Questions tagged [research]

for questions about the process of mathematical research itself

Filter by
Sorted by
Tagged with
0
votes
0answers
114 views

What are some interesting problems in the intersection of Diophantine Approx and Algebraic Geometry?

I am a first year graduate student and I am eager to work on irrationality/transcendental proofs of specific numbers like Euler's constant gamma. Because backgrounds for Elliptic Curves include very ...
1
vote
0answers
157 views

Ergodic Theory and Euler-Mascheroni Constant

I am highly interested in doing research on proving irrationality of some specific numbers like Euler-Mascheroni Constant or $\zeta(5)$. A professor guided me that arithmetic nature of constants are a ...
1
vote
0answers
108 views

Initiatives to systematically archive researchers' notes

Are there ongoing initiatives to systematically archive all notes of mathematicians? If not, what body (the IMU? the AMS? The Clay fundation?...) should I contact to make that case? Of course in the ...
10
votes
2answers
1k views

How professional mathematicians deal with discouragement? [closed]

All professional mathematicians feel discouraged occasionally due to some issue. My question is: How do professional mathematicians deal with discouragement? In this link , Andrew Wiles say ...
6
votes
0answers
575 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 ...
217
votes
8answers
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 ...
3
votes
0answers
271 views

How to put a monetary incentive on an open research problem? [closed]

Since the old days, many famous mathematicians have been attaching monetary rewards to problems. I would like to put monetary bounties on some research mathematics problems. Some of those problems ...
43
votes
11answers
4k views

Reference request: Examples of research on a set with interesting properties which turned out to be the empty set

I've seen internet jokes (at least more than 1) between mathematicians like this one here about someone studying a set with interesting properties. And then, after a lot of research (presumably after ...
7
votes
1answer
851 views

Do mathematicians use notebooks to keep their results these days? [closed]

Mathematicians work a lot and are usually inspired by many things. In their lifetimes they get to publish only portions of their results. There have been stories of how Gauss, Euler, Ramanujan, ...
2
votes
0answers
141 views

A taxonomy of proof methods [closed]

I am looking for a taxonomy of proof methods in mathematics. For basic proof methods I would think of proof by contradiction, mathematical induction, structural induction (yes I am a computer ...
34
votes
5answers
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 ...
14
votes
9answers
2k views

Tools from other disciplines useful to mathematics research?

Obviously, mathematics provides essential tools for physicists, biologists, economists, engineers and many others to use in their research. Equally obviously, physics, biology, economy and engineering ...
36
votes
9answers
3k views

Why is it still common to not motivate results in publications? [closed]

This is a question about practice and publication of research mathematics. On the Wikipedia Page for Experimental Mathematics, I found the following quote: Mathematicians have always practised ...
15
votes
7answers
5k views

Learning mathematics in an "independent and idiosyncratic" way

This is a question about learning mathematics outside of the standard undergraduate/graduate education. The following is a quote from Thurston's On Proof and Progress in Mathematics: My mathematical ...
63
votes
3answers
7k views

Replication crisis in mathematics

Lately, I have been learning about the replication crisis, see How Fraud, Bias, Negligence, and Hype Undermine the Search for Truth (good YouTube video) — by Michael Shermer and Stuart Ritchie. ...
10
votes
1answer
460 views

Basic prerequisite (topics) to read current research in Diophantine equation for an independent researcher

I have completed studying Galois theory, Fermat's Last Theorem for Regular prime and some number theoretic complex analysis (prime number theorem), and basic linear forms in logarithm. What else ...
3
votes
1answer
255 views

Is there a precise relationship between the goals of moduli theory and the minimal model program?

I want to get into some of the big classification problems in algebraic geometry, but have a very broad question. Ultimately we would like to classify all varieties over some field up to isomorphism, ...
25
votes
3answers
4k views

Evaluation of the quality of research articles submitted in mathematical journals: how do they do that?

I would like to know as curiosity how the editorial board or editors* of a mathematical journal evaluate the quality, let's say in colloquial words the importance, of papers or articles. Question. ...
14
votes
6answers
5k views

The work of mathematicians outside their professional environment

As it is reasonable to think the work of mathematicians will be developed/made in their offices of universities (or in eventual seminars or conferences), here are the colleagues, books and journals, ...
7
votes
1answer
397 views

Survey article model theory research

I've taken a graduate course in model theory and I like it so much that I can imagine doing research in this area. Are there survey articles or review papers on the current research topics in model ...
35
votes
3answers
4k views

On math looking obvious in retrospect [closed]

Admittedly, a soft-question. I, being a very young researcher (PhD student) have personally faced the following situation many times: You delve into a problem desperately. No progress for a very long ...
8
votes
0answers
481 views

When is a paper finished? [closed]

How much truth is there to Chomsky's remark that "mathematicians stop working when things get too difficult"? https://youtu.be/atupfHizJxM?t=453 Is this true in your own work? How do you know you ...
24
votes
5answers
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
0answers
199 views

When writing a research paper, what is the acceptable format for acknowledging my advisor?

I am writing a paper for an independent study course I am enrolled in. I have contributed all of the work to the project. My supervisor has been a guiding force during this research, suggesting things ...
0
votes
0answers
63 views

Is the exact solution of the wave equation for the scattering of waves by a disk/cylinder an open problem?

The solution exact solution of the Helmholtz equation for the scattering of waves by a sphere is relatively straightforward and has been known since the time of Lord Rayleigh. The exact solution of ...
1
vote
0answers
157 views

Rate of convergence for difference between conditional and marginal probability

Suppose $X\sim \text{Bin}(2n,p)$ and $X_1,X_2\sim\text{Bin}(n,p)$ are independent, with $X_1+X_2=X$. I'm interested in the rate of convergence for the absolute difference $$ \left\vert P(X>c|X_1\...
2
votes
0answers
218 views

Research trends on mean curvature flow

It's been a few months since I've been curious about mean curvature flow and now I'm reading Robert Haslhofer's lecture notes. I like the subject and would like to do research on it, but I know ...
1
vote
0answers
307 views

How to approach a respected researcher? [closed]

I'm developing a theory that (I think) is pretty good and something new. I'm thinking of contacting a respected researcher (one of the best in the field), mainly because I'm not 100% that this has not ...
2
votes
0answers
252 views

Currently active Research Areas in Topological Groups

I have done my Master's degree in mathematics and currently I am doing Ph.D. in mathematics in India. I have completed my course work and my supervisor works in Topological Groups. He suggests me some ...
2
votes
0answers
396 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 ...
7
votes
3answers
2k views

Which affiliation to use when publishing, when invited professor at second university

I am a PhD student at one university and an invited professor at a second, i.e. I do not have a permanent position in the second one. Now I need to indicate an affiliation in a journal paper but I do ...
83
votes
6answers
8k views

What’s the etiquette on using diagrams that need color to be understood?

I’m working on a paper that makes heavy use of colorful diagrams to supplement the text. For most of these it would probably not be possible to create grayscale versions that convey the same ...
3
votes
0answers
771 views

How to find research topics in Linear Algebra in Graph Theory [closed]

Note: My first question in this site. MSE users asked me to post this question here for better response I am a Masters student in Pure Mathematics. I need to do a Masters thesis in "Linear Algebra ...
3
votes
2answers
3k views

$\log(x)$ or $\ln(x)$ to denote the natural logarithm in research papers? [closed]

Since the natural logarithm, i.e. with base $e$, is very commonly used in research papers and that both $\ln(x)$ and $\log(x)$ are used to denote it, it is natural* to ask which of these notations to ...
2
votes
2answers
421 views

Names of convex geometry journals

What are the names of the research journals that focus on convex geometry? I know of "Advances in Geometry" and "Discrete & Computational Geometry" but no others. Context of question: I am a ...
41
votes
9answers
6k views

What problem in pure mathematics required solution techniques from the widest range of math sub-disciplines?

(This is a restatement of a question asked on the Mathematics.SE, where the solutions were a bit disappointing. I'm hoping that professional mathematicians here might have a better solution.) What ...