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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331 votes
16 answers
154k views

What's a mathematician to do?

I have to apologize because this is not the normal sort of question for this site, but there have been times in the past where MO was remarkably helpful and kind to undergrads with similar types of ...
2 votes
0 answers
128 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?
11 votes
1 answer
962 views

Use of an appendix in a long paper

I am writing a long paper (around 100 pages). I would consider 50 pages of it interesting in that it solves a problem of some significance in my field and contains an number of difficult ideas in the ...
12 votes
1 answer
621 views

What would you do if you improve your own result that is submitted but not published?

Here is a hypothetical situation: You have proven a result and written up a paper about it. You have submitted your article to some journal and it is being reviewed. While you are waiting, you have ...
13 votes
1 answer
777 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-...
12 votes
1 answer
792 views

Where can I find a collection of new errata for EGA?

There is an extensive list of EGA's errata on the books themselves, but my question is whether new errata, that is those found by various mathematicians after the publication, are collected somewhere. ...
9 votes
1 answer
955 views

How common is it for universities to create new positions for dual hires?

Let's say you happen to be a mathematician, and your spouse is also an academic and in a humanities field in which there are very few jobs advertised. Assuming that you can convince universities to ...
14 votes
2 answers
1k 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 ...
-1 votes
1 answer
970 views

Publication Of 50 pages [closed]

Does anyone know of a research journal in mathematics that is willing to publish 50 pages of peer-review research? I would like to submit research that explores how to develop predicate models for ...
7 votes
3 answers
602 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 ...
34 votes
7 answers
4k views

What is the best way to draw curvature?

This is more of a pedagogical question rather than a strictly mathematical one, but I would like to find good ways to visually depict the notion of curvature. It would be preferable to have pictures ...
13 votes
2 answers
985 views

Are there any organized websites for seminar/conference videos?

These days, there are many conference centers and universities recording seminars and conference talks and make them available on the web. Some examples: http://www.fields.utoronto.ca/video-archive ...
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 ...
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 ...
83 votes
28 answers
7k views

What could be some potentially useful mathematical databases?

This is a soft question but it's not meant as a big-list question. I have recently been asked whether I want to provide feedback at the pre-beta stage on a forthcoming website that will provide a ...
2 votes
1 answer
553 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 ...
9 votes
1 answer
808 views

How would you cite a result that it is not quite correct, but whose proof contains some useful ideas

There is a paper that was published 15 years ago; one of the theorems in it is wrong in general. A few years ago some people told the author that this theorem is wrong as stated, but yet a partial ...
8 votes
6 answers
767 views

Papers on history and philosophy of mathematics suitable for master's students

In the fall, I will give a course called "Perspectives in Mathematics". This is a mandatory course at our master's program in mathematics (including applied mathematics and statistics). The ...
3 votes
1 answer
706 views

Math graduate school applications and personal hardships [closed]

This question is on mathematics, career, and personal life. I.) Assumptions. i.) Suppose that I am a Junior in college majoring in mathematics at a top research institution in the U.S. I have "...
17 votes
1 answer
1k views

Application of higher categories in algebra

Higher categories and derived algebraic geometry are relatively new areas and probably fewer people are working on them compared to the majority of topologists or geometers. I believe higher ...
5 votes
2 answers
496 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 ...
9 votes
1 answer
924 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 ...
4 votes
2 answers
310 views

Reference on Operads

I was reading 'Category for Scientists' by David Spivak and I'd like some references on operads with that kind of approach, using only "basic category theory", nothing too advanced. I ...
1 vote
1 answer
538 views

I want to enter graduate school in pure math. Is doing REU in “mathematical modeling” a good idea? Is it an essential skill to learn?

(please let me know if this question is not suitable here) Hello! I'm an undergraduate rising senior majoring in mathematics and it seems that I got rejected by an REU that is held in my university ...
0 votes
1 answer
657 views

Advice for PhD in Algebra [closed]

I hope that this question is okay to post here. I'm in my final year of my master's degree in Sweden, and I'm starting to feel that some doors are closing in regards to applying for a postgraduate ...
4 votes
1 answer
229 views

Comments and reference-request on books for KK-theory

I am looking for a good reference to learn Kasparov's KK-theory, where my motivation is to understand (and hopefully can do something about) the Atiyah-Singer index theorem in terms of KK-theory. I ...
28 votes
4 answers
2k views

Advanced software for OEIS?

Is there (if not, why?) a software where I can input a sequence of integers, like into the OEIS, and then it makes some simple transformations on it to check whether the sequence can be obtained from ...
7 votes
1 answer
312 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 ...
17 votes
1 answer
834 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 ...
10 votes
0 answers
337 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 ...
57 votes
30 answers
16k views

Examples of conjectures that were widely believed to be true but later proved false

It seems to me that almost all conjectures (hypotheses) that were widely believed by mathematicians to be true were proved true later, if they ever got proved. Are there any notable exceptions?
290 votes
125 answers
90k views

What are some examples of colorful language in serious mathematics papers?

The popular MO question "Famous mathematical quotes" has turned up many examples of witty, insightful, and humorous writing by mathematicians. Yet, with a few exceptions such as Weyl's "angel of ...
4 votes
2 answers
382 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 ...
7 votes
1 answer
1k views

How to buy Spivak's A Comprehensive Introduction to Differential Geometry

This sounds a bit stupid, but how can I buy Spivak's A Comprehensive Introduction to Differential Geometry (the third edition)? It does not seem to be available on Amazon (at least most of it is not ...
27 votes
2 answers
2k views

Need for support and guidance for my near future as a PhD student (or: has stable homotopy theory become an overly algebraic theory?)

The question in brackets in the title is my main mathematical question, but does not reflect my initial motivation for writing this post. It is in fact above all for personal reasons that I'm ...
47 votes
6 answers
5k views

True by accident (and therefore not amenable to proof)

The graph reconstruction conjecture claims that (barring trivial examples) a graph on n vertices is determined (up to isomorphism) by its collection of (n-1)-vertex induced subgraphs (again up to ...
11 votes
2 answers
685 views

Where does the term "torsor" come from?

Is there a heuristic reason why principal homogeneous spaces of a group (object) $G$ (in some categories) are called $G$-torsors? Does it have anything to do with the idea of "torsion", ...
9 votes
1 answer
517 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 ...
12 votes
1 answer
1k views

Refereeing a paper containing strong statements about other papers

The title says it all. Suppose you are refereeing a paper where the author A makes strong statements about other papers by a different author B, like: the proof of Theorem 1 in paper [B] is wrong and ...
40 votes
8 answers
3k views

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

A little context and introduction: I'm currently working on a family of fonts ("Darwin") designed for use in formal writing and optimised in particular for use in mathematics articles, books,...
1 vote
0 answers
45 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: $\bullet \to \bullet$, ...
154 votes
11 answers
19k views

Why are flat morphisms "flat?"

Of course "flatness" is a word that evokes a very particular geometric picture, and it seems to me like there should be a reason why this word is used, but nothing I can find gives me a reason! Is ...
58 votes
7 answers
8k views

In what respect are univalent foundations "better" than set theory?

It was an ambitious project of Vladimir Voevodsky's to provide new foundations for mathematics with univalent foundations (UF) to eventually replace set theory (ST). Part of what makes ST so appealing ...
120 votes
33 answers
137k views

Mathematicians who were late learners?-list [closed]

It is well-known that many great mathematicians were prodigies. Were there any great mathematicians who started off later in life?
22 votes
5 answers
4k views

Collection of conjectures and open problems in graph theory

Is there something similar to the Kourovka Notebook for graph theory (or anyway an organized, possibly commented, collection of conjectures and open problems)?
183 votes
127 answers
62k views

Most memorable titles

Given the vast number of new papers / preprints that hit the internet everyday, one factor that may help papers stand out for a broader, though possibly more casual, audience is their title. This view ...
2 votes
0 answers
291 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 ...
38 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.)
13 votes
4 answers
976 views

Source for analysis of identification of structures in learner's mind and mathematical structures?

Concerning the structure of the learner's mind, psychologist Piaget claimed that There exists, as a function of the development of intelligence as a whole, a spontaneous and gradual construction of ...
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 ...

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