Questions tagged [mathematical-writing]

For questions about writing mathematical texts, e.g. questions of style, mathematical prose, structuring of mathematical exposition, referencing prior work etc.

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55 votes
8 answers
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Techniques for debugging proofs

After writing many proofs, most of which contained errors in their initial form, I have developed some simple techniques for "debugging" my proofs. Of course, a good way to detect errors in ...
32 votes
4 answers
2k views

Shapes for category theory

Most texts on category theory define a (small) diagram in a category $\mathcal{A}$ as a functor $D : \mathcal{I} \to \mathcal{A}$ on a (small) category $\mathcal{I}$, called the shape of the diagram. ...
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8 votes
1 answer
470 views

Exposition of concrete constructions

I am frequently interested to find less technical proofs of results which already appear in the literature, at least in some special cases of these results. Sometimes a published proof shows that an ...
4 votes
1 answer
1k views

How to cite an article with an article number (instead of page range)

I am curious to know what is the standard way (in AMS style) to cite a journal article that has an article number and/or a page range. For instance, here is a BibTex entry from MathSciNet of an ...
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1 vote
0 answers
152 views

What are some great examples of wordsmanship in published literature? [duplicate]

David L. Goodstein begins his book on statistical mechanics, ''States of Matter'', with the following introduction: "Ludwig Boltzmann, who spent much of his life studying statistical mechanics, ...
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0 votes
0 answers
124 views

Symbol directly after theorem number

I think it is generally agreed that one should not start a mathematical sentence with a symbol. But what about this: Theorem 7.1. $X$ is pseudoquasifinite. I would say that this is acceptable, as &...
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18 votes
3 answers
2k views

Is it a reasonable way to write a research article assuming truth of a conjecture?

I have found a conjecture in a research article (published in a good journal) on number theory, which is not well known but very reasonable. Let me be clear that, there is no counter-example that vote ...
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  • 754
9 votes
0 answers
428 views

How bad is it to publish a paper with an overcomplicated proof?

I don't want to go into details for anonymity purposes, but I have co-authored and submitted a paper with a long proof (dozens of pages), and I think that with some moderate effort, we could find a ...
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73 votes
6 answers
3k views

How to write a good MathSciNet review?

When reviewing for MathSciNet, I routinely find myself just paraphrasing and abbreviating the introduction provided by the author, and occasionally adding a few words about the quality of the research ...
4 votes
0 answers
187 views

Referring to computer software in a paper

I'm performing a calculation of the Smith normal form of an integral matrix based on the SageMath worksheet. Is it sufficient in the paper to say something like ``Using a software package like ...
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  • 311
5 votes
1 answer
442 views

Nice way of referring to “some cardinal that always exists”

My apologizes if this question is not MO-appropriate. Often I find myself wanting to state a hypothesis of a consistency result that can hold for an “aribtrary” regular cardinal. Only, it’s not ...
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-1 votes
1 answer
179 views

Typesetting of symbols and "operators" denoting sets [closed]

Question: what are the conventions for typesetting sets of certain objects, especially the vertices and edges of a graph or those adjacent to an edge or vertex. For vectors and matrices there is the ...
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8 votes
1 answer
651 views

Is there a canonical resource for mathematical Lorem ipsum text?

I'm designing a template intended for mathematical writing. I'd like to fill the template with Lorem ipsum text, but would like that text to showcase some of the common ways that mathematics is ...
4 votes
0 answers
161 views

Social media for a mathematics related idea buckets

Are there any good social media platforms that can recommended for communicating ideas related to mathematics? The reason for asking is that I am in the situation that, albeit having studied math, I ...
23 votes
2 answers
2k views

Conjecture vs open question on a paper

Suppose that you are concluding a paper and writing the open questions (or further research directions) section, and suppose that you have several claims related to the work in the paper that your ...
11 votes
1 answer
918 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 ...
-1 votes
1 answer
164 views

Can it be an application of a theorem if I only use it to generalize? [closed]

So I've been trying for a while to write an article on 3 applications of some theorem for a small journal. But after finding my second example I realized that I didn't need the theorem to prove it. ...
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86 votes
14 answers
7k 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 ...
1 vote
0 answers
81 views

Terminology: Existence + Representation

I'm looking to describe a result in a recent paper of mine, but I don't know if there is a term used for a result which is both an existence theorem and a representation theorem. Specifically, the ...
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45 votes
4 answers
954 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 ...
6 votes
4 answers
1k 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) $\underline{\quad \quad \quad \quad}$ ...
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21 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 ...
3 votes
1 answer
541 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 ...
3 votes
2 answers
693 views

What does the abbreviation "p.p." mean in the context of convergence [closed]

What does the abbreviation "p.p." mean when referring to convergence? E.g. in the following paper by Harry Pollard THEOREM. If $f \in L^p$ for some $p$ in the range $\tfrac{4}{3} <p < \infty$,...
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10 votes
0 answers
410 views

Including alternative proofs

Suppose I have found two or even more proofs of a theorem and I prepare a paper on it. Is it considered to be a good practice to write down all of them? Or is it considered to be my job as an author ...
2 votes
0 answers
114 views

Specific versus general in titles of papers [closed]

It may not be possible to use mathoverflow in the way I'm hoping to, but my question is this: Should the title of a research paper in mathematics be as accurate and specific as possible (at the cost ...
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2 votes
0 answers
124 views

Comma usage when defining symbols [closed]

Consider the following sentence that introduces a symbol, $f$, used later in the text (not shown): A classifier is a function $f$, which takes an image as input and produces a label as output. ...
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  • 379
27 votes
1 answer
2k views

How can I improve my formal definitions?

I am a Software Architect and not very familiarized with standard notation in mathematics. Nonetheless, I would like to write a paper explaining a normalization of a computing model for expert systems....
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24 votes
2 answers
2k views

Why would one number theorems, propositions and lemmas separately?

When it comes to numbering results in a mathematical publication, I'm aware of two methods: Joint numbering: Thm. 1, Prop. 2, Thm. 3, Lem. 4, etc. Separate numbering: Thm. 1, Prop. 1, Thm. 2, Lem. 1,...
24 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 ...
1 vote
0 answers
201 views

When writing a research paper, what is the acceptable format for acknowledging my advisor?

I am writing a paper for an independent study course I am enrolled in. I have contributed all of the work to the project. My supervisor has been a guiding force during this research, suggesting things ...
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1 vote
0 answers
127 views

What exactly is and is not a concentration inequality?

Hoeffding's inequality is surely a concentration inequality. It can be written in the form: $\Pr(\bar X + f(n,\delta) \geq \mu) \geq 1-\delta,$ for some function $f$, where $X$ is a set of i.i.d. ...
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  • 379
48 votes
8 answers
4k views

Examples of Mathematical Papers that Contain a Kind of Research Report

What are examples of well received mathematical papers in which the author provides detail on how a surprising solution to a problem has been found. I am especially looking for papers that also ...
3 votes
2 answers
830 views

Would a journal such as Bulletin of the AMS accept an article from a student? [closed]

I am a masters student, and am currently writing an expository article on an area of applied maths for a class project. I plan to work on it for several more months. One of my major goals is to ...
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14 votes
2 answers
824 views

How to handle results from an unpublished paper?

I am writing a paper right now, and part of the paper makes use of a (trivial) generalization of a number of really nice theorems and constructions from a paper that was never made public. The author ...
7 votes
2 answers
735 views

How Much Flesh to the Bones does an Initial Online Publication need?

Background of my question is the following: I have found a solution for my question Smoothness Conditions for Planar “Mock-parametric” Spline Interpolation and while developing the solution, I ...
35 votes
6 answers
5k views

Obsessive editing/revising of math papers

I've been wanting to ask this question, because I have no insights into the way other mathematicians prepare papers (for eventual publication). How much are editing, revising, updating, adding to, ...
22 votes
8 answers
4k views

Mathematical Writing: Proof Outlines/Overview in a Paper

While my question topic is that of mathematical writing of papers, which is a broad subject, the particular question is specific. I am writing a paper, in which we have a section called "Outline ...
43 votes
6 answers
3k views

Explaining the main ideas of proof before giving details

I'll be the first to admit that this is a risky question to try to get away with on math overflow, but I'm going to give it a shot anyway. Roughly speaking, the question is this: Is it good to try to ...
32 votes
2 answers
1k views

Is it possible to cite a page in n-Lab in a research paper?

One of the concepts I need in my paper is best summarized on the n-Lab page. I tried my best to find a similar description of the same concept in a more "classical" reference, such as a paper or a ...
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  • 271
7 votes
3 answers
2k views

Which affiliation to use when publishing, when invited professor at second university

I am a PhD student at one university and an invited professor at a second, i.e. I do not have a permanent position in the second one. Now I need to indicate an affiliation in a journal paper but I do ...
83 votes
6 answers
8k views

What’s the etiquette on using diagrams that need color to be understood?

I’m working on a paper that makes heavy use of colorful diagrams to supplement the text. For most of these it would probably not be possible to create grayscale versions that convey the same ...
23 votes
5 answers
1k views

Illustrating mathematics with wysiwyg tools

What tools are out there for creating mathematical illustrations in a what-you-see-is-what-you-get mode? Having struggled with tikz for several years, I've found creating figures in Omnigraffle (...
27 votes
5 answers
2k views

Main statement as theorem or corollary

In a text there will often be a few important results that are usually called Theorems. Intermediate statements are called Lemmas, and statements that follow immediately from previous results are ...
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  • 371
20 votes
4 answers
3k views

Using a known result without a specific reference

This is a question of mathematical writing. Let me know if it would be better suited to academia.SE. I am writing a paper in invariant theory. It uses some slightly heavy commutative algebra. There ...
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  • 2,609
10 votes
1 answer
1k views

How are constants/functions named after their discoverer?

In general, when a paper references an object discovered/defined in another paper by author X, it goes something along the lines of: "Let $\tau$ be the constant defined by X in 1999 [1]$\ldots$", or ...
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  • 1,841
17 votes
4 answers
1k views

Examples of (Git) open math (texts) projects

I am an active part of a research project on the positive effects of open math projects on the community. With open math projects I have in mind a particular thing, namely a GIT project on mathematics ...
40 votes
5 answers
5k views

How to improve writing mathematics?

My first language is not English. How can I improve my mathematical writing. I feel like the only things I can write down are numbers and equations. Is there any good suggestion for improving writing, ...
2 votes
2 answers
215 views

Expanding a combinatorial argument involving permutation coefficients

I have spent more time thinking than I would like to admit because of the following sentence: "Choose $t = c_6X^{1/e}$ and we obtain Theorem 2.". What obvious argument am I missing that allows us to ...
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7 votes
3 answers
793 views

Notable examples of syntactic proofs whose existence is guaranteed by completeness, but having been found later than a semantic proof?

Question. What are examples (preferably documented and explicitly commented on from this perspective in the literature, preferably in an article dedicated to this aspect alone) of the following well-...