# 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.

2,156
questions

-3
votes

0
answers

74
views

### Real Life applications of Ceva's Theorem

Are there any real-life applications of Ceva's Theorem, or is it a precursor to another theory that has real-life applications? I was thinking about the Arts, and Architecture domains.
Kindly give ...

1
vote

4
answers

599
views

### What's a wrong proof? [closed]

Premise: I think that a reasonable definition of what a "correct proof" is goes like: "one which is able to convince most mathematicians in the field that a formal proof can be written ...

32
votes

7
answers

8k
views

### Do mathematicians rely on senses other than vision and hearing?

The senses of vision and hearing are commonly recognized as being important for the study of mathematics, with fields like geometry and topology relying heavily on vision, while algebra and number ...

0
votes

0
answers

105
views

### Recent results about Galois groups of number fields [closed]

I recently stumbled upon The m-step solvable anabelian geometry of number fields, and I got the following question: Have there been any other significant results about Galois groups of number fields ...

20
votes

1
answer

1k
views

### Why do we need "canonical" well orders?

(I asked this question on Math.SE earlier but received no response and am therefore moving it here, please note that I realise this question is probably incredibly naïve for the experienced set-...

10
votes

5
answers

3k
views

### Are there any other examples where "weak" and "strong" are confused in mathematics?

What are some examples of logically weak (when there are more objects satisfying) but being called 'strong' or logically strong (when there are fewer objects satisfying) being called 'weak'?

-2
votes

0
answers

120
views

### Inspiring math documentaries [duplicate]

Mathematicians often require inspiration while doing research. That can come from colleagues and peers, but also from watching inspiring math documentaries. The following documentary on Fermat's last ...

3
votes

0
answers

145
views

### English references for SGA 7 chapter I

I am struggling to read SGA 7 chapter I mostly because it is in French. Actually my aim is to understand the theorem 6.1 and the proof of it. I noticed that the author sometimes refers to the book &...

2
votes

0
answers

166
views

### Phenomena of topos

These days I am wandering on a wild adventure in an incredible but intimidating land. Fortunately, I could find a guide to some animals of this land
Phenomena of gerbes
But someone said to me that ...

18
votes

7
answers

3k
views

### Do empirical studies have a place in contemporary mathematics research?

I was thinking about the Collatz conjecture a while back (I know, not the healthiest thing to think about). It occurred to me that while I might not be able to prove it true for all positive integers, ...

29
votes

2
answers

948
views

### The probabilistic method outside of discrete mathematics

The probabilitic method is a genius idea in combinatorics, graph theory etc, where instead of constructing something by hand, you construct the thing randomly and show that there is a positive ...

52
votes

11
answers

5k
views

### What is an important mathematical question?

$\DeclareMathOperator\GL{GL}$Many times I have heard people say sentences like X is an important question/ X is a natural question. I find this very surprising because to me it's all a matter of taste....

4
votes

1
answer

140
views

### Peterson's quantum cohomology of G/P lectures

Dale Peterson famously gave a series of lectures on the quantum cohomology of flag varieties $G/P$ at MIT in 1997. These lectures are often cited in subsequent papers by other authors on the subject (...

23
votes

1
answer

1k
views

### What happened to the Salem prize?

Is the Salem prize discontinued? On the relevant Wikipedia entry, I don't see anyone since 2018 on there. Why was it discontinued?

36
votes

2
answers

4k
views

### A book about mathematical drawing on the blackboard

Several years ago, when I was just starting undergrad, I ran across an instructional text on chalking beautiful mathematical diagrams while killing time in the college library. In my infinite wisdom, ...

-5
votes

1
answer

321
views

### How much would a mathematician cost? [closed]

Recently our department lost one of the best professors who was attracted by a better University. If we were a football club, and he were a leading player, we would receive many millions of ...

53
votes

10
answers

10k
views

### What do you do when you're stuck?

I'm pretty sure almost all mathematicians have been in a situation where they found an interesting problem; they thought of many different ideas to tackle the problem, but in all of these ideas, there ...

10
votes

7
answers

3k
views

### Books containing new results

In Endless controversy about the correctness of significant papers, Denis Serre writes:
The research community is able to point out incorrect statements, at least among those which have some ...

9
votes

1
answer

329
views

### Approach to learning constructive QFT

First I would like to apologize if this post breaks any rule regarding career advice or opinion-based questions. Given that construct QFT (CQFT) is a rather small community, I found this is the only ...

46
votes

2
answers

4k
views

### Well known theorems that have not been proved

I believe that there are numerous challenging theorems in mathematics for which only a sketch of a proof exists. To meet the standards of rigor, a complete proof of these theorems has yet to be ...

1
vote

0
answers

110
views

### A question about Araki's 1962 paper on classification of irreducible symmetric spaces

I am looking at Sôhô Araki's 1962 paper for the classification of real semisimple lie algebras. Here's the link to the paper: On root systems and an infinitesimal classification of irreducible ...

-3
votes

1
answer

380
views

### Birth of a mathematical journal: a question inspired in a letter by Mittag-Leffler [closed]

In recent days I read an article from the Spanish edition of Scientific American, the article quotes details of the creation of a mathematical journal ([1]). You can to read these extracts from second ...

4
votes

0
answers

99
views

### Formal and informal proofs: Is there any "bilingual corpus"?

There are extensive libraries of formalized mathematics like those of Lean, Coq or Isabelle/HOL. What I am interested in is documents of formalized mathematics that closely follow certain informal ...

41
votes

11
answers

4k
views

### Topology in non-mathematical literature

A great piece of knowledge that I heard from a talk of Robert Ghrist, is that one of the earliest instances of non-trivial manifolds (i.e. of dimension higher than 2) appears in Dante's Paradise, ...

1
vote

0
answers

78
views

### Advice on constructing a Non-structural Flood Mitigation Model [closed]

I am not sure if this is the right site to post this. But I seek some valuable suggestions, and I believe I can get them here.
At present, I am in the final semester of my BSMS Mathematics course. I ...

16
votes

2
answers

2k
views

### What should one do before submitting a paper?

Assume I just wrote a paper. Now I would like to publish it in a journal.
What kind of things I should do before its submission?
Should I first give a few talks at seminars or conferences? Upload to ...

3
votes

0
answers

161
views

### The site and the space

There is a (seemingly simple) statement in the literature on sheaf theory, namely,
If $E$ is the site of opens of a topological space $X$, the notion of sheaf over $X$ coincides with that of sheaf of ...

8
votes

1
answer

773
views

### Re-typesetting historic math papers

What do I have to take into consideration when re-typesetting mathematical papers that are freely avaible online
if the authors are still living
if the authors have already passed away
as there won'...

18
votes

4
answers

3k
views

### Should one state the sharpest version of a Lemma even if only a weaker version is needed?

When writing a paper, it's possible that some auxiliary results hold in more generality or in a stronger version than what's actually needed to prove the main results of the article. And so here comes ...

7
votes

1
answer

441
views

### Are there journals for "fun mathematics"?

Are there peer-reviewed journals that focus on "fun mathematics"?
By this I mean fun things that do involve nontrivial mathematics and which I think other mathematicians would enjoy reading ...

1
vote

0
answers

260
views

### Cartier and the continuity of the early history of schemes

If you allow me I would divide the early history of schemes this way
_ Weil, Zariski, Bourbaki, Nagata, Van der Waerden,... up to Chevalley (you can find an interesting blog here)
J P Serre varieties ...

17
votes

3
answers

2k
views

### Why do Grothendieck topologies used in algebraic geometry typically involve finiteness conditions?

There are many Grothendieck topologies used in algebraic geometry, with complex interrelations. Generally in one of these topologies, a cover of schemes is a family of maps which is jointly surjective ...

0
votes

1
answer

93
views

### Journals of applied mathematics with an economics bent?

I'm asking here instead of the economics stackexchange because I'm interested more in the applied mathematics part, instead of just the economics; I'm interested in seeing what new research is being ...

6
votes

2
answers

393
views

### Domains that may require a good categorical background

I'm a PhD student in category theory, more specifically I study 2-dimensional category theory, that means bicategories, pseudofunctors, careful definitions of various structures you can put on this ...

2
votes

1
answer

846
views

### Is there an alternative to the arXiv for uploading mathematical papers?

Is there an alternative to the arXiv for uploading mathematical papers?
Here is the story. Upon attempting to upload a modified version of a published paper to the arXiv, it was put "on hold"...

3
votes

0
answers

150
views

### Transitive action on domino tilings

Fix a $n \times m$ rectangle and consider the set $S_{n,m}$ of all its dominos tilings.
Here are examples with $n=m=8$.
The set $S_{n,m}$ is empty if and only if $nm$ is odd, and for small $nm$, its ...

1
vote

0
answers

310
views

### Use of singular pronoun 'I' in the acknowledgements

I understand that in mathematical writing, it is standard to use 'we' regardless of how many authors there are because it includes the reader(s). In the acknowledgements, however, it seems to me that '...

9
votes

0
answers

369
views

### Useful applications of applied category theory

Led by John Baez, applied category theory (e.g. [1]) seems to accumulate much popularity. As someone who has noticed the importance of category theory in pure mathematics (e.g. homotopy theory, tqfts, ...

2
votes

0
answers

80
views

### Which definitions of "local module" have gotten traction?

It seems like "local module" has been defined a lot of ways:
if 𝑀 has a largest proper submodule. (This math.se post)
if it is hollow and has a unique maximal submodule (Singh, Surjeet, ...

40
votes

4
answers

8k
views

### Math papers where the only issue is that someone else could've done it but didn't

Do editors for top math journals ever read a submitted paper, agree that there are no mistakes and the result is new, yet still reject it on the basis that this is a top math journal and someone could'...

14
votes

2
answers

2k
views

### How do I, as an undergraduate, find interesting, accessible questions to work on to see if I'd be interested in research mathematics? [closed]

For a little more context: I'm currently an undergrad (sophomore) at a small liberal arts college with a (from my experience so far) solid math program. So far, I've taken Calc I, II, III, linear ...

12
votes

1
answer

3k
views

### How to indicate when another author has done nothing significant

Context: I am currently working on a rather important paper for my career, in the sense that it is a culmination of the past 5 years of (post Ph.D.) research. I started this particular article with 3 ...

5
votes

4
answers

405
views

### Funding programs for mathematical research [closed]

In the USA, as far as I know, the main grants available to mathematicians are collected on the NSF or the AMS websites [please, correct me if this perception is inaccurate]. On the other hand, for ...

1
vote

0
answers

190
views

### On the definition of "natural" in Mathematics [duplicate]

Often in mathematics we found objects which are qualified as "being natural". The first example appears in the vector space $\mathbb R^n$, where we say that we have the "natural basis&...

11
votes

2
answers

1k
views

### Examples of mathematical work that gained recognition after it was outlined by journalists

Having a background in both mathematics and journalism, I'm interested in examples of previously barely recognized mathematical achievements that received recognition after having been given attention ...

67
votes

8
answers

7k
views

### What to do after a pure math academic path?

I don't know whether my question is in the appropriate place. I've studied physics, and then did a PhD in (pure) math and 2 postdocs. I definitely love math research, but I am not ready to apply all ...

5
votes

1
answer

242
views

### Classification results

A typical classification result for a class $C$ of objects looks like that:
Theorem. Each object of $C$ is isomorphic to one object of the following list: [insert list here].
Examples are the ...

4
votes

1
answer

247
views

### Springer GTM Series statement of purpose (early editions)

Earlier editions of the Springer Graduate Texts in Mathematics series include a motivating statement about the purpose of the series. The current statement of purpose is as follows:
Graduate Texts ...

1
vote

0
answers

170
views

### Future of complexity classes in case NP=P

The P=NP question is still unresolved and there is no hope that the situation will ever change.
Assume now the hypothetic situation that P=NP had been confirmed:
Questions:
what will become of the ...

7
votes

2
answers

1k
views

### Mathematics of sustainable development and energy sobriety in the classroom

Faculty members are encouraged to highlight the connection between the courses we teach and climate change, and raise awareness of the issue in our lectures, across subjects in my university. I am ...