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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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 ...
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 ...
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 ...
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 ...
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 ...
135 votes
14 answers
28k views

Careers advice for Ph.D.s without current postdocs or university jobs

Hi, I'm sure I'm not the only Ph.D. mathematician on MO in serious need of career advice. I'm sure there will be other readers in similar situations, who will find any good advice very helpful. Can ...
93 votes
5 answers
12k views

Note rejected from arXiv: what to do next?

Short version: A note of mine was rejected by the arXiv moderation (something I didn't even know was possible) on account of being “unrefereeable”. The moderation process provides absolutely no ...
92 votes
7 answers
18k views

Lost soul: loneliness in pursing math. Advice needed. [closed]

This is a atypical question for the forum. I'd like to get some advice on whether I should keep pursuing Math in the traditional route, i.e. get a PhD, do research & teach, etc. Due to financial ...
91 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,...
75 votes
7 answers
18k views

What items MUST appear on a mathematician's CV?

Writing a CV makes me paranoid that I'm failing to abide by unwritten rules. Of course CVs are flexible to capture the diversity of accomplishments someone might have. But there must be plenty of ...
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 ...
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 ...
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 ...
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 ...
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 ...
55 votes
18 answers
8k views

How can an extremely mathematically talented young person be helped to fulfill his/her potential?

Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented $11$ years old student and I don't know how I can help him. For ...
55 votes
5 answers
48k views

Advice for pure-math Phd students [closed]

Pursuing a Phd in pure math can be a daunting task. A number of students who begin a Phd in pure math don't complete it, and there are high-quality dissertations and those which are not so high ...
54 votes
8 answers
6k views

Proper way to deal with papers you've already refereed.

This question is anonymous for obvious reasons. I referee what feels like a decent number of papers (though I don't know how many is normal!), and I try to take it seriously. Sometimes, based on ...
53 votes
16 answers
66k views

Undergraduate math research

I believe this is the right place to ask this, so I was wondering if anyone could give me advice on research at the undergraduate level. I was recently accepted into the McNair Scholars program. It ...
52 votes
8 answers
10k views

Publishing a bad paper?

First, I apologize if mathoverflow is a bad fit for this question, but it is the only place where I can think to get advice from professionals given my circumstance. I'm also sorry about any vagueness ...
49 votes
3 answers
13k views

how to use arxiv?

This is a soft question. How do people usually use arxiv to put their papers? At which stage does one usually put his/her paper/report there? Someone suggests me to submit a paper while putting it on ...
47 votes
4 answers
6k views

How much reading do you do before you attack a problem?

When going off on a tangent from your regular area, where, presumably, you have such mastery of all cutting-edge research from your routine reading that you hardly need to do any extra (if this is ...
45 votes
3 answers
18k views

Submission of a paper with a serious error to a good journal

I recently obtained (or so I thought) a good result, and after a month of reading and rereading what I'd written, submitted my paper to a very good journal. I'm early in my career (got my Ph.D. a few ...
44 votes
8 answers
6k views

Should one attack hard problems? [closed]

When I applied for a PhD student position I had an interview with two professors. Somehow we touched the problem if $P$ is $NP$ and, once we got there, for some reason both professors made it clear ...
44 votes
3 answers
9k 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 ...
43 votes
11 answers
8k views

Research topics restricted to students at top universities?

Hello everybody. I am a Ph.D student in North America looking for advice about my prospective research area. My supervisor works in a research area, let's say area A, so as soon as I was accepted as ...
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.)
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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 ...
36 votes
5 answers
4k views

Advice for researchers outside academia

Perhaps some personal background is relevant to this question. A couple of years ago, I graduated with a master's degree in Applied Mathematics from a good Dutch university. Even though I obtained ...
36 votes
3 answers
28k views

What counts as an 'invited' talk?

When you write your CV, what do you count as an invited talk? Does it count if you're invited but not provided funding (this has happened to me several times at AMS special sessions)? What if someone ...
34 votes
3 answers
25k views

How to transition from pure math PhD to nonacademic career?

I'm finishing up a PhD in math and am thinking about options outside of academia. So far, I've really only focused on pure mathematics, but I have a year left of grad school. Suppose I am interested ...
31 votes
6 answers
8k views

Pros and cons of specializing in an esoteric research area

If a mathematician specializes in a popular research area, then there are many job positions available, but at the same time, many competitors who are willing to get such job positions. For an ...
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 ...
31 votes
2 answers
5k views

A question about rejected journal submissions, similar results, and discrepancies between the order of submission and the order of publication [closed]

Today I just received the decision of my paper from a journal. The paper was submitted last December and my paper is kind of long (about 40 pages), so I think it's reasonable to take such a long time ...
30 votes
7 answers
13k views

Advice on doing mathematical research [closed]

Please share any general tips or advice you have on doing mathematical research. How do you identify good problems to work on or to think about? What do you do when you get stuck on a problem? Etc.
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 ...
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 ...
29 votes
17 answers
7k views

Research-only permanent positions worldwide

Most academic jobs involve some amount of teaching. Post-docs generally do not, but they are only short-term positions. Question: in which countries can one obtain a research-only permanent ...
29 votes
11 answers
9k views

Switching Research Fields

I am a recent PhD specializing in algebraic geometry. But I also want to do research in some other areas of math (e.g. quantum computation, compressed sensing, and PDE's). What would be a good way of ...
29 votes
3 answers
3k views

Etiquette of publishing folklore results

I am wondering what is the etiquette of publishing a "folklore" result? Though special cases of the result are well-known, the proof is not readily available in any reference text or paper I've seen....
28 votes
9 answers
4k views

Can breadth hurt a job candidate? [closed]

I am a junior mathematician, currently on the job market. I have been involved in a number of projects spread over several very different topics of mathematics, some being very mathematical projects ...
28 votes
6 answers
4k views

Oneupsmanship and Publishing Etiquette

Apologies for the anonymous (and, in hindsight, mildly longish) question. I have an etiquette question on publishing an improvement of another author's work, but I figured a thread on the matter to ...
28 votes
2 answers
2k views

When should I publish my results?

I just finish my masters thesis, and I was told by one of the referees that I should publish some of the results in there. However I feel that I mainly repeat arguments by other people in a slightly ...
27 votes
2 answers
2k views

How to balance writing professionally and being able to have a conversation with your reader?

Background. I am someone at the very very beginning stages of my career as a mathematician, and am, for example, almost ready to (re)submit my first paper. I have already read a lot of essays on how ...
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 ...
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26 votes
5 answers
3k views

Presenting work in progress [closed]

At some point in the evolution of a project, one has to decide when to start talking about it in seminars and at conferences. I am interested in hearing about how other mathematicians make this ...
26 votes
2 answers
2k views

When a journal doesn't give your work a fair chance [closed]

There is no way around the fact that determinations about the relative contributions of papers and journal acceptances will always be highly subjective. In addition, editors and referees are busy ...
24 votes
5 answers
6k views

Is the field of q-series 'dead'? [closed]

I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead ...
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 ...