# 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

**51**

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**7**answers

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### When is one 'ready' to make original contributions to mathematics?

This is quite a philosophical, soft question which can be moved if necessary.
So, basically I started my PhD 9 months ago and have thrown myself into learning more mathematics and found this an ...

**9**

votes

**1**answer

1k views

### How reliable is arXiv to use as a reference in a paper?

I'm writing a small and simple paper to finish my graduation, I never wrote or published anything before. Is about some irrational/transcendental numbers. I was mentioning some numbers that it's not ...

**8**

votes

**0**answers

467 views

### When is a paper finished? [closed]

How much truth is there to Chomsky's remark that "mathematicians stop working when things get too difficult"?
https://youtu.be/atupfHizJxM?t=453
Is this true in your own work? How do you know you ...

**2**

votes

**1**answer

413 views

### Cute/striking application(s) of snake lemma outside homological algebra

I already asked this question on MSE here https://math.stackexchange.com/questions/3254184/cute-striking-applications-of-snake-lemma-outside-homological-algebra, but still received no answer. I hope I ...

**7**

votes

**0**answers

308 views

### The meaning of this mysterious remark in Littlewood's Miscellany

In the well known book by Littlewood (Mathematician's Miscellany, or the later edition called Littlewood's Miscellany) there is a remark made in the chapter 'A Mathematical education', the meaning of ...

**37**

votes

**3**answers

3k views

### A map of non-pathological topology?

I think of topological spaces as coming in several "islands of interestingness" (the CW island, the Zariski archipelago,...) dotting a vast "pathological sea" (the long line ocean, the gulf of the ...

**19**

votes

**0**answers

816 views

### What examples of existence forcing proofs are there?

Forcing proofs tend to be fairly constructive, in the sense that if I claim that there is a forcing that does something, I usually prove this by constructing that forcing.
There are only a handful of ...

**5**

votes

**2**answers

409 views

### Tricks for getting a creative idea [closed]

Caveat: I fear that people will criticize me for asking this potentially inappropriate question here, but I guess that the community here is quite unique in the ability of potentially answering my ...

**16**

votes

**2**answers

2k views

### Is differential topology a dying field? [closed]

I recently had a post doc in differential topology advise against me going into the field, since it seems to be dying in his words. Is this true? I do see very little activity on differential topology ...

**2**

votes

**0**answers

368 views

### Reading list in dynamical systems

So I’ve managed to gather from various sources, a plethora of books in dynamical systems. Now I’m wondering which of them to read, and in what order.
So far these are the books I’ve found/been ...

**0**

votes

**0**answers

74 views

### Fractional and Exterior Calculus

I am interested in fractional calculus and was wondering is there an equivalent/analagous fractional exterior calculus or fractional theory of differential forms? If so can someone point me out to ...

**25**

votes

**5**answers

4k views

### Is the field of q-series 'dead'? [closed]

I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead ...

**0**

votes

**0**answers

81 views

### Alternate Ways of Writing Complex Summations

In my writing, I often have to consider summation formulas where describing the terms of the summation make the equation rather weirdly spaced out. For instance, I am currently considering the formula
...

**12**

votes

**4**answers

3k views

### Grade-school elementary algebra presented in an abstract-algebra style?

I remember once hearing a (probably apocryphal) story about a university math professor that tried to teach a gradeschool class about algebra by telling them a few simple axioms and definitions and ...

**0**

votes

**1**answer

71 views

### Focusing and nonfocusing nonlinear terms

What is the mathematical and physical meaning of the terms focusing and nonfocusing when they refer to nonlinear terms in a dispersive equations?

**1**

vote

**1**answer

385 views

### Rejection of article without mentioning specific reason [closed]

After 3 months of submission I got this mail from EJC without any specific reason of rejection.
"We regret to inform you that we have decided not to proceed with publication of your submission "......

**2**

votes

**0**answers

175 views

### Lecture notes in complex algebraic geometry (which might follow Voisin's book)

I have two questions here,
Whats the difference in the target audience/required-background between Voisin's two volumes and Griffiths-Harris' book on algebraic geometry which also seems highly tied ...

**22**

votes

**8**answers

3k views

### How do we explain the use of a software on a math paper?

Suppose one has written a math/computer science paper that is more focused in the math part of it. I had a very complicated function and needed to find its maximum, so I used Mathematica (Wolfram) to ...

**3**

votes

**0**answers

68 views

### Is projection method really applicable for numerical solution of linear integral equations in $ L^p \ (p \neq 2)$ setting?

Projection method is a traditional method to numerically handle problem of linear integral equation. The routine way is to do it in $ L^2 $ setting. For example:
Let $ A:L^2(a,b) \to L^2(a,b) $ be a ...

**8**

votes

**1**answer

663 views

### How many graduate students in mathematics are there worldwide?

There is already a question about the number of research mathematicians here, but I was wondering :
is it possible to estimate the number of graduate students in mathematics worldwide in 2019 ? (...

**2**

votes

**0**answers

434 views

### Does a result remain known after everyone who knew it has died? [closed]

When working on a research project,
one tries to spend their time answering questions that have not yet been answered.
There enters the terminology of "known" versus "unknown" results,
which we ...

**8**

votes

**1**answer

365 views

### Reciprocal sum of binomials and divisibility by $3$

We all know that $\sum_{k=0}^n\binom{n}k$ is not divisible by $3$.
QUESTION. Is it true that the numerator of $a_n$ (in reduced form) is never divisible by $3$?
$$a_n=\sum_{k=0}^n\frac1{\binom{n}...

**23**

votes

**3**answers

4k views

### How come mathematicians published in Annals of Eugenics?

I was surprised to see that On the construction of balanced incomplete block designs by Raj Chandra Bose was published (in 1939) in a journal named Annals of Eugenics (see here) (published between ...

**3**

votes

**2**answers

192 views

### One generating function, two-fold sums

This comes out of a series of transformations, so I'll just get to the main focus here.
Define the functions
$$F_n(x)=\frac12\left(x+2+2\sqrt{x+1}\right)^n+\frac12\left(x+2-2\sqrt{x+1}\right)^n. \...

**4**

votes

**3**answers

524 views

### Problem based representation theory book

I am trying to find books similar in the spirit of Ram Murty's Problems in Analytic Number theory or Murty Esmonde's Problems in Algebraic number theory in the field of Representation Theory (of ...

**115**

votes

**17**answers

14k views

### Pressure to defend the relevance of one's area of mathematics

I am a set theorist. Since I began to study this subject, I became increasingly aware of negative attitudes about it. These were expressed both from an internal and an external perspective. By the “...

**2**

votes

**0**answers

51 views

### Is there a function $u \in BV_{loc}(\mathbb{R}^2)$ such that $Du$ is an $s$-dimensional Hausdorff measure restricted to the Koch curve?

Motivated by my previous question Alberti rank-one theorem and irregular jump discontinuities, I'd like to ask the following:
Is there a function $u \in BV_{loc}(\mathbb{R}^2)$ such that $Du$ is an ...

**2**

votes

**0**answers

52 views

### Alberti rank-one theorem and irregular jump discontinuities

Is it fair to say that Alberti rank one theorem means that a BV functions $u \in BV(\mathbb{R}^2)$ has $Du = D^{cantor}u$ if and only if it has a jump discontinuity across a curve that is not smooth (...

**2**

votes

**2**answers

246 views

### Concrete example of BV function $u:\mathbb{R}^2 \to \mathbb{R}$ with singular derivative

What are examples of two BV functions $u:\mathbb{R}^2 \to \mathbb{R}$ with singular derivative?
More precisely, I'd like to see an example (and a plot using Mathematica or Matlab) of
a function
$$...

**2**

votes

**0**answers

56 views

### “Almost” absolute continuity of derivative of BV function if ${\rm Tr}\,D_Sf = 0$

Let $f: \mathbb R^N \to \mathbb R^N$ be a $BV$ function.
Suppose that $\mathrm{div} f$ is absolutely continuous with respect to the Lebesgue measure: $\operatorname{div} f \ll \mathcal L^N$. This ...

**7**

votes

**1**answer

135 views

### BV functions and wave equation

What is the role played by BV functions in the study of (possibly nonlinear) wave equations?
I think that one would need assume small initial data in $L^1$ or $H^1$ to get a well-posedness result (...

**2**

votes

**0**answers

168 views

### What are the points about representation of groups? [closed]

For a fixed (let say finite-, or Lie-, to respect the historical motivations) group, why does the study of all its linear representations over a fixed field, leads to some knowledge about its ...

**3**

votes

**0**answers

218 views

### Research on formalization of what constitutes a good theorem

This question is about automating theorem proving. Now automated theorem proving, as currently understood in CS literature, has little to do with pure mathematics as practiced on this site (I believe ...

**16**

votes

**2**answers

919 views

### Examples of problems where considering “discrete analogues” has provided insight or led to a solution of the original problem

The Kakeya conjecture posits that any Kakeya set in $\mathbb{R}^n$ has dimension $n$.
A discrete (finitized?) version of this problem is the Finite Field Kakeya conjecture, which was proved by Dvir ...

**5**

votes

**0**answers

151 views

### Heuristic and graphic representation of BV functions and their singularities

This question is about some heuristics and graphs of BV functions.
In 1-dimensional setting, two key examples of $BV$ functions $u: \mathbb R \to \mathbb R$ are
the Heaviside function, whose ...

**2**

votes

**1**answer

335 views

### Mathematical background required to learn about sheaves

Due to my interest in type theory (and higher type theory), I have found that learning about sheaves might be useful (for, e.g., sheaf models of type theories). There is Kashiwara and Schapira's ...

**3**

votes

**0**answers

136 views

### Partially BV vector fields and renormalization

Why does the approach used to prove Theorem 4.1 in the paper by Le Bris and Lions on Renormalized solutions of some transport equations with partially $W^{1,1}$ velocities and applications not work ...

**12**

votes

**2**answers

1k views

### Where are Serre’s lectures at Collège de France to be found?

Having run into several references, at various places and occasions, to "Serre’s Course at Collège de France, 19xy-19xy+1" for various values of xy, I would genuinely like to know where these lectures ...

**3**

votes

**0**answers

174 views

### Has the external knit product been used to construct a previously unknown group?

In the Wikipedia article
Zappa–Szép product
, the knit product (a.k.a. Zappa–Szép product, Zappa–Rédei-Szép product, general product, exact factorization) is defined, and its basic properties are laid ...

**3**

votes

**1**answer

141 views

### Lusin Lipschitz approximation in BV and Sobolev space

Theorem 5.34 in Functions of bounded variation by L. Ambrosio, N. Fusco and D. Pallara states that
Let $u \in [BV(\mathbb{R}^N)]^m$. Then there exists a constant $\kappa>0$ such that for every $...

**4**

votes

**1**answer

148 views

### Alberti rank one theorem and a blow-up argument

In this paper, it is written that Alberti’s rank
says that the singular part $D^s u$ with respect to $\mathcal L^d$ of the distributional derivative $Du$ of a function $u \in BV_{loc}(\mathbb R^d; \...

**6**

votes

**0**answers

157 views

### The distributional gradient of the closest isometry to the differential of a smooth map

The setting-a "linear algebra" fact:
Let $A$ be a real $n \times n$ matrix, and suppose that $\det A<0$ and that the singular values of $A$ are distinct. Then, there exist a unique matrix $Q(A) \...

**11**

votes

**6**answers

997 views

### Interesting examples of non-locally compact topological groups

Harmonic analysis is concentrated mostly on studying locally compact groups. I would like to ask people about examples of non-locally compact topological groups that are interesting in connection with ...

**16**

votes

**0**answers

405 views

### Reference request for Grothendieck's work on “Integration with values in a topological group”

Disclaimer. This question was already asked in Mathematics Stack Exchange (see the link here). I wanted the question to be migrated here but I was told by a moderator that a question that old is ...

**7**

votes

**1**answer

390 views

### Divisibility of sum of multinomials

Let $n, m$ and $t$ be positive integers. Define the multi-family of sequences
$$S(n,m,t)=\sum_{k_1+\cdots+k_n=m}\binom{m}{k_1,\dots,k_n}^t$$
where the sum runs over non-negative integers $k_1,\dots,...

**8**

votes

**2**answers

424 views

### Hyperbolic PDE in mathematics

Hyperbolic PDE (like the wave equation) are roughly speaking, PDE that satisfy the “finite propagation speed of information” property. They are ubiquitous in mathematical physics (essentially, most ...

**10**

votes

**0**answers

2k views

### Story of “Grothendieck's prime number” 57

I asked this question earlier, at hsm.stackexchange.com without much luck. Maybe somebody can answer it here.
There is a story about Alexander Grothendieck and the "Grothendieck Prime" 57, which ...

**0**

votes

**0**answers

335 views

### The collected works of John von Neumann

Might there be an online collection of John von Neumann's collected works in pdf format? I'm particularly interested in his approach to applied mathematics(ex. shockwaves, hydrodynamics).
Note: I ...

**22**

votes

**3**answers

2k views

### Why is the standard definition of a $(p, q)$-tensor so bizarre?

At time of writing the first definition of a $ (p, q) $-tensor on the Wikipedia page is as follows.
Definition. A $ (p, q) $-tensor is an assignment of a multidimensional array $$ T^{i_1\dots i_p}_{...

**30**

votes

**8**answers

6k views

### Example of a Mathematician/Physicist whose Other Publications during their PhD eclipsed their PhD Thesis

I am wondering if there is some example of a mathematician or physicist who published other papers at the same time as their PhD work and independently of it which actually eclipsed the content of the ...