# 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

**3**

votes

**2**answers

605 views

### What are your opinions on Zeidler's QFT books? [closed]

I am interested in mathematically rigorous treatment of quantum field theory, constructive QFT in particular.
I have read 'QFT, A Tourist Guide for Mathematicians' and am going to read "Quantum ...

**7**

votes

**2**answers

3k views

### Publishing undergraduate research

Sorry if something like this has already been asked, I searched but I couldn't find anything similar to my question.
I'm a senior undergraduate and currently doing my senior thesis. My senior thesis ...

**22**

votes

**3**answers

3k views

### A global mathematics library

Just for personal interest, I am not (yet) professionally involved in it. My question is about the state of arts in digitalization of mathematics and to what extent it is possible and reasonable.
...

**38**

votes

**4**answers

3k views

### Access to journals during pandemic

I have just graduated from the University of Chicago and no longer have access to online journal resources, but I cannot afford to pay for them directly. Normally, I would be able to access library ...

**74**

votes

**14**answers

5k views

### Time-saving (technology) tricks for writing papers

I have over the years learned some tricks which saves a lot of time,
and I wish I had known them earlier. Some tricks are LaTeX-specific, but other tricks are more general. Let me start with a few ...

**6**

votes

**0**answers

152 views

### Online study groups for individual mathematical texts

This has been one of my earlier academic dreams. I have pitched the idea to Prof Ravi Vakil, among others. Recently, because of participation in the mathematical competition hosted by Alibaba, I have ...

**3**

votes

**1**answer

234 views

### Recommendations for mathematical essayists

I was wondering if people had recommendations for mathematical essays (by this I mean essays on a mathematical topic, not necessarily essays written by mathematicians).
A person who I used to find ...

**13**

votes

**1**answer

276 views

### Good overviews on $\phi^{4}$-field theory?

I'm looking for nice overviews on $\phi^{4}$-field theory from the mathematical-physics point of view. To be a little more specific, here are some topics I'd like to read about:
(1) What are the ...

**7**

votes

**1**answer

826 views

### Are categories special, foundationally?

Some folks over at nLab want to use categories as a foundation for all of mathematics, I'm guessing as an alternative to sets. Sets work fine, and so do categories, so I have started wondering what ...

**42**

votes

**4**answers

838 views

### How to write computer-assisted mathematics well?

Much has been said about writting good papers in mathematics. A short google query yields countless sources of advice. This skill also appears to be quite transferrable between basic branches of ...

**0**

votes

**1**answer

81 views

### On relating $l(A), l(B)$ and $l(A+B)$ for Weil divisors on a smooth projective curve where one of the divisors is effective

Let $X$ be a smooth projective curve over an Algebraically closed field $k$. Let $k(X)$ denote its function field.
If $A, B$ are Weil divisors on $X$ such that $A$ is effective (i.e. $A\ge 0$) , then ...

**13**

votes

**2**answers

545 views

### Papers with a large number of coauthors

I recently submitted a paper to the preprint arXiv, which was rejected because we didn't list all of the authors on the first page. We chose to follow the polymath model, using a generic name for our ...

**6**

votes

**1**answer

523 views

### Explanations simple enough that non-mathematical audiences can understand [closed]

The following (debatable) quote is attributed to Einstein:
"You do not really understand something unless you can explain it to your grandmother."
I feel very enlightened when there is a ...

**3**

votes

**1**answer

429 views

### Why did mathematical notation stay so hard to read? [closed]

One of the first things you learn in a programming 101 course is to write readable code, and to name your variables properly. This notion has seemingly never translated into mathematics. Everywhere ...

**6**

votes

**0**answers

440 views

### Math graduate school applications and personal hardships

This question is on mathematics, career, and personal life.
I.) Assumptions.
i.) Suppose that I am a Junior in college majoring in mathematics at a top research institution in the U.S. I have "...

**1**

vote

**1**answer

538 views

### Is it all right to invite a professor to cowrite a paper

I managed to improve the techniques of a year-old paper to get a significantly stronger result. I used original ideas, but a large part relies upon results of the original paper. (to the point that ...

**6**

votes

**3**answers

889 views

### The name for an assumption made for the sake of contradiction

What is the name (or adjective) for an assumption made for the sake of contradiction?
To be clear, I'm in search of an expression in the form "a(n) $\underline{\quad \quad \quad \quad}$ ...

**54**

votes

**15**answers

4k views

### Request for examples: verifying vs understanding proofs

My colleague and I are researchers in philosophy of mathematical practice and are working on developing an account of mathematical understanding. We have often seen it remarked that there is an ...

**3**

votes

**2**answers

326 views

### Which fields of mathematics are most straightforward for a statistician to do research in, other than probability theory?

I have a Ph.D. in Statistics and have always been interested in pure mathematics, but never had a chance to really pursue it. My mathematics background includes real analysis, linear algebra, ...

**13**

votes

**2**answers

1k views

### Categorification of probability theory: what does a “probability sheaf” tell us (if anything) about probability theory?

Disclaimer: I only have a superficial knowledge of what category theory and related subjects are concerned with.
So, my understanding is that category theory and related fields of higher mathematics ...

**2**

votes

**0**answers

127 views

### An alternative proof of Künneth spectral sequence, independent of Künneth formula for homology

I am currently reading Künneth spectral sequence, which is given below.
Let $R$ be a ring and A$=\big\{A_n,d_n:A_n\longrightarrow A_{n-1}\big|d_{n-1}\circ d_n=0\big\}_{n\in \Bbb Z}$ be a chain ...

**6**

votes

**0**answers

139 views

### My research paper involves computing additional terms of an existing OEIS sequence. Should I first amend the sequence or publish the results?

In the course of my research I computed terms of an existing OEIS sequence that are currently unknown. Having prepared my paper for publication, I am now faced with a (small) dilemma:
Do I first ...

**1**

vote

**0**answers

123 views

### What benefits of math can be conveyed to mid/high schoolers? [closed]

I'm teaching mathematical proof writing to a few of math teachers (in the US) this summer. In the beginning of class, I send a survey asking them why they are here. Most of them are here for getting ...

**5**

votes

**5**answers

1k views

### Terminology introduced in recent years with more than one meaning

Suppose a term(inology) is recently (in last 20 years) introduced in research mathematics.
It might happen that some one who wish to use it, in the same area of research, for different purposes or ...

**5**

votes

**1**answer

137 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 ...

**40**

votes

**7**answers

5k 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 ...

**-2**

votes

**2**answers

232 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**

votes

**1**answer

381 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**

votes

**0**answers

158 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 $n$ ...

**34**

votes

**4**answers

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 ...

**20**

votes

**2**answers

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**

votes

**1**answer

661 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**

votes

**0**answers

116 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**

votes

**2**answers

220 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 ...

**22**

votes

**7**answers

1k views

### Examples of improved notation that impacted 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**

vote

**1**answer

170 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**

votes

**1**answer

134 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 ...

**-1**

votes

**1**answer

474 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 ...

**6**

votes

**0**answers

224 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**

votes

**1**answer

274 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

**1**answer

661 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**

votes

**0**answers

160 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**

votes

**1**answer

871 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 ...

**24**

votes

**3**answers

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**

votes

**0**answers

99 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 ...

**3**

votes

**1**answer

193 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, ...

**65**

votes

**7**answers

16k 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**

votes

**0**answers

163 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**

votes

**1**answer

466 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 ...

**76**

votes

**5**answers

7k 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 ...