submitting a paper?

Assume I just wrote a paper. Now I would like to publish it in a journal. What kind of things I should do before its submission? Should I first give a few talks at seminars or conferences? Upload to ...
3 votes
0 answers
147 views

The site and the space

There is a (seemingly simple) statement in the literature on sheaf theory, namely, If $E$ is the site of opens of a topological space $X$, the notion of sheaf over $X$ coincides with that of sheaf of ...
8 votes
1 answer
746 views

Re-typesetting historic math papers

What do I have to take into consideration when re-typesetting mathematical papers that are freely avaible online if the authors are still living if the authors have already passed away as there won'...
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18 votes
4 answers
3k views

Should one state the sharpest version of a Lemma even if only a weaker version is needed?

When writing a paper, it's possible that some auxiliary results hold in more generality or in a stronger version than what's actually needed to prove the main results of the article. And so here comes ...
3 votes
0 answers
222 views

Are there journals for "fun mathematics"?

Are there peer-reviewed journals that focus on "fun mathematics"? By this I mean fun things that do involve nontrivial mathematics and which I think other mathematicians would enjoy reading ...
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1 vote
0 answers
252 views

Cartier and the continuity of the early history of schemes

If you allow me I would divide the early history of schemes this way _ Weil, Zariski, Bourbaki, Nagata, Van der Waerden,... up to Chevalley (you can find an interesting blog here) J P Serre varieties ...
16 votes
3 answers
2k views

Why do Grothendieck topologies used in algebraic geometry typically involve finiteness conditions?

There are many Grothendieck topologies used in algebraic geometry, with complex interrelations. Generally in one of these topologies, a cover of schemes is a family of maps which is jointly surjective ...
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0 votes
1 answer
83 views

Journals of applied mathematics with an economics bent?

I'm asking here instead of the economics stackexchange because I'm interested more in the applied mathematics part, instead of just the economics; I'm interested in seeing what new research is being ...
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6 votes
2 answers
376 views

Domains that may require a good categorical background

I'm a PhD student in category theory, more specifically I study 2-dimensional category theory, that means bicategories, pseudofunctors, careful definitions of various structures you can put on this ...
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2 votes
1 answer
793 views

Is there an alternative to the arXiv for uploading mathematical papers?

Is there an alternative to the arXiv for uploading mathematical papers? Here is the story. Upon attempting to upload a modified version of a published paper to the arXiv, it was put "on hold"...
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3 votes
0 answers
143 views

Transitive action on domino tilings

Fix a $n \times m$ rectangle and consider the set $S_{n,m}$ of all its dominos tilings. Here are examples with $n=m=8$. The set $S_{n,m}$ is empty if and only if $nm$ is odd, and for small $nm$, its ...
1 vote
0 answers
298 views

Use of singular pronoun 'I' in the acknowledgements

I understand that in mathematical writing, it is standard to use 'we' regardless of how many authors there are because it includes the reader(s). In the acknowledgements, however, it seems to me that '...
9 votes
0 answers
358 views

Useful applications of applied category theory

Led by John Baez, applied category theory (e.g. [1]) seems to accumulate much popularity. As someone who has noticed the importance of category theory in pure mathematics (e.g. homotopy theory, tqfts, ...
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2 votes
0 answers
73 views

Which definitions of "local module" have gotten traction?

It seems like "local module" has been defined a lot of ways: if 𝑀 has a largest proper submodule. (This math.se post) if it is hollow and has a unique maximal submodule (Singh, Surjeet, ...
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40 votes
4 answers
7k views

Math papers where the only issue is that someone else could've done it but didn't

Do editors for top math journals ever read a submitted paper, agree that there are no mistakes and the result is new, yet still reject it on the basis that this is a top math journal and someone could'...
14 votes
2 answers
2k views

How do I, as an undergraduate, find interesting, accessible questions to work on to see if I'd be interested in research mathematics? [closed]

For a little more context: I'm currently an undergrad (sophomore) at a small liberal arts college with a (from my experience so far) solid math program. So far, I've taken Calc I, II, III, linear ...
12 votes
1 answer
3k views

How to indicate when another author has done nothing significant

Context: I am currently working on a rather important paper for my career, in the sense that it is a culmination of the past 5 years of (post Ph.D.) research. I started this particular article with 3 ...
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5 votes
4 answers
394 views

Funding programs for mathematical research [closed]

In the USA, as far as I know, the main grants available to mathematicians are collected on the NSF or the AMS websites [please, correct me if this perception is inaccurate]. On the other hand, for ...
1 vote
0 answers
189 views

On the definition of "natural" in Mathematics [duplicate]

Often in mathematics we found objects which are qualified as "being natural". The first example appears in the vector space $\mathbb R^n$, where we say that we have the "natural basis&...
11 votes
2 answers
1k views

Examples of mathematical work that gained recognition after it was outlined by journalists

Having a background in both mathematics and journalism, I'm interested in examples of previously barely recognized mathematical achievements that received recognition after having been given attention ...
64 votes
8 answers
6k views

What to do after a pure math academic path?

I don't know whether my question is in the appropriate place. I've studied physics, and then did a PhD in (pure) math and 2 postdocs. I definitely love math research, but I am not ready to apply all ...
5 votes
1 answer
234 views

Classification results

A typical classification result for a class $C$ of objects looks like that: Theorem. Each object of $C$ is isomorphic to one object of the following list: [insert list here]. Examples are the ...
4 votes
1 answer
230 views

Springer GTM Series statement of purpose (early editions)

Earlier editions of the Springer Graduate Texts in Mathematics series include a motivating statement about the purpose of the series. The current statement of purpose is as follows: Graduate Texts ...
1 vote
0 answers
164 views

Future of complexity classes in case NP=P

The P=NP question is still unresolved and there is no hope that the situation will ever change. Assume now the hypothetic situation that P=NP had been confirmed: Questions: what will become of the ...
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7 votes
2 answers
1k views

Mathematics of sustainable development and energy sobriety in the classroom

Faculty members are encouraged to highlight the connection between the courses we teach and climate change, and raise awareness of the issue in our lectures, across subjects in my university. I am ...
36 votes
1 answer
5k views

Published AI-generated nonsense math papers

I guess most of us know that one can easily automatically generate a math-like nonsense paper, and that it is possible to have such a paper published. However, I was quite sure that nobody actually ...
28 votes
4 answers
2k views

What to do with a collection of theoretical math books?

My father had a Ph.D. in mathematics. He was a consummate mathematician and enjoyed reading about all topics related to math. He passed away a couple of years ago. I have yet to find a suitable place ...
1 vote
0 answers
155 views

Research directions in complex differential geometry

Not sure if my question makes sense. Is there an area in complex geometry that is as analytic as possible? Actually what I wanted to ask is an area in complex geometry that is as non-algebraic as ...
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1 vote
0 answers
224 views

Could there be a better classification of finite simple groups?

The current classification of finite simple groups puts every finite simiple group in one of a few categories. There are the "nicely" behaved infinite categories (cyclic, alternating, Lie-...
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14 votes
1 answer
355 views

Fourier's proof of reality of all roots of Bessel function $J_0(x)$

In his "Théorie de chaleur" Fourier proves that the zeros of Bessel function $J_0(x)$ are all real. I want to ask if there is a modern version of this proof exist in literature? If someone ...
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1 vote
1 answer
96 views

Notation for infinite cartesian products

This is a soft question, feel free to delete it if deemed inappropriate for the site. What is the best notation for the cartesian product of an infinite number of copies of the same set $E$? Maybe one ...
2 votes
1 answer
537 views

Most efficient way of getting a brief overview of the current active research areas in Algebraic Topology

I'd be applying for a Ph.D. at various grad schools in the U.S. in the coming months and while I know I'd like to pursue research in the field of Algebraic Topology, I am not knowledgeable enough yet ...
3 votes
0 answers
156 views

What does a character of a scheme mean?

Here is a soft question I met in the book Introduction to Grothendieck Duality Theory by Altman and Kleiman. In Chapter I the proposition 2.1 uses a term called "a character of $X$" where $X$...
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2 votes
1 answer
319 views

(Dis)prove : if every function with closed graph are continuous then the target space is compact

$(X, \tau_X) $ and $(Y, \tau_Y) $ be two topological spaces. $\forall f\in Y^X$ with $\text{Gr}(f) $ is closed implies $f\in C(X, Y) $. Question : Does this implies $(Y, \tau_Y) $ is compact? ...
5 votes
2 answers
1k views

Poincaré recurrence and its implications for statistical physics and the arrow of time

A very important theorem in mathematical physics is Poincaré’s recurrence theorem. As you recall, this theorem states that given a dynamical system $(M , \phi , \mu)$ with $ \mu M < +\infty$, for ...
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3 votes
0 answers
182 views

Resources for PhD students to guide through the research [duplicate]

I am living in a poor country but I have managed to get admission for a PhD program in Western Europe. This was a daunting task for me due to my family background and also social conditions. ( I don't ...
12 votes
4 answers
2k views

How about a statement without proof?

Consider a statement without proof in a paper, with the following assumptions: it is unknown, it is unused in the paper, it is not written as a theorem (or proposition, or lemma…), but just a free ...
0 votes
0 answers
76 views

Relevance of the deduction of similar theorems than Maier's theorem for other prime constellations

A year ago I asked this question on Mathematics Stack Exchange with identifier 4245823 and same title Relevance of the deduction of similar theorems than Maier's theorem for other constellations of ...
14 votes
0 answers
543 views

Where did the military money go?

In older papers, one sometimes finds references to sources of funding directly linked to or overseen by military agencies. For example, I have memories of seeing acknowledgments to DARPA funding in a ...
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7 votes
0 answers
146 views

Intuition for branch uniqueness in inner model theory

In inner model theory, what is the intuition behind the expectation that under appropriate conditions, we should have a single preferred branch to continue an iteration at a limit stage? At the level ...
1 vote
0 answers
88 views

Formalizing intuition of search hardness

Basically, this is a search problem of an object that is promised to exist. Suppose we have an object that can be described completely and uniquely by $m$ properties (each n bits). Suppose a search ...
33 votes
1 answer
5k views

The editor wrote the paper for me

I submitted a short paper and received a positive review and a negative review. The editor (he) briefly wrote the following things: He thinks my original result could be mistaken because of XYZ He ...
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1 vote
1 answer
314 views

Adjunctions in the real world

What concepts in the real world can be described by adjunctions? For example, parents and children are adjoint to one another. Specifically, work in $ZFC$ plus a finite class of atoms $\mathscr{X}$ (...
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1 vote
0 answers
120 views

Translation of an article by Šapirovskiĭ

The AMS has a book, Fourteen Papers Translated from the Russian, containing an article by Šapirovskiĭ, "Cardinal invariants in compact Hausdorff spaces", that I would very much like to ...
  • 620
4 votes
1 answer
456 views

Supervision numbers in pure mathematics

My faculty imposes some numerical "recommendations" for promotions. Instead of arguing this sort of recommendation is ridiculous, I think it is wiser to provide some evidence the recommended ...
1 vote
0 answers
49 views

Asymptotic behaviors of different types of equations with capillarity or viscous terms

Let us consider $$ \begin{align} u_t + \left(\frac{u^2}{2}\right)_{\!\!x} = 0 \\ v_t + \left(\frac{v^2}{2}\right)_{\!\!x} - v_{xx} = 0 \\ \tilde v_t -\tilde v_{xx} = 0 \\ w_t + \left(\frac{w^2}{2}\...

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