# 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.

1,877
questions

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### Online seminars [duplicate]

In the time of COVID-19 everything went online including seminars. A good thing about online seminars is that they can be attended by everyone and many seminars that I attended had more than 50 ...

**21**

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**0**answers

546 views

### Need for support and guidance for my near future as a PhD student (or: has stable homotopy theory become an overly algebraic theory ?)

The question in brackets in the title is my main mathematical question, but does not reflect my initial motivation for writing this post. It is in fact above all for personal reasons that I'm ...

**2**

votes

**0**answers

101 views

### 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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votes

**0**answers

161 views

### How to understand if one is capable of doing mathematical research or not? [closed]

This is a website for professional research mathematicians so I think nothing can be the best option else this site to ask my question. But, still I am apologizing for asking this question as it's ...

**21**

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**10**answers

4k views

### Best Springer mathematics books [closed]

I received an email from zbMATH today to the effect that, as a result of their going open access in January 2021 (which is awesome), they will no longer be able to offer their reviewer discount for ...

**29**

votes

**3**answers

1k views

### Wiki for consequences of axiom of choice?

I raised the following question as part of another MO question, but I am following the suggestion of Nate Eldredge to make it a question in its own right.
For many years, there has a been a valuable ...

**31**

votes

**2**answers

1k views

### Wayback Machine for mathematics?

I have had a couple of experiences recently which have made me wonder whether the mathematics community should try to establish and maintain something like the Wayback Machine, but specifically ...

**10**

votes

**0**answers

355 views

### Recommendations on PhD programs in Europe on number theory

I am a Master student of math in the UK, and I would like to do a PhD in number theory, preferably the algebraic side of it. Given that I am in the UK, I would probably prefer staying here or going to ...

**11**

votes

**1**answer

874 views

### Treating citation numbers as objects [duplicate]

The following item appears in the $\LaTeX$ style-guide for the Journal of Integer Sequences:
To me this seems correct and reasonable, but it in most articles I read, authors tend toward the first ...

**6**

votes

**3**answers

2k views

### Can American Math. Monthly be used to publish hard research?

My question pertains to the journal "American Mathematical monthly" published by the MAA.
I wish to ask whether a paper as a part of a PhD thesis (subject: Combinatorics ) can be submitted ...

**32**

votes

**5**answers

3k views

### 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 ...

**33**

votes

**5**answers

4k views

### How to deal with an advisor that offers you nearly no advising at all?

I am a young PhD student (24) at a Germany university and I am not sure whether this is the right place to ask this kind of question. If not feel free to move it elsewhere or delete it completely.
...

**24**

votes

**2**answers

698 views

### Sustainability of ZBmath unrestricted access

ZBmath (formerly Zentralblatt für Mathematik) will become "Open access" in 2021 (see for instance at EMS site and at FIZ Karlsruhe site). It used to be under paywall, although some partial ...

**3**

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**0**answers

405 views

### Has anyone discovered a flaw in a published proof and no one wants to rectify the situation? [closed]

A post appeared yesterday (9/22/2020) entitled ``Fear of publishing a wrong result'' on the Mathematics Stack Exchange.
https://math.stackexchange.com/questions/3836536/fear-of-publishing-a-wrong-...

**2**

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**0**answers

94 views

### Frobenius reciprocities

An adjunction of the form $\mathrm{Hom}(A \otimes X, Y) \cong \mathrm{Hom}(X, A^* \otimes Y)$ in a rigid monoidal category is sometimes called Frobenius reciprocity. Is there a result that unifies ...

**13**

votes

**9**answers

2k views

### 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 ...

**15**

votes

**4**answers

1k views

### Which mathematics book would you wish theoretical physicists had read?

It is a well-known phenomenon that mathematicians and physicists working on closely-related topics (say in gauge theories, or in general relativity etc.) generally approach the problems from very ...

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**0**answers

95 views

### Engineering mathematics course and the order of the teaching of its topics

I am going to teach a course names "Engineering Mathematics" and the topics in it, are:
Fourier series and integrals; including the motivation and computational aspects and their ...

**2**

votes

**0**answers

336 views

### Reference request for Miyaoka's wrong proof of FLT [duplicate]

Before Wiles and Taylor's proof of Fermat's Last Theorem, Yoichi Miyaoka famously (and wrongly) claimed to have solved the problem, at least for sufficiently large prime exponents. However, i have ...

**25**

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**0**answers

2k views

### What do you like in the mathematics of Vaughan Jones? And how Vaughan Jones liked mathematics to be? [closed]

Edit: Directed to mathematicians ,I think this is a suitable time to open this question to know more about the creative mathematician Vaughan Jones Probably his students are ready for getting answers ...

**4**

votes

**0**answers

237 views

### Are there topics of contemporary mathematics that simply require too much knowledge to be given as 3-year PhD problems? [closed]

Just out of curiosity, is there a topic where even an excellent graduate student wouldn't be able to master all the necessary background within 3 years (I say 3 because in many European countries a ...

**5**

votes

**1**answer

264 views

### loop space of a finite CW-complex

Let $X$ be a finite connected pointed CW-complex and $H_{\ast}(\Omega X)$ the integral homology of the loop space on $X$. Are the homology groups $H_{n}(\Omega X)$ finitely generated abelian groups ...

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**0**answers

88 views

### Leonhard Euler's Opera Omnia editions. Are old books reprint houses any good?

I am looking for Euler's Opera Omnia (in Latin), but it seems to be published ("officially") only by Birkhauser, and each volume costs about 140$, from what I have seen.
I found some of ...

**26**

votes

**1**answer

1k views

### Public games for solving open problems

Many people in the world like playing games. Also, maybe we can design special interesting games for some open problems in mathematics (or physics).
In quantum mechanics, there are some games (for ...

**2**

votes

**0**answers

166 views

### What will stand in for the JMM Employment Center this year?

The Joint Mathematics Meetings will be virtual this year, and there is no indication of there being an Employment Center (virtual or otherwise). What is the story with the Employment Center? Will it ...

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votes

**1**answer

163 views

### Why is the Dyck language/Dyck paths named after von Dyck?

The Dyck language is defined as the language of balanced parenthesis expressions on the alphabet consisting of the symbols $($ and $)$. For example, $()$ and $()(()())$ are both elements of the Dyck ...

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votes

**1**answer

424 views

### Public personal ideas: using contributions from other people

Let's say I'm thinking about an unsolved mathematical problem for a hobby and I draw some conclusions of my own. I'd like to make these ideas public, allow anyone to use them absolutely freely (even ...

**29**

votes

**4**answers

2k views

### Online, evolving, collaborative foundational text projects

There are two online, evolving, collaborative "foundational text" projects for research mathematicians that I am aware of:
(1) The Stacks Project for algebraic geometry
(2) Kerodon for ...

**48**

votes

**62**answers

12k views

### Prominent non-mathematical work of mathematicians

First of all, sorry if this post is not appropriate for this forum.
I have a habit that every time I read a beautiful article I look at the author's homepage and often find amazing things.
Recently I ...

**6**

votes

**2**answers

440 views

### Is $C^{*}$-algebra the most modern way to study QFT?

I am not an expert on either QFT or $C^{*}$-algebras, but I'm trying to learn the basics of QFT. In all books/papers and other materials that I know, QFT is studied mainly using a lot of functional ...

**3**

votes

**1**answer

126 views

### Reference for “the algebra of multiplication by all measurable bounded functions acts in Hilbert space in a unique manner”

I read a paper of Alain Connes on "Duality between shapes and spectra" and in page 4, he says
Due
to a theorem of von Neumann the algebra of
multiplication by all measurable bounded ...

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**0**answers

235 views

### Theorems with many proofs

Q. What are the characteristics of theorems that seem to invite (or possess) several or even many distinct proofs?
What I have in mind are examples such as these:
Proofs that there are infinitely ...

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votes

**4**answers

2k views

### Australian Mathematical Society journal rankings

I apologize for a question that is not about mathematics, but I believe it is of interest to research mathematicians, and I believe there may be people on MathOverflow who can answer it objectively. ...

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votes

**21**answers

8k views

### Small ideas that became big

I am looking for ideas that began as small and maybe naïve or weak in some obscure and not very known paper, school or book but at some point in history turned into big powerful tools in research ...

**6**

votes

**2**answers

147 views

### Reference for rigorous second quantization

I'd like to get acquainted with the basics of mathematical rigorous second quantization, so I'm looking for an adequate reference on this subject. I've a background in quantum mechanics, but I don't ...

**9**

votes

**1**answer

897 views

### Example of a mathematician who had problems with peer review system? [closed]

I am wondering if there is some example of a famous or well-known mathematician who often had trouble with peer review, or who often had to publish in obscure journals because referees didn't 'get' ...

**11**

votes

**1**answer

376 views

### Gromov's articles suitable for master students

I'm a master student and I have read "Monotonicity of the volume of intersection of balls" by Gromov and it was a great experience. When trying to fill the gaps, I often end up finding some ...

**9**

votes

**1**answer

351 views

### 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 ...

**15**

votes

**1**answer

642 views

### Tips to organize a successful math workshop

I am a PhD student from India working on representations of quantum groups. I want to organize a workshop on Hopf Algebra and Quantum groups but there are only 2 or 3 specialists in India currently ...

**127**

votes

**18**answers

9k views

### Suggestions for special lectures at next ICM

(I am posting this in my capacity as chair of the ICM programme committee.)
ICM 2022 will feature a number of "special lectures", both at the sectional and plenary level, see last year's ...

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votes

**0**answers

209 views

### Is the DispersiveWiki website down?

Somewhat recently I learned about a website called the DispersiveWiki which is/was maintained by James Colliander. I have found a few different links to the website from around the web (e.g. http://...

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**0**answers

58 views

### On noncommutative transcendence degrees

The original transcendence degree for (noncommutative) division algebras is the Gelfand-Kirillov transcendence degree, due to I. Gelfand and K. Kirillov ([ Sur les corps li´es aux algèbres ...

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votes

**1**answer

381 views

### Deep applications of the Pettis integral?

In the Notes section of chapter 2 of Diestel and Uhl's Vector Measures they make the comment:
"Presently the Pettis integral has very few applications. But our prediction is that when (and if) ...

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**0**answers

139 views

### Does the “coproduct-elimination transform” have an accepted name, and where can I learn more about it?

Suppose we're in a bicartesian closed category. Then given a morphism $$f : X \rightarrow Y_1 + \ldots + Y_n$$ and a test object $T$, we get a corresponding morphism
$$T^f : X \times [Y_1,T] \times \...

**14**

votes

**2**answers

575 views

### Appearance of proof relevance in “ordinary mathematics?”

I've been wondering recently what—if any—applications proof theory has to ordinary mathematics (by which I mean algebra, analysis, topology, and so on). In particular, I'd be fascinated to see a proof ...

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votes

**3**answers

377 views

### Oldest abstract algebra book with exercises?

Per the title, what are some of the oldest abstract algebra books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there. I am already aware of ...

**78**

votes

**10**answers

49k views

### What are the benefits of writing vector inner products as $\langle u, v\rangle$ as opposed to $u^T v$?

In a lot of computational math, operations research, such as algorithm design for optimization problems and the like, authors like to use $$\langle \cdot, \cdot \rangle$$ as opposed to $$(\cdot)^T (\...

**39**

votes

**4**answers

4k views

### When size matters in category theory for the working mathematician

I think a related question might be this (Set-Theoretic Issues/Categories).
There are many ways in which you can avoid set theoretical paradoxes in dealing with category theory (see for instance ...

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votes

**0**answers

282 views

### Mathematical blogs on “non-standard” platforms (Telegram, Twitter, Dzen , … )

There are many well-known excellent blogs like the ones by T. Tao, G. Kalai, J. Baez, etc. Many of them use the WordPress engine.
I have been surprised to find that there are some excellent blogs on ...

**10**

votes

**1**answer

742 views

### What kinds of papers does the Indiana University Mathematics Journal publish?

I am wondering if anyone can provide information on the Indiana University Mathematics Journal, as I have been able to find very little (ie aims and scope) on their website. I have the following list ...