Questions tagged [advice]

This tag is for questions requesting advice (e.g. on a suitable publishing venue, presentation strategy, career move, ethical dilemma). It should be used in conjunction with a more specific tag, such as [journals], [teaching], [career], or [ethics].

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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 ...
2 votes
1 answer
548 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
806 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 ...
3 votes
1 answer
703 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 "...
1 vote
1 answer
533 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
655 views

Advice for PhD in Algebra

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
2 answers
374 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 ...
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 ...
9 votes
1 answer
508 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 ...
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.)
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 ...
36 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 ...
1 vote
2 answers
383 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 ...
30 votes
5 answers
5k views

Beginner's questions on the post-doc application

I am going on the (research oriented) post-doc job market (mainly in the US) this winter and would like to ask some questions. I am aware of the site http://academia.stackexchange.com, but I am ...
158 votes
8 answers
6k views

Resources for mathematics advising.

This question is possibly ill-advised. (If it is not right for this site I will delete it.) I, suddenly, have students. It is very clear to me that there is nothing in my education that has ...
57 votes
4 answers
5k views

Advice for PhD Supervisors

My first PhD student is having his viva tomorrow. Hence, I began contemplating a bit about the whole process of supervising. One thing I realized is that while there seems to be plenty of advice for ...
7 votes
2 answers
1k views

Question on academic affiliation when submitting a paper

I just finished grad school, earning a Ph.D. 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 ...
2 votes
1 answer
695 views

Where to find "Families of curves on a surface of general type" (MR0457450)?

I am currently doing some research on surfaces of general type and I need some results from Bogomolov's paper: Bogomolov, F. A. Families of curves on a surface of general type. Dokl. Akad. Nauk SSSR ...
244 votes
8 answers
30k views

Need advice or assistance for son who is in prison. His interest is scattering theory

The letter below is written by my son. I have been sending him text books and looking for answers on the internet to keep his interest up. He has progressed so far on his own and now he needs ...
2 votes
0 answers
330 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 ...
207 votes
14 answers
58k views

Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?

To begin with, I am aware of these questions, which seems to be related: How do I fix someone's published error?, Examples of common false beliefs in mathematics, When have we lost a body of ...
10 votes
3 answers
1k views

Research in mathematics without a degree in mathematics

This question might not make much sense or be a big deal for someone but I genuinely would like to know the opinions. I am currently a software developer in a small start-up. I had to drop out of ...
4 votes
0 answers
109 views

Advice on results for balls on regular $N$-dimensional grids

I have obtained some results regarding balls on regular $N$-dimensional grids. I would like expert opinion on wether the results are significant or interesting enough for (trying to) publish them in a ...
-4 votes
1 answer
422 views

Amount of mathematical knowledge required for starting Ph.D. in pure mathematics [closed]

How much mathematics should one know before starting a Ph.D. program in pure mathematics? For example what topics one must understand well to pursue a Ph.D. in US University in Number Theory (...
57 votes
16 answers
8k views

What are examples of books which teach the practice of mathematics?

One may classify the types of mathematics books written for students into two groups: books which merely teach mathematics (i.e., they present theorems and proofs, ready-made, as it were) and those ...
60 votes
10 answers
12k views

What do you do when you're stuck?

I'm pretty sure almost all mathematicians have been in a situation where they found an interesting problem; they thought of many different ideas to tackle the problem, but in all of these ideas, there ...
1 vote
0 answers
83 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
846 views

How to find research topics in Linear Algebra in Graph Theory [closed]

Note: My first question in this site. MSE users asked me to post this question here for better response I am a Masters student in Pure Mathematics. I need to do a Masters thesis in "Linear Algebra ...
90 votes
4 answers
4k views

How do you select an interesting and reasonable problem for a student?

I am interested in how to select interesting yet reasonable problems for students to work on, either at Honours (that is, a research-based single year immediately after a degree) or PhD. By this I ...
81 votes
18 answers
25k views

What programming language should a professional mathematician know? [closed]

More and more I am becoming convinced that one should know at least one programming language very well as a mathematician of this century. Is my conviction justified, or not applicable? If I am right,...
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 ...
5 votes
4 answers
456 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 ...
72 votes
8 answers
11k 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 ...
23 votes
5 answers
4k views

How to get a research paper published after the author has died?

Sometimes, a mathematician dies suddenly, leaving behind very good mathematics that didn't make it through the publication pipeline. For example, it is possible they had a paper entirely ready to ...
173 votes
8 answers
19k views

How to escape the inclination to be a universalist or: How to learn to stop worrying and do some research.

As an undergraduate we are trained as mathematicians to be universalists. We are expected to embrace a wide spectrum of mathematics. Both algebra and analysis are presented on equal footing with ...
31 votes
5 answers
5k views

How to pass on research posthumously

I've been independently researching math, for a while in the homeless community. While I am generally safe, situational realities (weather, equipment stress, health and especially how cities can ...
8 votes
1 answer
1k views

Advice: What topics to study now in analytic number Theory( And if there are video lectures( Open Online course) / Course notes available on website)

I am a person living in a 3rd world country and completed my masters in mathematics in July 2020. Then I began to study some additional topics in Pure Mathematics as I was applying for Ph.D. abroad( ...
10 votes
2 answers
1k views

Undergraduate research in Topological Quantum Field Theory

I'm really interested in Topological Quantum Field Theory (TQFT) and am currently planning to focus on it in my undergraduate thesis. My university, unfortunately, does not allow double majors in ...
2 votes
0 answers
279 views

How does one build and refine strong technical skills relevant to research?

I am an early career researcher working in an area of "hard" analysis but this is a fairly broad question. My technical skills are likely below par and my greatest hindrance to my research ...
10 votes
1 answer
1k views

Is it OK to send a manuscript to good mathematicians in the field of your paper even if they don't know you before

I am wondering if it is OK to send a finished manuscript to some mathematicians in your field for initial references or feedbacks in addition to just posting it in Arxiv, even if they do not know you ...
30 votes
3 answers
3k views

How can I seek help in preparing a very long research article for publication?

Some background first. I recently graduated with a master's degree in applied mathematics. During graduate school I began working on a paper, which I continued to work on post-graduation. A complete ...
0 votes
0 answers
184 views

Advice on how to deal with an elementary "long-to-prove" statement

I am not entirely sure if this question totally fits here. If it doesn't, I apologise in advance. In a paper I've been working on, we have a very elegant result which, when forgetting about the ...
9 votes
3 answers
2k views

Should every modern day mathematician care about category theory? [closed]

As far as I know, category theory is used mainly in topology. I have a dislike towards category theory, similar to my dislike of Bourbakism, and want to avoid it as much as I can. However, the head of ...
13 votes
2 answers
2k views

Math overdose? Professional advise how to cope with it [closed]

I'm a PhD student, currently working on my Thesis. Over the years I have many time encountered a problem. Maybe professional mathematicians know what I'm talking about? When I study a math topic, ...
-5 votes
1 answer
457 views

Rejection of a paper because of not suitable level of rigor without a single example of a mathematical error/imprecision [closed]

Question 1. A paper was rejected because of 'not suitable level of rigour' without a single example of a mathematical error/imprecision. What can the author do in this situation? It sounds a matter of ...
-1 votes
1 answer
369 views

Soft Question: Asking for advice: how to study math? [closed]

(I am aware that some people might frown on this question, but I had no place to ask; this will definitely be voted to be closed in SE. I apologize in advance.) I am currently a 1st year grad student ...
0 votes
1 answer
652 views

Applying Phd directly after undergraduate [closed]

I'm a math undergraduate and I'm about to finish my second year at UCL. It's time to consider my graduate school, and I have some questions about it. In the UK, many universities provide math PhD ...
15 votes
2 answers
2k views

How to structure a proof by induction in a maths research paper?

I am 16 years old at the time of writing (so I have no supervisors to seek advice from) and I have written a mathematics research paper, which I plan on submitting to a journal for publication. I ...