The advice tag has no usage guidance.

**8**

votes

**2**answers

561 views

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

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 ...

**10**

votes

**1**answer

389 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

453 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 ...

**134**

votes

**8**answers

5k 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 ...

**12**

votes

**1**answer

966 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 ...

**48**

votes

**8**answers

4k 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 ...

**30**

votes

**8**answers

3k 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 ...

**20**

votes

**7**answers

7k views

### Advice on doing mathematical research

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.

**-5**

votes

**1**answer

346 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 ...

**36**

votes

**16**answers

28k 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 ...

**16**

votes

**2**answers

3k views

### How to make the move to a research university from a liberal arts school?

Some mathematicians are in positions that emphasize teaching at predominantly undergraduate colleges but find themselves desiring positions at research universities. This may happen because their ...

**18**

votes

**10**answers

4k views

### Research Experience for Undergraduates: Summer Programs

Some time ago, I found this list of REU programs held in 2009.
The main aspects that characterize such programs are: (a) a great deal of lectures on specific topics; and, admittedly more ...

**0**

votes

**1**answer

283 views

### What would undergraduate research consist of? [closed]

For undergraduate mathematics students looking to go to grad school, what kind of opportunities are open for research? I would assume undergrads would not be under any pressure or obligations to write ...

**39**

votes

**4**answers

3k 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 ...

**17**

votes

**7**answers

1k 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 ...

**43**

votes

**18**answers

6k 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 ...

**99**

votes

**14**answers

17k 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 ...

**5**

votes

**0**answers

436 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 ...

**28**

votes

**5**answers

14k 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 ...

**10**

votes

**2**answers

1k 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 ...

**21**

votes

**3**answers

16k 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 ...

**61**

votes

**7**answers

7k 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 ...

**16**

votes

**14**answers

2k views

### Teaching a pedagogy course

At my institution incoming graduate students must take a semester long course on pedagogy taught by current grad students. I may soon be in the position of having to teach this course and I'm looking ...

**4**

votes

**1**answer

1k 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 ...

**21**

votes

**9**answers

3k 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 ...

**10**

votes

**0**answers

443 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 ...

**13**

votes

**2**answers

2k 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 ...

**8**

votes

**8**answers

3k views

### Mathematical Advice for Interested Highschool Students

This may not be a research level math question, but I believe it is still relevant to Math Overflow.
What general resources exist for students in highschool who are very interested in ...

**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

396 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 ...

**19**

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 ...

**3**

votes

**1**answer

656 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 ...

**24**

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 ...

**9**

votes

**6**answers

2k 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 ...

**44**

votes

**8**answers

5k 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 ...

**7**

votes

**2**answers

1k 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 ...

**61**

votes

**7**answers

9k 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 ...

**9**

votes

**2**answers

3k views

### Does it ever make sense NOT to go to the most prestigious grad school you can get into? [closed]

I'm a senior undergrad at a top-ish(say, top 15) math school. I'm a solid, not stellar, student. This year I'm taking the qualifying exam grad courses in algebra and analysis and have been taken aback ...

**2**

votes

**0**answers

567 views

### Advanced High-Schooler Seeking Career Advice [closed]

Hello,
I have looked around quite a bit on Math Overflow and haven't found a similar question, so I'm posting it here. I understand that this isn't the typical forum for such a question but it's as ...

**15**

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 ...

**25**

votes

**2**answers

1k 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 ...

**21**

votes

**3**answers

1k 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' ...

**12**

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 ...

**3**

votes

**4**answers

631 views

### 2 short article vs. a long one [closed]

Hi,
I am a beginning mathematician and I need some publishing advice. I have some results obtained during my PhD research and I was wondering about the best way to publish them.
My initial intuition ...

**6**

votes

**2**answers

1k views

### Should I write to the referee? [closed]

I have submitted a paper to a good journal about 3 months ago. Now I have realized that there is a mistake in the paper. Now I have completely corrected it. It is not a very serious error, but I ...

**26**

votes

**5**answers

2k 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 ...

**8**

votes

**7**answers

7k views

### Undergraduate approach to learning math [closed]

I am going into my sophomore year as an undergraduate and I would like to ask the more experienced folks a couple questions about learning math and related things. What are your experiences and advice ...

**24**

votes

**9**answers

3k views

### Can breadth hurt a job candidate?

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 ...

**145**

votes

**16**answers

57k views

### What's a mathematician to do? [closed]

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 ...

**6**

votes

**0**answers

838 views

### Advice on submission of a paper. [closed]

Dear all,
I just received a letter from editors of one of top journals, saying
"Though the expert consulted felt that your paper, "is a solid paper,"
the expert did not recommend publication in ...