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71
votes
19answers
9k views

Mathematical habits of thought and action which would be of use to non-mathematicians

Once again I come to MO for help with something I'm writing for the public. Which habits of mathematicians -- aspects of the way we approach problems, the way we argue, the way we function as a ...
67
votes
14answers
4k views

How do I fix someone's published error?

Paper A is in the literature, and has been for more than a decade. An error is discovered in paper A and is substantial in that many details are affected, although certain fundamental properties ...
29
votes
8answers
8k views

Modern algebraic geometry vs. classical algebraic geometry

Can anyone offer advice on roughly how much commutative algebra, homological algebra etc. one needs to know to do research in (or to learn) modern algebraic geometry. Would you need to be familiar ...
9
votes
0answers
273 views

What is a good poster for a math conference?

I'm going to participate to a conference and they ask me to do a poster on my research. I've never made a poster for a conference/seen a poster session in a conference. So what is important? What do ...
82
votes
107answers
26k views

Most memorable titles [closed]

Apparently, for a large number of readers, the choice whether they select to read a paper or not is often strongly influenced by the title. I was wondering if the MO-users would be willing to share ...
38
votes
18answers
5k 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 ...
84
votes
14answers
12k 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 ...
1
vote
1answer
188 views

Submitting lecture purposal to conferences. (lecture about a thesis) [closed]

I wish to consult with you about something: I have recently given a lecture about my master's Thesis in a local conference organized by my advisor. The subject had a lot to do with algebraic geometry ...
4
votes
0answers
150 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 ...
22
votes
5answers
2k 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 ...
5
votes
2answers
348 views

Mazur's torsion theorem on elliptic curves and its generalisations

I want to study Mazur's torsion theorem for elliptic curves over $Q$ and its generalizations for number fields, i.e., papers by Kamienny, Kenku & Momose, Filip Najman. So please suggest to me what ...
9
votes
2answers
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 ...
23
votes
3answers
1k views

Is “problem solving” a subject to be taught?

I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all grades. The peoples involved has sent me the textbook for seven graders (13 ...
16
votes
3answers
11k 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 ...
50
votes
7answers
5k 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 ...
26
votes
16answers
18k 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 ...
6
votes
4answers
2k views

Help me find good math questions for my students

I am a teacher at 西铁一中。 I teach mathematics in English for students going abroad. Now this is my problem, there are few mathematics books written in English that are at the level of high school, ...
16
votes
14answers
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 ...
8
votes
3answers
736 views

What´s essential to learn about complex spaces and several complex variables for an algebraic geometer?

Hi, I don´t know if this question is suitable for this site. The field of several complex variables is too broad, so I would like to know what´s essential to learn about complex spaces and several ...
35
votes
15answers
3k views

How does the work of a pure mathematician impact society? [closed]

First, I will explain my situation. In my University most of the careers are doing videos to explain what we do and try to attract more people to our careers. I am in a really bad position, because ...
6
votes
3answers
730 views

How to Discover Counterexamples and Required Objects [closed]

What are strategies or tips, which research mathematicians have discovered through their work and experience, that would help undergraduates learn how to discover counterexamples or find an object on ...
4
votes
1answer
792 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 ...
20
votes
9answers
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 ...
8
votes
0answers
281 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 ...
12
votes
2answers
1k 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 ...
7
votes
9answers
2k 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 ...
22
votes
7answers
2k views

Should one attack hard problems?

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
2answers
1k 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 ...
9
votes
0answers
338 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 ...
18
votes
3answers
2k 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
1answer
608 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 ...
22
votes
2answers
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
6answers
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 ...
40
votes
8answers
4k 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
5answers
1k views

Permission to use Online Notes

Hello, I am a new professor in Mathematics and I am running an independent study on Diophantine equations with a student of mine. Online I have found a wealth of very helpful expository notes ...
4
votes
2answers
779 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 ...
50
votes
7answers
7k 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
2answers
2k 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 ...
116
votes
8answers
4k 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 ...
19
votes
9answers
1k views

What are some interesting problems in the intersection of Algebraic Number Theory and Algebraic Topology?

I'm a beginning graduate student and while my background is primarily in algebraic number theory, I've found myself a bit smitten with the subject of algebraic topology recently after only having read ...
3
votes
0answers
335 views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-modules and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, A Primer of Algebraic D-Modules ...
39
votes
4answers
3k views

before taking on a graduate student [closed]

This post asks for resources to handle the following situation: "I, suddenly, have students" and many wonderful answers have been provided. My question here is sort of a prequel: recently, a ...
2
votes
0answers
521 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 ...
14
votes
2answers
918 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 ...
23
votes
2answers
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 ...
20
votes
3answers
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' ...
11
votes
2answers
1k 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
4answers
614 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 ...
15
votes
2answers
2k 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 ...
6
votes
2answers
944 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 ...