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.

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5
votes
1answer
71 views

Why do people study Weyl asymptotics and partial-spectral-projections?

The major focus of the research that my advisor has me doing centers around the idea of asymptotic behavior of partial-spectral-projections on compact manifolds. In a few sentences, here is the ...
18
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3answers
2k views

What are some examples of theorem requiring highly subtle hypothesis?

I would like you to expose and explain briefly some examples of theorems having some hypothesis that are (as far as we know) actually necessary in their proofs but whose uses in the arguments are ...
0
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0answers
282 views

What question does category theory answer? [closed]

I have been studying category theory for the past couple of months and I'm struggling to understand what's the point? I'm going to build up an intuition from what I know to understand if I am on the ...
-2
votes
2answers
171 views

Basic research problems references [closed]

I have been looking for research problems in pure mathematics that I can try to solve for publishing papers. I am quite aware that it takes a lot of time and effort to get to a level where I can do ...
0
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1answer
352 views

Mathematics based only on real numbers [closed]

I'm aware that >90% will outright reject this, so feel free to ignore it. I'd much appreciate those trying to figure out in which way this question (or rather its eventual answer) would make sense. ...
0
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0answers
113 views

Status of the $n$ conjecture, and, as secondary question or reference request, what about a transfer method for this conjecture $n>3$

The n conjecture is a generalization of the abc conjecture. What is the current status of the $n$ conjecture? See also [1] Question 1. Can you tell us what about the current status of the $n$ ...
31
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4answers
3k views

How do you check that your mathematical research topic is original?

Sorry if this question is not well-suited here, but I thought research in mathematics can be identified from other science field, so I wanted to ask to mathematicians. I am just starting graduate ...
18
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2answers
2k views

Can the place of publication be harmful to one's reputation?

What can be said about publishing mathematical papers on e.g. viXra if the motivation is its low barriers and lack of experience with publishing papers and the idea behind it is to build up a ...
16
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1answer
584 views

Current status of axiomatic quantum field theory research

Axiomatic quantum field theory (e.g. the wightman formalism and constructive quantum field theory) is an important subject. When I look into textbooks and papers, I mostly find that the basic ...
4
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0answers
95 views

Book on Rigorous Renormalization

Many years ago I came across Salmhofer's Renormalization book and I studied its first chapter for a while. At the time, a professor told me the aim of the book was to develop a perturbative fermionic ...
4
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2answers
201 views

Compact spaces whose compactness does not come from a product of compact spaces

For the (Hausdorff) compact spaces I can think of, compactness is established either using a product of compact spaces (including the Heine-Borel Theorem, the Banach-Alaoglu Theorem, Stone-Čech ...
17
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3answers
728 views

Examples of improved notation that impacted your research?

The intention of this question is to find practical examples of improved mathematical notation that enabled actual progress in someone's research work. I am aware that there is a related post ...
1
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1answer
157 views

How are Poisson brackets and the variational principle related?

In the lecture Space and spaces, Segal argues that the origin of non-commutativity in classical mechanics “which is encoded in the Poisson Bracket” is the fact that the evolution of classical states ...
3
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1answer
109 views

More important or relevant progress in discretizing hard problems in physics in last decade

This is a reference request, and soft question as companion. I'm curious to ask, from an informative point of view, what about the more important progress in the goal to discretize hard problems in ...
0
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1answer
385 views

A soft question on the ABC conjecture

In Nature Vol 580, in an article about Shinichi Mochizuki's proposed proof of the abc-conjecture, there is a formulation saying: The conjecture roughly states that if a lot of small primes divide ...
5
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0answers
194 views

Interesting things you learned while grading/marking? [closed]

What are some interesting mathematical things you have learned while grading (or marking, if you prefer) student work? For example, clever proofs that students came up with; nice counterexamples or ...
6
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1answer
256 views

Game on a square grid

Not research level, comments are welcome. Consider the following game: The board is the vertices of an $n$ by $n$ square grid. Two players take moves in turns. A move is picking two vertices and ...
8
votes
1answer
630 views

Recreational mathematical papers [closed]

Sometimes it is nice to get a less technical paper on mathematics to read and learn something different for a change. These papers often make us discover some new curiosity, to think about the process ...
3
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0answers
156 views

Universal property for derived category of coherent sheaves

Let $X$ be a scheme, and let $D^{*}(X)$ be the unbounded (resp. unbounded, resp. bounded below/above, etc) derived category of coherent sheaves on $X$. The work of Robalo establishes a universal ...
0
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1answer
826 views

Do mathematicians ignore mathematical works from non-mathematicians? [closed]

Is it true that mathematicians ignore and do not like to take a look at or comment on any mathematical work or manuscript from a person outside the field of mathematics (meaning is not a professional ...
25
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3answers
1k views

What aspects of math olympiads do you find still useful in your math research?

I was rereading the book Littlewood's Miscellany and this passage struck me: It used to be said that the discipline in 'manipulative skill' bore later fruit in original work. I should deny this ...
2
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0answers
94 views

Adjoining data about singularities to “correct” the category of pure motives?

There are a few well known constructions of potential categories of pure motives for smooth projective varieties over a field. My understanding is that modulo the standard conjectures these should be ...
2
votes
1answer
165 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, ...
60
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7answers
15k views

Results that are widely accepted but no proof has appeared

The background of this question is the talk given by Kevin Buzzard. I could not find the slides of that talk. The slides of another talk given by Kevin Buzzard along the same theme are available here....
5
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0answers
157 views

To what extent is the derived category of coherent sheaves on a scheme a “homotopy type” of the scheme?

It is well known that the derived category of coherent sheaves (unbounded, bounded, and all cousins) on a scheme $X$ contain most - if not all (depending on specifics) - of the cohomological ...
3
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1answer
441 views

What are some efficient ways to keep a note of results when reading a research article in mathematics?

I learn and produce mathematics. In that process, I had to read quite a number of research articles. Question : What are some efficient ways to keep a note of results when reading a research ...
71
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4answers
6k 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 ...
36
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7answers
3k views

Interpretation of the action in classical mechanics

In classical mechanics the dynamics on a manifold $M$ are characterised by the minimisation of a functional $$ \min_{q \in C^\infty(\mathbb{R},M)} \int_{\mathbb{R}}L(q(t),\dot{q}(t))dt, $$ where $L:TM\...
4
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0answers
216 views

Hassan Akbar-Zadeh's mathematical legacy

Professor Hassan Akbar-Zadeh (Born: March 23, 1928- Iran), a prominent Iranian mathematician has died (March 23, 2020) in Paris after years of research and study. (I'm not sure of the exact dates.) ...
15
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3answers
2k views

How do mathematicians find coauthors? [closed]

I am totally new to academia so I am really not sure how mathematicians works together, can more experienced mathematicians here shed some light on how you find coauthors? I guess one way to do this ...
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2answers
338 views

Asking for advice (references/papers) in masters project in analytic number theory as i have no other source of help and i am stranded midway [closed]

Please don't downvote it. I have no other guidance. Edited as suggested by User Shreya -> I have studied number theory from David M Burton and apostol introduction to analytic number theory and ...
5
votes
2answers
240 views

Progress on a problem list

There is a list of open problems in my sub-field that was published in a journal some time ago and has had an impact on the area. Many of the problems have been solved, some have partial solutions, ...
1
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1answer
78 views

Is there a rectangular tiling based on the Padovan sequence? [closed]

I'm thinking of developing a rectangular tiling based on the Padovan sequence (think of the Fibonacci mosaic). It seems like something that should exist, but I can't find anything in the literature. ...
5
votes
0answers
399 views

Learning a new field under publishing pressure? [closed]

This question is about real situation and I do not say anything about the field of research or any name. Also, I do not have any special opinion. I just want to say a real story and know the experts ...
2
votes
0answers
249 views

Journal of serious opinions on weighty matters for mathematicians

Is there any scholarly journal of opinion on professional matters, for mathematicians, that would exclude things just as relevant to other fields as to mathematics, that is not just $\text{“}\,$...
1
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0answers
151 views

Categorical view of Hilbert’s Nullstellensatz, and Zariski topology

Let k be algebraic closed field. then $\mathbb{A}_n(k)$ as $\operatorname{Hom}(k_n,k)$ and $V(\alpha)$ as $\operatorname{Hom}(k_n/\alpha,k)$ which is true by using noether normalization theorem. so ...
44
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5answers
13k views

How and when do I learn so much mathematics?

I am about to (hopefully!) begin my PhD (in Europe) and I have a question: how did you learn so much mathematics? Allow me to explain. I am training to be a number theorist and I have only some read ...
31
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6answers
6k 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 ...
62
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30answers
4k views

Atlas-like websites on specific areas of mathematics

In this post, we look for the existing atlas-like websites providing well-presented classifications or database about some specific areas of mathematics. Here are some examples: GroupNames: https://...
5
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0answers
309 views

How often do you put your research into trash?

A soft question. I am a PhD student, at early stages of my academic career; and have personally experienced the following many times. Sometimes you come up with a result, that you are not quite ...
7
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3answers
350 views

Examples of complicated parametric Jordan curves

For test purposes I need parametric Jordan curves that are complicated in the sense of having many inflection points and ideally no symmetries. When doing online search I always land at complex ...
15
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0answers
699 views

Application of higher categories in algebra

Higher topos and derived algebraic geometry are relatively new areas and probably fewer people are working on them compared to the majority of topologists or geometers. I believe higher categories ...
3
votes
1answer
52 views

Uniqueness constraints for Delaunay triangulation

Commonly the assumption that is made on point sets that shall be Delaunay-triangulated is that no three are collinear and no four are cocircular. Those assumptions are however too restrictive: if ...
24
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3answers
3k 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. ...
11
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0answers
504 views

The status of the journal “Forum Geometricorum”

The online journal Forum Geometricorum is a sort of central organ of elementary geometry (mainly triangle geometry and related topics). It has been published regularly since 2000 but seems to have ...
21
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10answers
4k views

The meaning and purpose of "canonical''

This question is jointly formulated with Neil Barton. We want to know about the significance of canonicity in mathematics broadly. That is, both what it means in some detail, and why it is important....
57
votes
6answers
10k views

Why is the Fourier transform so ubiquitous?

Many operations and equivalences in mathematics arise as some sort of Fourier transform. By Fourier transform I mean the following: Let $X$ and $Y$ be two objects of some category with products, and ...
-2
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2answers
210 views

Early examples of proof appraisals [closed]

What are the earliest known examples for attributing proofs as 'deep', 'elegant' or 'beautiful' (or their equivalents in other languages)? Gauß for example called one of his results 'remarkable' ...
67
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9answers
17k views

Nontrivially fillable gaps in published proofs of major theorems

Prelude: In 1998, Robert Solovay wrote an email to John Nash to communicate an error that he detected in the proof of the Nash embedding theorem, as presented in Nash's well-known paper "The Imbedding ...
3
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1answer
304 views

Journey into a strange wilderness [closed]

W. S. Anglin wrote Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the ...

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