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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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11 votes
5 answers
4k views

Who says understanding physics helps mathematicians? (A reference request) [Take the word "who" literally.]

If I wanted to make a somewhat bold and rather vague claim in print that it is widely acknowledged among mathematicians that knowledge of mechanics (in the sense in which physicists understand that ...
0 votes
0 answers
246 views

Possible research topics for a beginner in Topological QFT?

I am highly interested in Topological Quantum Field Theory (TQFT) and am currently planning on doing a project on this topic this year. Some relevant background: Algebra (Groups, Rings, Fields, basics ...
math-physicist's user avatar
0 votes
0 answers
116 views

Fibration exact sequence in homotopy vs spectral sequence in (co)homology

Perhaps this should be obvious but why is it that one may associate to a fibration exact sequences of topological spaces a long exact sequence of fundamental groups, but in (co)homology, one only has ...
kindasorta's user avatar
  • 1,995
4 votes
1 answer
202 views

Math conference-organizing checklist?

I am intimately involved in the organization of a relatively high-profile conference. It's a special situation -- I don't want to get into it -- and we have essentially zero admin support. The ...
2 votes
0 answers
47 views

Terminology: generalized Laplacian of arbitrary signature

Let $(M,g)$ be a Riemannian manifold and $E$ any real or complex vector bundle. A linear partial differential operator $D:\Gamma(E)\to\Gamma(E)$ is called generalized Laplace operator, if its ...
B.Hueber's user avatar
  • 1,077
14 votes
2 answers
992 views

Why is inner model theory evidence for consistency of large cardinals?

I want to understand the viewpoint that existence of canonical inner model for a large cardinal notion is strong evidence for its consistency. For example, below is Trevor Wilson's answer to What &...
n901's user avatar
  • 555
7 votes
0 answers
264 views

Applications of Banach space homology

There is a well-developed theory of Banach space homology. What are some of its useful applications to Banach space theory and which important questions can one answer using it? In other words, how ...
Andromeda's user avatar
  • 159
-3 votes
1 answer
299 views

What is the best way to introduce tensor products to undergrads? [closed]

What is the best way to introduce vector space tensor products to undergrads? We have a number of options, given in no particular order. The universal property proving uniqueness and not existence. ...
Zoltan Fleishman's user avatar
2 votes
0 answers
149 views

Search publications for LaTeX code

Is there a way to search the literature for specific instances of formulas (and variants), perhaps using $\rm\LaTeX$ code?
Pace Nielsen's user avatar
  • 18.2k
14 votes
2 answers
2k views

How can I (semi-formally) convince myself that Euclidean geometry comports with visual intuition?

I originally posted this question on Math.SE and received some interesting comments but no answers. Now that some time has passed I thought that it might be appropriate to post here as well; perhaps ...
M. Sperling's user avatar
7 votes
3 answers
705 views

What are journal rankings that employers look at? [closed]

What are journal rankings that employers look at? There are few questions on this topic already, but I don't think they fully address my question. Please close this one if it is not appropriate for ...
10 votes
1 answer
961 views

Is it fine to correct and extend texts of a late colleague when publishing them?

Our colleague has passed away in autumn. He was active till the last days of his life; respectively, several texts of his authorship remain unpublished. We would like to publish them; yet the problem ...
Mikhail Bondarko's user avatar
7 votes
1 answer
329 views

Literature about formalization of "natural reasoning" in mathematical logic

In "Logic of sheaves of structures", X. Caicedo justifies the logic he introduces stating (more or less) that assertions about a point should really be understood as assertions about a ...
user avatar
5 votes
2 answers
547 views

Algebra/Algebraic geometry in statistical mechanics

This is a soft question. I am currently studying statistical mechanics and I found this one by chance: Algebraic statistical mechanics And I also found some workshops on interactions between ...
FFjet's user avatar
  • 282
11 votes
1 answer
437 views

Examples of games developed purposely to analyze players' strategies for mathematics research

Background This question is about games that were created, developed, deployed and popularized1 by researchers because they wanted to learn more about some mathematical structure, and did so by ...
Max Muller's user avatar
  • 4,595
4 votes
2 answers
403 views

Are there any undergraduate-friendly research areas in algebra? [closed]

I don't know if this question is more appropriate for the academia stack exchange, but I'm posting it here because it's more closely related to math itself. I'm not actually an undergraduate, I'm a ...
1 vote
0 answers
48 views

Defining properties of categories out of an indicial category

$\newcommand{\Hom}{\operatorname{Hom}}$Suppose we want to define the category of arrows of $S$. Below are two forms of doing it. Definition 1: If $D$ is of the following type: $\bullet \to \bullet$, ...
user234212323's user avatar
3 votes
0 answers
352 views

What's up with old volumes of the Journal of Algebraic Geometry?

I'm not sure if this question is appropriate for MO, but I'm certain that some people visiting MO must have been confronted with the same issue as mine. It happened several times that a reference ...
Suzet's user avatar
  • 697
49 votes
1 answer
8k views

What mathematical problems can be attacked using DeepMind's recent mathematical breakthroughs?

I am a research mathematician at a university in the United States. My training is in pure mathematics (geometry). However, for the past couple of months, I have been supervising some computer science ...
Ryan Hendricks's user avatar
44 votes
8 answers
3k views

Suggestions and feature requests for the design of a font for math articles/books

Edit: The project website, GitHub repository, and Discord server for Darwin are now up! A little context and introduction: I'm currently working on a family of fonts ("Darwin") designed for ...
39 votes
3 answers
4k views

How to write mathematics without typing?

What solutions exist for mathematicians who need to write papers, but can't type? (I'm an early-career research mathematician and I can't type for the next few months.)
Anonymous's user avatar
  • 401
24 votes
2 answers
4k views

Tips for reading arXiv papers in mathematics

What tips do you have for reading arXiv papers in mathematics? This could be too broad if I'm not careful, so here are some limitations on how to make the question appropriate for MO: I'm interested ...
37 votes
7 answers
17k views

Daunting papers/books and how to finally read them

Most people throughout their career encounter at least one paper that seems especially daunting to them. I'm interested in real stories of how you successfully overcame that to extract the knowledge ...
3 votes
1 answer
152 views

Cartesian product of $[(k-2)\text{-times Interval}_1] \times [\text{Interval}_2] \times [\text{Interval}_2]$

This is a soft question, hoping that it is still appropriate for this forum. I need to describe twice the following region of $\mathbb{R}^k$ (i.e., we are in a $k$-dimensional Euclidean space, where $...
Marco Ripà's user avatar
  • 1,129
1 vote
2 answers
393 views

Are there grants supporting sabbatical year in US? [closed]

I am a tenured mathematician at a university outside of the US. I would be interested to spend my sabbatical year in one of the US universities. Are there grants I can apply to partially support my ...
9 votes
4 answers
2k views

A starting point for research in Graph Theory as a high schooler [closed]

I am a 10th grader and I'm very interested in mathematics. As of now, I'm into math contests and I take great pleasure in solving problems from contests such as the AIME/USAMO/IMO. These only require ...
3 votes
0 answers
175 views

Does "derived" make anything constant in non-flat families?

This is an extremely basic (and surely amateurish) question that might be about derived geometry. In usual algebraic geometry, if we have a flat projective morphism $f:X \to S$ with $S$ integral, and ...
adrian's user avatar
  • 121
9 votes
0 answers
1k views

How complicated can an elementary antiderivative get?

I asked this question on MSE here. I recently learned that there are many very large numbers that have been defined, such as $\operatorname{TREE}(3)$ and many others that are too big to be written ...
pie's user avatar
  • 349
4 votes
2 answers
518 views

Zentralblatt MATH volume numbering

Recently, I learned how to read some of codes that appear on specific pages in zbMATH Open, formerly known as Zentralblatt MATH. For example, in the above review, the circled code "Zbl 1218....
xFioraMstr18's user avatar
0 votes
0 answers
105 views

Software for Intersection of Ideals in Noncommutative Polynomial algebra

I am looking for software which can compute an intersection of ideals (in particular right ideals) in a noncommutative polynomial algebra and then find its Gröbner Basis. Most software somehow does ...
Mukilraj K's user avatar
5 votes
1 answer
257 views

Why include $0$ and $1$ in the signature of Presburger arithmetic?

I recently became interested in some problems concerning decidability of extensions of Presburger arithmetic. However, being a number-theorist rather than a logician, I am confused by some notational ...
Jakub Konieczny's user avatar
14 votes
4 answers
2k views

AI tools for editing and re-generating old math documents

What AI-powered or multi-modal LLM (Large Language Model) apps/interfaces are available to edit/revise pdf or Word documents by automatically producing LaTex for the math expressions within the ...
27 votes
5 answers
9k views

Why does mathematics seem to have a polarity bias?

Why does mathematics seem to have a polarity bias, i.e., why are products more common than coproducts, algebras more common than coalgebras, limits more common than colimits, monads more common than ...
Cameron Zwarich's user avatar
87 votes
9 answers
12k views

Breakthroughs in mathematics in 2023

At the end of 2021, Johnny Cage asked about breakthroughs in 2021 in different mathematical disciplines. A similar question has been asked at the end of 2022, so it looks like Johnny Cage originated a ...
3 votes
0 answers
223 views

Uses of excluded middle on a conjecture that can be rewritten constructively with this trick

An interesting proof technique is to use the law of excluded middle on a conjecture. There are proofs using LEM on the Riemann hypothesis for example. Constructively this is disallowed (if you can ...
Christopher King's user avatar
23 votes
5 answers
3k views

What phenomena are better modelled by SDE instead of ODE?

Both stochastic differential equations (SDE) and ordinary differential equations (ODE) can be used to model a variety of different phenomena, whether physical or otherwise. Most deterministic ODE ...
Nate River's user avatar
  • 4,987
9 votes
1 answer
546 views

Where can I publish a paper about how to write mathematical papers?

I am thinking about writing a paper: "How (not) to write a mathematical paper." I want to share my thoughts and experience about good and bad habits, and common mistakes. While it will be a ...
Piotr Hajlasz's user avatar
10 votes
2 answers
2k views

Is an easy proof of an interesting result worth publishing?

I am a Phd math student, and I was wondering what was the general consensus on what is publishable and what is not. I've come here with an example in mind which should give some insight. I recently ...
56 votes
10 answers
8k views

A clear map of mathematical approaches to Artificial Intelligence

I have recently become interested in Machine Learning and AI as a student of theoretical physics and mathematics, and have gone through some of the recommended resources dealing with statistical ...
8 votes
1 answer
821 views

Examples of ZBMath reviews that motivated you to read the paper

This is community wiki question. I will be writing my first review for ZBMath. I would like to take some suggestion through examples. In general, abstract is too small and introduction is too lengthy ...
14 votes
1 answer
508 views

How exactly are realizability and the Curry-Howard correspondence related?

Consider, on the one hand: the Curry-Howard correspondence between, on the one hand, types and terms (programs) in various flavors of typed $\lambda$-calculus, and on the other, propositions and ...
Gro-Tsen's user avatar
  • 30.3k
2 votes
0 answers
327 views

What's the definition of a mouse in Mitchell's handbook article "the covering lemma"?

In the book "handbook of set theory", in the chapter "the covering lemma", definition 3.24, Mitchell defines what is mouse. However he did not give any definition of $\mathcal{U}_\...
Reflecting_Ordinal's user avatar
34 votes
4 answers
4k views

When has the scaffolding been more important than the completed building?

Niels Abel once said(1) of Gauss, "He is like the fox, who effaces his tracks in the sand with his tail." to which Gauss replied, "No self-respecting architect leaves the scaffolding in ...
3 votes
1 answer
287 views

Sparse representation for continuous function?

I recently came across the field of "Sparse representation". A talk is given here : https://www.youtube.com/watch?v=2bW4TkfTk-M. The goal of sparse representation is taking a signal and ...
user8469759's user avatar
59 votes
11 answers
6k views

What are some ways to stay engaged with the mathematical community from outside academia?

I will be graduating with a Masters degree soon in mathematics. For various reasons I have decided not to pursue a career in academia for now and will instead be working a job in industry that will ...
5 votes
2 answers
752 views

How to effectively search Internet for graphs not for function graphs? [closed]

So, is there any way to distinguish graphs and plots in Internet? I was looking for (Olivier-)Ricci curvature of graphs and found a lot about Ricci curvature of function graphs and not so much about ...
zroslav's user avatar
  • 1,412
-1 votes
1 answer
372 views

How to select suitable journals for submission? [closed]

I think this post should be made community wiki, as there may not be some definitive answer, and it's more like a discussion. My question is actually more subtle than the title of the post. What I ...
Ho Man-Ho's user avatar
  • 1,107
2 votes
0 answers
347 views

How to handle a research identity crisis

I have studied applied math and got a PhD (3yrs) in that field with applications in fluid dynamics. Then in my first postdoc (1.5yrs) I did again a postdoc in applied math but studied applications in ...
Riri's user avatar
  • 31
7 votes
0 answers
303 views

A citation from Dieudonné about existence, classification and construction

I am looking for an exact quote from Jean Dieudonné saying more or less that there are three kinds of important problems in mathematics: problems of existence, classification and construction. The ...
coudy's user avatar
  • 18.6k
34 votes
6 answers
4k views

Why study finite topological spaces?

In rereading Thurston's essay On Proof and Progress in Mathematics I ran across this passage: … this means that some concepts that I use freely and naturally in my personal thinking are foreign to ...
Wahome's user avatar
  • 737

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