Questions tagged [soft-question]
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
2,320 questions
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Known examples of conjectures stated while suspected false, to invite counterexamples?
Sometimes, in computational or experimental mathematics, one faces statements that seem almost certainly false yet are not directly refutable by current methods or feasible computation.
In such cases, ...
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Which fields use homological algebra extensively?
I am currently very invested in homological algebra and since it is not a good research field itself (correct me if I’m wrong), I was wondering which fields use it much. My professor suggested ...
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My dissertation is wrong, but I already defended. How to remedy?
When I first started working with my PhD advisor, he gave me a problem to work on. When my 5 years was about to be up, I had not published any papers but managed to write up solutions to two ...
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Why it takes so long to referee a paper in some journals?
Some of the top mathematics journals typically take around two years to referee a paper, and sometimes even longer.
I am aware of a case in which a paper was under review for three years before being ...
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Examples of mathematically interesting numbers that can be expressed as an integer tetration (besides Graham’s number)
It is well-known that Graham's number, $G$, can be expressed in radix-$10$ as a (very large) base-$3$ tetration with hyperexponent $n_{G} \in \mathbb{N}$ (i.e., $G := {^{n_{G}}{3}}$).
So, my natural ...
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How can referees verify computationally intensive results when HPC resources are required?
This question is somewhat related to my previous question and is also inspired from this other question concerning the credibility of extensive computations (although from a different perspective).
In ...
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Stone–Čech remainder of countable sets
In general topology, the most common example for countable space is $\omega$ with the discrete topology. Also, we "know" very well the topological properties and the structure of $\beta \...
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Source of a quote on boxed formulas
I vividly remember once reading (or hearing?) a claim that the level of a mathematical text is inversely proportional to the
$$
\boxed{\text{density of boxed formulas}}.
$$
Now I can’t find/remember ...
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How to share algorithms for testing a conjecture?
I am preparing a paper where some results involve computational verification of a conjecture. Of course, I am not proving the conjecture in full, but I verify it for some large values of the involved ...
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Which pairs of mutually contradicting conjectures are there?
Years ago I had the pleasure of witnessing Simon Thomas giving a wonderful talk about Martin's conjecture, which I just now fondly remembered reading this question. Even though I am not well-versed in ...
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Graphical software tools for quick and easy diagrams
What tools do people use for quickly and easily creating presentable, if not publication quality, diagrams of various kinds?
When I need to make a high quality diagram, I'm happy to whip up some TikZ. ...
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Improving readability of proofs
What do you do to improve the readability of finished proofs?
I basically found out that I keep a small mental checklist of criteria that I always go through after a proof is finished to improve the ...
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When did the OEIS get even better?
I'm asking this question out of curiosity, but also (and more importantly) to publicize to the research community something great that OEIS.org is doing.
Recently, I put a sequence into OEIS and got ...
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How long are you allowing yourself to be stuck on a problem? How do you know when to stop?
I searched for this question on the site but couldn't find it, so I'm asking it.
As a researcher, how long do you allow yourself to be stuck on a problem before deciding to move on? And how do you ...
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How might mathematics have been different?
I think most people believe that mathematical truths are logically necessary. The fact that $\sqrt{2}$ is irrational doesn't depend on who proved it, when they proved it, whether they liked it, or ...