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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31 votes
5 answers
4k 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 ...
9 votes
2 answers
672 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 ...
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1 vote
0 answers
181 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 ...
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9 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 ...
0 votes
0 answers
169 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 ...
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29 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 ...
user avatar
8 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
1k 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, ...
-4 votes
1 answer
346 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 ...
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6 votes
1 answer
622 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( ...
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  • 522
2 votes
0 answers
297 views

I want to enter graduate school in pure math. Is doing REU in “mathematical modeling” a good idea? Is it 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 REU that is held in my university over ...
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  • 131
-1 votes
1 answer
277 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 ...
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  • 107
0 votes
1 answer
345 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 ...
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13 votes
2 answers
1k 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 ...
user avatar
1 vote
1 answer
322 views

What qualities and achievements can outweigh bad grades? [closed]

I will try to formulate my question so that the answer is not opinion-based. My question: Considering a undergraduate math student planning to pursue a PhD program, what qualities and achievements can ...
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6 votes
0 answers
663 views

How difficult will it be to start doing research in pure mathematics in the near future? [closed]

I am a first year PhD student in mathematics (complex differential and Kahler Geometry) and the other day I had a thought about the difficulty of starting to do research. This is my first post here ...
221 votes
8 answers
28k 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 ...
4 votes
0 answers
187 views

Referring to computer software in a paper

I'm performing a calculation of the Smith normal form of an integral matrix based on the SageMath worksheet. Is it sufficient in the paper to say something like ``Using a software package like ...
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  • 311
9 votes
1 answer
734 views

Is it possible to jump ship to mathematics?

A few years back, I did an undergrad double major in math and physics, and afterwards went to a top-tier university to work on a physics Ph.D. Around about my third year of the Ph.D., I started to ...
10 votes
0 answers
570 views

Recommendations on PhD programs in Europe on number theory

I am a Master student of math in the UK, and I would like to do a PhD in number theory, preferably the algebraic side of it. Given that I am in the UK, I would probably prefer staying here or going to ...
34 votes
5 answers
3k 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 ...
10 votes
2 answers
3k views

Publishing undergraduate research

Sorry if something like this has already been asked, I searched but I couldn't find anything similar to my question. I'm a senior undergraduate and currently doing my senior thesis. My senior thesis ...
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1 vote
1 answer
473 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 ...
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81 votes
5 answers
9k 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
7k 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
546 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 ...
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  • 157
2 votes
0 answers
223 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 ...
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192 votes
13 answers
54k 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
469 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 ...
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24 votes
5 answers
5k 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
144 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 ...
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41 votes
3 answers
7k 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 ...
56 votes
15 answers
7k 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 ...
80 votes
18 answers
24k 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
421 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 ...
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3 votes
1 answer
501 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 ...
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  • 355
0 votes
1 answer
243 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 ...
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  • 303
1 vote
0 answers
96 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 ...
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  • 151
28 votes
17 answers
6k 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
151 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 ...
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  • 129
2 votes
2 answers
155 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 ...
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  • 21
27 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....
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  • 5,301
5 votes
0 answers
514 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 ...
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  • 175
27 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
2k 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 ...
user avatar
8 votes
1 answer
997 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 ...
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  • 223
-5 votes
1 answer
542 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 ...
23 votes
7 answers
3k 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 ...