Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

The tag has no usage guidance.

15
votes
2answers
570 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How to handle results from an unpublished paper?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 ...
-2
votes
0answers
110 views

Publishing recreational mathematics on geometry,numbers etc [closed]

I would like to know where I submit my papers on recreational mathematics - on triangles, numbers and other elementary matters ?
8
votes
2answers
638 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 ...
31
votes
6answers
4k 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, ...
21
votes
7answers
2k 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 of ...
43
votes
5answers
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 ...
29
votes
2answers
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 ...
7
votes
3answers
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 ...
76
votes
6answers
6k 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 ...
20
votes
4answers
719 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 (...
26
votes
5answers
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 ...
20
votes
4answers
2k 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 ...
8
votes
1answer
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 ...
11
votes
2answers
446 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 ...
37
votes
5answers
4k 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
2answers
196 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 ...
7
votes
3answers
528 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-...
15
votes
2answers
948 views

Rights to edit “Archives Grothendieck”

The Archives Grothendieck are now "Archives en accès libre", I would like to know if one can edit them... I would like to take an excerpt (split some pages of the archive i.e. from page 10-30 of ...
2
votes
2answers
184 views

Technical term for representing object of a presheaf determined by a left-adjoint?

If $\mathcal{D}$ is a locally-small category, then a functor $F\colon\mathcal{C}\rightarrow\mathcal{D}$ has a right-adjoint if and only if for each object $d$ of $D$, the presheaf $$\mathcal{C}^{\...
19
votes
4answers
2k views

Reproving a known theorem in an article

Suppose one wants to use a theorem that was published quite a long time ago (+80 years) in a paper that is using a terminology and notations that are very much out-dated (making the paper very hard to ...
2
votes
0answers
106 views

General treatments of the problem of extending a functor from a small category to its power set to an endofunctor on it?

Suppose you analyse a small category $\mathsf{C}$ whose set of objects you again denote by $\mathsf{C}$. Suppose you have found a natural categorical structure on $2^{\mathsf{C}^{\mathrm{op}}}$ (...
3
votes
1answer
249 views

Usual technical term for replacing a set by the set of singletons of its members?

What is a standard technical term in axiomatic set theory for the operation which sends a given set $A$ to the set $A':=\{\{a\}\colon a\in A\}$? (Replacement implies that $A'$ is a set.) Some ...
44
votes
3answers
2k views

Citing exercises in an article

I'm writing a paper in which I cite a lot of results that appear in Schikhof's Ultrametric Calculus. Some of these results are exercises in Schikhof's book. These exercises are not difficult, but are ...
1
vote
1answer
191 views

“Pointwise” defintions in category theory

In category theory it is often said that certain operations are defined "pointwise". For example, limits in a functor category $[\mathcal{C},\mathcal{D}]$ can be defined "pointwise" (if $\mathcal{D}$ ...
47
votes
12answers
3k views

Examples of advance via good definitions

In my research I came across a case where I could derive a known theorem with rather straightforward way by choosing "non-standard" definitions using my knowledge from a related field. This particular ...
1
vote
0answers
658 views

Proof of the ABC conjecture - how feasible would it be to automate some of the deciphering of Shinichi Mochizuki’s proof?

This is a question I will come back to. I am very interested in Shinichi Mochizuki’s proof, and in particular, the idiosyncrasies of his notation, which I understand to be at the root of why it is ...
4
votes
1answer
300 views

Why are affine functions called “affine” functions? [closed]

I am learning about affine functions and I do not understand why a certain type of function (functions that are in the form of $f(x)=ax+b$) are called affine functions. I read about the word "affine" ...
15
votes
1answer
449 views

Arrangement of the introduction of a paper

In my understanding the introduction of a paper is a very important section because it not only gives a concise summary of the results, but it is also the only section most people will read at all. ...
7
votes
3answers
349 views

Given alphabetical ordering of authors, how to establish level of contribution? [closed]

I learned recently that in mathematics, the authorship order is virtually always alphabetical. I have recently collaborated on a paper where I did the vast majority of the work (everything but the ...
13
votes
2answers
782 views

Is it acceptable to use the citation references like [1] or [Joh] as nouns in mathematical writing?

I have seen this enough times that I thought it was common practice, but I recently saw someone on a website about writing tips (can't find the link now) say that this was not good. I am hoping to get ...
0
votes
2answers
354 views

Use of ternary operator in formal writing

I would like to write $$ f(x) = \begin{cases}1&\mbox{if }x = 1\\ 0&\mbox{otherwise.}\end{cases} $$ However, this eats up a lot of vertical space for a very simple statement. Is there agreed ...
8
votes
1answer
155 views

Style guide for referring to past work

Has anyone written or expressed a coherent position on how to refer to mathematical results (theorems, proofs) by past authors? Even if there are no hard and fast rules, I find it helpful to have a ...
-2
votes
1answer
282 views

Correction symbols used for mathematical texts [closed]

When proof reading and correcting a mathematical text, I sometimes see people use special notation symbols in the margin to indicate correction, deletion, replacement and so on. Is there any standard ...
6
votes
0answers
199 views

When do you use “s” apostrophe to refer to authors ($e.g.$ of inequalities)? [closed]

I remarked that there does not seem to be a general rule whether one should use or not an "s" apostrophe for inequalities For example, we can encounter Hölder's inequality, but Minkowski or Sobolev ...
20
votes
6answers
2k views

How to cite authors from any country correctly?

It has always seemed to me that the Mathematical Community gives a high importance to the act of properly citing an author (Do not write Erdos! It's Erdős. Cauchy must be read as in French, not as in ...
5
votes
3answers
666 views

“Let” versus “for all” [closed]

I have noticed that many authors tend to use "let" instead of "for all". For example, they write something like this: Let $n$ be an even natural number. Then also $n^2$ is even. I wonder, why they ...
53
votes
33answers
10k views

Most intriguing mathematical epigraphs

Good epigraphs may attract more readers. Sometimes it is necessary. Usually epigraphs are interesting but not intriguing. To pick up an epigraph is some kind of nearly mathematical problem: it ...
12
votes
1answer
2k views

Mathematical writing : using an “out-of-date” notation

When I wrote my master's thesis, a professor who read it said that I should not use the phrase "A function of class $k$." but instead "A function of class $C^k$". I am not an expert about mathematical ...
41
votes
2answers
2k views

When to postpone a proof?

One possible practice in writing mathematics is to prove every theorem and lemma right after stating it. A long, technical proof — and sometimes even a short one — can interrupt the flow ...
18
votes
3answers
9k views

How to write an abstract for a math paper? [closed]

How would you go about writing an abstract for a Math paper? I know that an abstract is supposed to "advertise" the paper. However, I do not really know how to get started. Could someone tell me how ...
21
votes
3answers
3k views

Style of mathematical writing vs. too many lemmas

I work in PDEs. I have now written 3 papers. I find my style is of the form: introduction, statement of results, paragraphs to introduce something, lemma, more text, lemma, more text, lemma, more text,...
74
votes
24answers
15k views

Parodies of abstruse mathematical writing

Perhaps under the influence of a recent question on perverse sheaves, in conjunction with the impending $\pi$-day (3/14/15 at 9:26:53), I recalled a long-ago parody of abstruse mathematical language ...
34
votes
2answers
1k views

Different styles of writing/reading articles

Recently, I discovered a rather unexpected thing. We are writing an article in collaboration and we permanently have some discussions about how to write, in which order, how to organize material etc. ...
11
votes
3answers
3k views

How to refer to plural of mathematical symbols - with or without an apostrophe [closed]

Which one is correct, $x_i$s or $x_i$'s? Example sentence: The $x_i$s form a sequence. The $x_i$'s form a sequence.
27
votes
5answers
3k views

Collaboration or acknowledgment?

This post is a sequel of: When should a supervisor be a co-author? This time the topic is about the interaction between two professional mathematicians (in particular junior-senior, but not ...
11
votes
3answers
1k views

How were formulas / images added to books in post-printing-press / pre-digital times?

I have seen that Euclid's Elements was written 300 BC and first set in type in 1482. Are there scans of that old versions available? How were formulas / images added to the books created with ...
9
votes
5answers
1k views

Proof or citation?

I'm writing an article. I suppose that I'll submit it to a more or less decent journal (in English). I have doubts about the following: I have a lemma (with quite a trivial proof). I don't want to ...
28
votes
1answer
905 views

Good ways to organize old personal mathematical resources

I am wondering how the other Mathematicians organize their old mathematical resources, like calculation drafts, class and seminar notes etc. These old resources may be related to a wide range of ...
18
votes
8answers
1k views

Should a theorem be numbered by where it is first stated or where it is proven?

Suppose I am writing a paper in which an important lemma has a proof which is either long and unenlightening or requires additional background of the reader (or both). Thus, to avoid disrupting the ...
1
vote
1answer
417 views

Choosing Notation for Variable Substitution into Derivative Expressed with Differentials [closed]

Consider function $f(x)$. I've counted 4 possible notations to write a derivative of $f(x)$ at point $x = a$: $f'(a)$; $\frac{\operatorname{d}{f(a)}}{\operatorname{d}x}$; $\left.\frac{\operatorname{d}...