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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36
votes
8answers
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
245 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.) ...
16
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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 ...
5
votes
2answers
258 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
vote
1answer
86 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
413 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
267 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
154 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 ...
43
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5answers
14k 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
votes
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
votes
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
votes
0answers
334 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
votes
3answers
383 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
719 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
55 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 ...
23
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. ...
11
votes
0answers
621 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
votes
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....
60
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
votes
2answers
214 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' ...
69
votes
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
votes
1answer
314 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 ...
15
votes
1answer
813 views

Are evil properties really evil

I have this question for a moment now, so I think it is time that I sort it out. I got into category theory and homotopy type theory at the same time, and so I have always read and been told that one ...
24
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5answers
3k views

Examples of incorrect arguments being fertilizer for good mathematics? [duplicate]

Sometimes (perhaps often?) vague or even outright incorrect arguments can sometimes be fruitful and eventually lead to important new ideas and correct arguments. I'm looking for explicit examples ...
3
votes
0answers
168 views

What do you call an object constructed as part of a proof? (Terminology)

I find myself wanting to talk about parts of a proof, e.g. the role played by mathematical expressions within a proof. When proving a theorem it is common to construct some kind of object and then ...
93
votes
2answers
8k views

Extent of “unscientific”, and of wrong, papers in research mathematics

This question is cross-posted from academia.stackexchange.com where it got closed with the advice of posting it on MO. Kevin Buzzard's slides (PDF version) at a recent conference have really ...
15
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4answers
1k views

Quirky, non-rigorous, yet inspiring, literature in mathematics

In contrast with such lucid, pedagogical, inspiring books such as Visualizing Complex Analysis by Needham and Introduction to Applied Mathematics by Strang, I've had the pleasure of coming across the ...
2
votes
1answer
380 views

What are some problems for research in functional analysis that can possibly be solved by someone with basic knowledge of the subject? [closed]

I wanted to know are there any problems in Functional Analysis (FA) that can possibly be successfully tackled by someone like me who does not have any expertise in this area but is only familiar with ...
6
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2answers
678 views

Why do we study complex orientable cohomology theories

It seems that much of the literature in stable homotopy theory seems to study complex orientable cohomology theories. What is the reason of restricting to this class of multiplicative cohomology ...
0
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0answers
331 views

Artificial intelligence simulating mathematicians (what a distopia!)

This is kind of soft and naive question, so feel free to shame on me :) I start from the fact that, in my opinion, what humans are interested in about mathematics are things that we find deep and ...
0
votes
1answer
94 views

Visualization of the disintegration theorem [closed]

Where can I find a picture that gives a visualization of the disintegration theorem? If such reference does not exist, what would a nice visualization of this fundamental result look like?
3
votes
1answer
125 views

“discrete” objects of a $2$-category

Let $\mathcal{K}$ be a $2$-category. Is there a special name of those objects $B \in \mathcal{K}$ which have the property that the category $\mathrm{Hom}_{\mathcal{K}}(B,C)$ is essentially discrete ...
0
votes
2answers
738 views

Should the “L” in the term latin/Latin square be capitalized? [closed]

In Denes and Keedwell's book the word "latin" is not capitalized, and there seems to be some precedent in the literature for this usage. However, the vast majority of work on the subject capitalizes ...
2
votes
1answer
271 views

Having a paper published via both Conference Proceedings and via a refereed journal

Forgive me if this isn't the right place to pose this question. I do need guidance on this. In 2018 I had submitted a paper to a refereed journal. It had gotten accepted for publication by said ...
57
votes
62answers
11k views

Mathematicians with both “very abstract” and “very applied” achievements

Gödel had a cosmological model. Hamel, primarily a mechanician, gave any vector space a basis. Plücker, best known for line geometry, spent years on magnetism. What other mathematicians had so distant ...
25
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4answers
2k views

Software and ideas for workshops and conferences with long-distance participants

Conferences and workshops are often great - getting together and being together is an ideal setting for doing research and learning things. However, there are various reasons to encourage the ...
1
vote
0answers
109 views

Mathematical problems reducing to the traveling salesman problem

The superpermutation problem is: what is the shortest word that contains every permutation of $k$ letters as a substring. This can phrased as a Travelling Salesman Problem, where the nodes of your ...
1
vote
1answer
244 views

Examples of “irregularities” in mathematics, other than prime numbers [closed]

Prime numbers are the prime example (no pun intended) for something that arises apparently without describable patters; we know that infinitely many exist, that gaps between them can be arbitrarily ...
14
votes
5answers
815 views

Mathematical words outside of mathematics [closed]

We've all heard expressions like "We need to factor this into the equation," where mathematical words have broader meanings than strictly mathematical. I'd like to develop a collection of such usages. ...
28
votes
18answers
6k views

Modeling in pure math

We all know that models play a major role in scientific practice. (By "model" here I mean any of various kinds of entities that function as representations or descriptions of real-world phenomena. ...
1
vote
1answer
159 views

Transitive closure in category setting

Let $\mathscr C$ be a category so that every morphism is 'invertible' only up to equivalence and so that it makes sense to say two morphisms are 'homotopic to each other'. Probably this is called $(2,...
8
votes
1answer
999 views

Wikipedia article on forbidden graph substructures

I apologies if this is too trivial a question or if I am over complicating anything here. But I was hoping for some clarification in an article I was reading about forbidden graph substructures on ...
10
votes
1answer
379 views

Examples of proofs using induction or recursion on a big recursive ordinal

There are many proofs use induction or recursion on $\omega$, or on an arbitary (may be uncountable) ordinal. Are there some good examples of proofs which use a big but computable ordinal? The ...
73
votes
10answers
10k views

What are examples of (collections of) papers which “close” a field?

There is sometimes talk of fields of mathematics being "closed", "ended", or "completed" by a paper or collection of papers. It seems as though this could happen in two ways: A total characterisation,...
5
votes
1answer
449 views

Adding something to a book from an unpublished paper

As many of the people that I am spamming in real life might at this point know, I am turning my coend note into a book. I would like to add a few pages taken from a (still) unpublished paper of mine (...
1
vote
1answer
133 views

Results on additive structure of polynomial rings?

Cross-posted from Math.SE. I've been wondering recently about results for irreducibility that use the "additive structure" of the polynomial ring at hand. For instance, can we say anything about the ...
11
votes
1answer
632 views

Searching for a Thurston paper with egg / 3-manifold analogy?

I remember coming across some article of Bill Thurston’s where he describes a 3-manifold (with boundary?) as being like an egg. In my recollection the interior of the egg, the shell, and even the ...
5
votes
1answer
163 views

Grauert's Contractibility Theorem

I am interested in reading the proof of Grauert's Contractibility Theorem, asserting that an integral compact curve in a smooth compact surface (without the projectivity assumption - this is the case ...
13
votes
1answer
538 views

Constructing computable synthetic differential geometry?

I'm a computer scientist, not a mathematician, so apologies if I've messed up a lot of things greatly. I've been reading about synthetic differential geometry, and trying to formalize it in Coq. ...
1
vote
1answer
111 views

'Quotient' of indexed categories and pushforward congruence relations

If $R\subset C$ is a vector subspace of $C$, and $F: C \to D$ is a linear map, then we have a natural linear map $C/R\to D/F(R)$. I was wondering if this can be also generalized to categorical ...

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