Questions tagged [research]
for questions about the process of mathematical research itself
34 questions
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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 ...
user288447
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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 ...
user288447
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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, ...
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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. ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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\...
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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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$\log(x)$ 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 ...
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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 ...
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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 ...