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.
2,330 questions
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Recursive pointfree approach to algebraic topology
$\newcommand\seq[1]{\langle#1\rangle}$A large number of important topological results require simplicial-algebraic machinery (or comparable) to prove. This machinery is ingenious, impressively so even,...
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$p$-adic concepts having no analogue in the real case
I've always been fascinated how among completions of $\mathbb{Q}$, the real field $\mathbb{R}$, althrough historically more "ancient", seems to be the odd one out. Many interesting concepts ...
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What happened to the second volume of Scharlau's biography of Grothendieck?
I am not sure whether this is the right place to ask this question, but I do not know a better place. Feel free to close it if you think that it is off-topic.
I recently discovered that the number ...
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Simplicial complexes arising from Young diagrams and their homotopy type as wedges of spheres
My coauthors and I are finishing a paper in combinatorial and topological algebra, in which we define a class of simplicial complexes arising from Young diagramin the following way.
Let $\lambda = (\...
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Retiring early to pursue research in Pure Mathematics
I would like some advice in my situation. I am currently a medical student at the verge of graduation. I will start practicing after 2 years. Where I work, the pay is very good for physicians and I ...
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Great theorems with elementary statements: 2026-onward
My 2021 book
Landscape of 21st Century Mathematics, Selected Advances, 2001–2020
collects great theorems with elementary statements published in 2001-2020. I now finishing the second edition of this ...
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Restrictions of metrics
A metric $d:M^2\rightarrow \mathbb{R}$ is any mapping that satisfies the well-known textbook definition of metric space $(M, d)$. In certain areas (optimal transport, topometric spaces, and quantum ...
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How different are the categories $\mathbf{Ring}$ and $\mathbf{Ring} \hookrightarrow \mathbf{Rng}$?
When we define a group homomorphism $\theta \colon G \to H$, we do not have to specify that $\theta(e_G) = e_H$. On the other hand, most literature defines a ring homomorphism $h \colon R \to S$ with ...
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Which exact sections of Higher Topos Theory are required for “Higher Algebra”?
I am currently reading Lurie’s “Higher Topos Theory” as a prerequisite for his book “Higher Algebra”. At the start of HA he mentiones that an exposition to $\infty$-categories is required and cites ...
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How to refer to Russian mathematicians?
I need to cite several Russian mathematicians in a paper and I would like some advice on how to write their names and how to write the bibliography. My main concern is to respect the name they were ...
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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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