# Questions tagged [advice]

The advice tag has no usage guidance.

95
questions

**1**

vote

**1**answer

210 views

### Kashiwara-Schapira Trilogy

I’m going to start reading Kashiwara-Shapira’s trilogy Categories and Sheaves, Sheaves on Manifolds, and Perverse Sheaves with someone soon. Flipping through the table of contents for Sheaves on ...

**71**

votes

**4**answers

6k 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 ...

**31**

votes

**6**answers

6k 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 ...

**2**

votes

**1**answer

363 views

### What are some problems for research in functional analysis that can possibly be solved by someone with basic knowledge of the subject? [closed]

I wanted to know are there any problems in Functional Analysis (FA) that can possibly be successfully tackled by someone like me who does not have any expertise in this area but is only familiar with ...

**2**

votes

**0**answers

168 views

### What kind of work experience should be included in a math CV?

I am applying to numerous PhD programs in number theory for admission next Fall and I want to have a CV prepared, in part because I want to attach a CV to emails I send out to professors at some of my ...

**168**

votes

**13**answers

48k 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 ...

**5**

votes

**2**answers

389 views

### Tricks for getting a creative idea [closed]

Caveat: I fear that people will criticize me for asking this potentially inappropriate question here, but I guess that the community here is quite unique in the ability of potentially answering my ...

**25**

votes

**5**answers

4k 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 ...

**1**

vote

**0**answers

117 views

### Doubts related Shifting from Pure to Applied math [closed]

I am a second year (Pure) Math and (Theoretical) Physics undergraduate in India. I want to do a masters in Applied/Computational Science or Math, for which I have apply after next 7 months.
I have ...

**37**

votes

**3**answers

5k 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 ...

**55**

votes

**16**answers

5k 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 ...

**75**

votes

**18**answers

21k 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,...

**2**

votes

**0**answers

324 views

### How practical is it to change research areas within math after a PhD? [closed]

The title says most of it really. How constrained are you in an academic career based on the topic of your PhD thesis? Is it plausible for someome to be researching in an area of math vastly different ...

**3**

votes

**1**answer

413 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 ...

**0**

votes

**1**answer

233 views

### What are problems at the center of geometric topology of 2 dimensions? [closed]

I am working on Geometric Topology in 2 dimensions but I don't know which problems are important and make many connections between different areas. I hope Mathematicians can give me some ideas? Thank ...

**1**

vote

**0**answers

76 views

### I am seeking advice for a general audience expository journal [duplicate]

Prefatory note: This be off-topic for this site and, if so, I apologize and seek direction. I am seeking advice for a general audience expository journal to submit my article, “An Application of a ...

**25**

votes

**17**answers

5k 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 ...

**2**

votes

**0**answers

141 views

### Advice on research ideas on Non Linear Dynamics [closed]

I am interested in Non Linear Dynamics.
I am just a beginner to this research area in the sense that I am starting to read the research papers.
My aim is to make my project to a research paper.
But ...

**2**

votes

**2**answers

149 views

### A general question on comparison of integrals and a specific problem

When working on an applied math topic, I have come across the following general problem.
Let $f(x_1, x_2, ..., x_n)$ be a real function of $n$ real variables $x_1, x_2, ..., x_n$ which is ...

**26**

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....

**5**

votes

**0**answers

495 views

### Result About Zeta Function Worth Publication? [closed]

Over the past two years at my high school a friend and myself have been working on a paper about the Riemann Hypothesis.
In this paper we derive several definitions of the zeta function from the ...

**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 ...

**4**

votes

**2**answers

1k views

### A new result on the Diophantine equation $x^3 + y^3 +z^3 = 3$ [closed]

The above Diophantine equation is unknown to have any further integer solutions other than $(x, y, z) = (1, 1, 1)$ and $(4, 4, -5)$.
I am a prospective undergraduate mathematics student in Zimbabwe ...

**13**

votes

**1**answer

1k views

### Arithmetical results to help study arithmetic geometry?

I'm very keen to deepen my understanding of arithmetic and diophantine problems. In the past I studied some algebraic, analytic and sieve based number theory. Recently I've been reading Weil - Basic ...

**8**

votes

**1**answer

871 views

### Asking for Advices for Choosing a Ph.D thesis problem (in PDE area)

I'm a first year phd student in Germany. I've started my phd study one year ago and I'm currently confused about the topic I've chosen. The program is in the area of PDEs, and actually I didn't learn ...

**-5**

votes

**1**answer

501 views

### What's the minimum amount of knowledge to start doing research? [closed]

There are cases in which you have too much knowledge of something to do anything interesting ,and cases in which a lack of experience with a problem (and the prejudices about it) helps someone solve ...

**15**

votes

**1**answer

2k views

### Research and exposition: how does writing “basic” books affect your “serious” research work?

I can see the benefit of writing a mathematical monograph: you revise and organize your own work and recollect the key ideas of your own research. But this applies only to books aimed at researchers ...

**20**

votes

**7**answers

2k views

### Where to find (personal) motivation [closed]

I think it would be appropriate to make this question CW...
It is likely that this question will not survive here on MO for long, but I do hope that the community gives it a chance. I also hope to ...

**6**

votes

**0**answers

811 views

### Design slides for presentation (conference talk) [closed]

Question: What are approved guidelines for design good slides for a
conference talk, especially with focus on mathematics?
I'm aware of the following, general best practices for holding a ...

**51**

votes

**5**answers

42k 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 ...

**50**

votes

**18**answers

7k 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 ...

**10**

votes

**2**answers

3k views

### How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?

I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in ...

**4**

votes

**1**answer

2k views

### Preparing for Set Theory Research

Is reading Jech's text on Set Theory too little, just enough, or overkill to prepare oneself to do independent research in set theory? This would be my first attempt at doing independent research ...

**12**

votes

**0**answers

759 views

### State of research in moduli space of flat connections

I am a recent PhD student trying to settle into a research topic. Even though I have a current project I am working on, I am not particularly enjoying it and would like to switch. Before braving the ...

**37**

votes

**11**answers

6k 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 ...

**14**

votes

**2**answers

3k views

### Is it possible to get another math PhD

My undergrad being in a field other than mathematics (and not in the US), I couldn't get into the Princeton/Harvard/MIT tier of universities for my math PhD. I settled for a lesser program and got my ...

**41**

votes

**8**answers

5k 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 ...

**7**

votes

**2**answers

2k views

### How should a professor feel peace of mind when a student leaves academia? [closed]

I apologize if this is the wrong forum for this question -- if so, could somebody please point me to the correct one?
I'm a professor who recently started advising graduate students, and I'm trying ...

**10**

votes

**0**answers

487 views

### Where to find NSF Reports (For mathematical expository purpose)? [closed]

This is not asking about how to apply for funding.
I just find that some NSF funding report (near the end of the funding cycle) is quite interesting read. In particular, it's almost like a research ...

**3**

votes

**1**answer

768 views

### Math major at 36 [closed]

I decided to go for math at 36. Is this idea possible? I studied literature, political science and international relations and still I am not really sure what I am doing.
Since I was kid, I was not ...

**11**

votes

**6**answers

3k views

### submit the second part of a paper

I couldn't find similar question being asked here. The closest one I can find is When to split/merge papers?. Here is my situation: I proved a theorem. When I try to type it, I found that it's very ...

**52**

votes

**8**answers

9k 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 ...

**13**

votes

**2**answers

3k views

### Training towards research on birational geometry/minimal model program

Being a not yet enrolled independently supervised graduate student in mathematics, with prospects of applying to American graduate schools hopefully in a 1-2 years' time, I have a background of having ...

**81**

votes

**7**answers

15k 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 ...

**27**

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 ...

**18**

votes

**3**answers

3k views

### Contacting an eminent mathematician

I have recently started a PhD. and am researching an area that two now eminent mathematicians devoted considerable time to in the 1980s. However, there appears to have been fairly moderate focus on ...

**16**

votes

**2**answers

1k views

### Submitting papers “out of logical order” due to different review times or rejections

I am asking this question anonymously and apologize for the paranoia.
Suppose you submit a paper on a topic and, while the paper is under review, continue to work on the topic and make enough ...

**26**

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 ...

**23**

votes

**3**answers

2k views

### How to assess research “impact” for tenure/promotion committees

Over the last several years, the college-level promotion & tenure committee at my university has increasingly been seeking to apply "objective" criteria for assessing the impact of candidates' ...

**13**

votes

**2**answers

2k views

### Problems with Journal Submissions due to arXiv Submission? [closed]

Hello,
I wanted to ask people if they know of any journals that will not accept papers for submission if they have been already posted on arxiv. I am personally interested in Logic Journals, but ...