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32
votes
2answers
940 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 ...
12
votes
3answers
683 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 ...
17
votes
3answers
2k 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 ...
2
votes
0answers
154 views

When is it appropriate to name something a 'fundamental lemma'? [closed]

The term 'fundamental lemma' refers to many results in mathematics. I don't know too many results referred to by that name, but I am familiar with, for example, the 'fundamental lemma of sieve theory' ...
46
votes
17answers
10k 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 ...
27
votes
2answers
803 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. ...
9
votes
3answers
779 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.
25
votes
5answers
2k 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 ...
6
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 ...
22
votes
0answers
589 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 ...
17
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 ...
0
votes
1answer
228 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 $x = a$: $f'(a)$; $\frac{\operatorname{d}{f(a)}}{\operatorname{d}x}$; ...
8
votes
3answers
319 views

Punctuation and Other Rules for Variables and Their Verbal Definitions in Math Narrative [closed]

To better understand what I'm asking about, let's immediately define some examples. Imagine that you are writing some paper which involves a lot of math narrative. And you have a term, say, computing ...
0
votes
0answers
241 views

Applied Math author order

In applied math it seems to be more common to list authors according to their contribution rather than alphabetically. This being the case, in the instance where there are more than 2 authors, I was ...
0
votes
1answer
91 views

Inserting maple or macaulay script in a paper [closed]

I see many wonderful papers where the authors include some script written in Maple, Macaulay or other software that are needed for their proof. How do you insert that in your tex file?
11
votes
1answer
321 views

Quoting mathreviews

I would like to credit a reviewer who made a very nice corollary to the paper he was reviewing. Is there any more or less common standard of quoting MathReviews? I would be most grateful for an ...
16
votes
4answers
1k views

What is a good poster for a math conference?

I'm going to participate to a conference and they ask me to do a poster on my research. I've never made a poster for a conference/seen a poster session in a conference. So what is important? What do ...
6
votes
2answers
155 views

How to write this result (successive Schur complements compose nicely)

There is an easy theorem in linear algebra that "successive Schur complementations compose nicely": for instance, let's say I have a matrix $$ M_0= \begin{bmatrix} A & B & C \\ D & E & ...
4
votes
1answer
468 views

What is the correct preposition? (And is there one?)

I just stumbled upon a linguistic problem I wasn't able to resolve via web search. Suppose we're given some geometric set $A$ and subset $B\subset A$. Isn't there a compact way of saying that there ...
2
votes
2answers
553 views

Authorship, and order of authors [duplicate]

Currently I am writing a paper with several collaborators; although I am the primary author to this (I have done a large (>85%) majority of the work and have actually written the paper) my last name ...
3
votes
1answer
570 views

Equal signs with fancy marks

Some people use $\stackrel{\mathrm{def}}{=}$, $:=$ or $\stackrel{\Delta}{=}$ for definitions. In more informal contexts, I have also seen $\stackrel{?}{=}$, for "I wish to prove this equality, which ...
13
votes
3answers
849 views

Writing Mathematics : Linking words

I'm trying to write mathematics in English and I'm clearly missing something : linking words. I'm writing "so, we get", "Observe that" too many times and I'm afraid to use some expressions : "it ...
16
votes
3answers
820 views

Where to break paragraphs in a proof?

I have some rules of thumb about writing research papers that I can actually articulate. For example, leave all definitions as late as possible (but not later!), so the reader won't fear "Do I need to ...
6
votes
1answer
618 views

What are good ways to present proofs of theorems requiring auxiliary lemmas? [closed]

I am writing an academic paper for submission to a journal. One of my co-authors wrote the following: Theorem Statement of the theorem Proof of theorem We first show the following result ...
18
votes
5answers
902 views

Historical use of figures in geometry

I was surprised to learn from John Stillwell's comment in answer to the question, "Can the unsolvability of quintics be seen in the geometry of the icosahedron?", that There is not a single ...
2
votes
1answer
291 views

fixedpoint or fixed point or fixed-point

I am unsure which is the right spelling (if there even is a ‘right’ spelling), but maybe native speakers can enlighten me: When should I use fixed point fixed-point fixedpoint when I refer to the ...
0
votes
1answer
301 views

Do you set a one or two commas when using \mapsto?

I am currently revising a paper and I am completely confused about the commas. Is it correct English to write 1) "The canonical map $X \to Y$, $x \mapsto f(x)$, is injective." or is it 2) "The ...
4
votes
1answer
242 views

Can I use both of setbuilder notations in one article?

I am sorry if this question is not for mathoverflow. I asked the same question in tex stackexchange and got an answer that this question is out of topic. If it's the same here, please let me know. ...
13
votes
3answers
739 views

Is there an editors checklist for mathematics?

I always have trouble with editing math papers for publication. I know there are plenty of checklists for English exposition but is there one for math specific exposition errors?
7
votes
3answers
669 views

Formal writing: numbers under 10

I've been tasked with proofreading an Engineering/Mathematics thesis paper. I was always told that numbers under 10 should be spelled out (one, two, three, ...) but I was wondering if this rule holds ...
1
vote
1answer
399 views

About writing of mathematical papers [closed]

Is not it better to use a mathematical language for writing mathematical papers. For example, use the logic of mathematical symbols more tnan additional comment. Is it feasible?
-3
votes
2answers
886 views

Should science authors discourage / boycott the recent push for author IDs [closed]

In recent years, several organizations (publishers, arXiv, universities) started pushing for systems of a reliable author identification, gaining considerable traction with the recent launch of ORCID. ...
14
votes
2answers
1k views

the use of parentheses to mean “I won't tell you this again”

A reader of one of my drafts found fault with my use of parentheses; I put the word "bounded" in parentheses in a statement of a certain theorem, and he replied "But the statement isn't true if the ...
2
votes
2answers
534 views

When a name is used for two different notions!

What would you do if you see a notion which you used to work with has two names and the same name you use for this notion is used for another notion too. For example, after the work of J.B. Bost, A. ...
9
votes
2answers
699 views

Capitalization of named theorems [closed]

I would like to extend a previous question on the capitalization of theorem names . This time, it's not about numbered theorems like "Lemma 1.1", but about theorems that carry a name. Question: ...
24
votes
2answers
1k views

How to balance writing professionally and being able to have a conversation with your reader?

Background. I am someone at the very very beginning stages of my career as a mathematician, and am, for example, almost ready to (re)submit my first paper. I have already read a lot of essays on how ...
4
votes
3answers
292 views

Typographically separating logical argument from explanation and example [closed]

I am currently writing a master's dissertation. In this dissertation I have chosen to typographically separate logical argument, (Theorems, Proofs, and Definitions) from aids to understanding ...
1
vote
1answer
781 views

Do you know readers of your papers ? [closed]

Do you know readers of your papers ? Or - is it true that if paper is not groundbreaking no one (except very few people, working very closely and hence known for you) will read it ? If it is so - ...
8
votes
2answers
1k views

Graph of dependencies from a Latex file [closed]

This question has been "manually migrated" to TeX-SX: http://tex.stackexchange.com/q/40200/86 Apologies if the question is not very appropiate for Mathoverflow. It seems to me more appropiate here ...
62
votes
14answers
6k views

How to write popular mathematics well?

Recently, some classmates and I were lamenting the fact that our classmates in other disciplines had almost no conception of what we did, despite the large mathematics population at Waterloo. Instead ...
8
votes
0answers
1k views

Blinding a paper : the acknowledgements section [closed]

I am about to submit a paper (my first!) to a journal in statistics. There is a requirement to submit a "blinded" version. Should I remove the acknowledgements section too for this? If I do, what are ...
17
votes
4answers
2k views

What is the main goal of a paper, really? [closed]

My question, motivated by idle curiosity while sitting in LaGuardia airport, is the following. You've just proved nice result A and it is time to write the paper. What is the real goal of the paper? ...
21
votes
3answers
2k views

Citation of a paper with a proof you would like to improve [closed]

Imagine that you are in the following situation: You write up a proof which eventually gets published. There you need a result which is not so well-known but it is contained in another paper P; ...
22
votes
4answers
2k views

When is it appropriate to entitle a paper “A note on…” or “On the …”? [closed]

I rarely find modern research papers (on mathematics) that are less than 5 pages long. However, recently I came across a couple of mathematical research papers from the 1960/1970's that were very ...
8
votes
1answer
291 views

Tags for theorems, definitions, examples, etc. in monographs

I write many telegraphic reviews of monographs and textbooks. Occasionally I see certain books do something I think should become an industry standard, namely tagging nearly every theorem, lemma, ...
18
votes
2answers
1k views

What is due diligence when translating a paper?

EDIT: Part of the community has decided on a less catchy and more representative title than "Socially acceptable plagiarism (with regards to translation)". Let's run with that for a while. GRP.10.27 ...
9
votes
2answers
1k views

Am I allowed to do non-rigorous numerical analysis?

I have a paper where I am trying to show that the growth of a certain function is exponential of the order $a^n$. I would like to compute $a$, at least approximately. The base $a$ satisfies a very ...
13
votes
4answers
1k views

Notation in Frege's Grundgesetze der Arithmetik: The U with a flourish

In the Grundgesetze der Arithmetik, Frege used a number of strange characters for notation. I would be most interested to know anything about the typography (origin, usage and so on) of the strange U ...
1
vote
1answer
184 views

Style question — approximate exponential bound

This is a question about recommended style for a paper. I am able to show an upper bound of the form $f(n) = O(c^n)$. While I have a formula satisfied by $c$, it is a messy formula and I cannot solve ...