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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2answers
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
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2answers
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
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3answers
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
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4answers
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
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14answers
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
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0answers
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
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1answer
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
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1answer
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
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1answer
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
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4answers
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
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1answer
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
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2answers
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
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1answer
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
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1answer
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
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0answers
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
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1answer
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
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3answers
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
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15answers
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
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2answers
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
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2answers
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
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0answers
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
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0answers
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 ...
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0answers
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
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5answers
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
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1answer
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
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7answers
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
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2answers
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
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1answer
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
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0answers
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
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4answers
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
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2answers
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
1answer
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
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0answers
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
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2answers
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
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7answers
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
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1answer
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
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1answer
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
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1answer
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
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0answers
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
1answer
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
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1answer
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
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0answers
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
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1answer
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
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3answers
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
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0answers
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
1answer
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
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7answers
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
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0answers
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
1answer
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
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5answers
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 ...

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