Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.

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70
votes
11answers
10k views

Using “we have” in maths papers

I commonly want to use the phrase "we have" when writing mathematics, to mean something like "most readers will know this thing and I am about to use it". My primary question is whether this is too ...
63
votes
5answers
2k views

How are mathematicians taught to write with such an expository style?

I wasn't sure if this question was appropriate for MSE. One of the major complaints we see in industry is a person's ability to communicate which includes writing. We see the same thing on questions ...
44
votes
5answers
4k views

How to write a good mathematical paper?

I hesitate to ask this question. However I read many advices from math.stackexchange, and I couldn't find anything similar. A good time always goes too fast! Two years are fled. In the third year of ...
27
votes
4answers
4k views

Why do proof authors use natural language sentences to write proofs?

I haven't read very many proofs. The majority of the ones that I've read, I've read in my first-year proofs textbook. Nevertheless, its first chapter expatiates on the proper use of English in ...
21
votes
8answers
3k views

LaTeX/TeX Vs. Mathematica for Typesetting [closed]

I know Mathematica like the back of my hand, but I do not know a speck of $\LaTeX$ or $\TeX$. With regards to mathematical typesetting, is there something significant I can do in $\LaTeX$/$\TeX$ that ...
18
votes
4answers
758 views

Advice for writing good mathematics?

It's been a (far-fetched, possibly) goal of mine to some day write a math Textbook. I've been thinking about writing this question for a while, but reading an exceedingly mediocre text on Mathematical ...
17
votes
7answers
2k views

Mathematical writing: why should we not use the phrase “we have that”?

In Knuth's Mathematical Writing, he writes on page 2, at number 8: Don't omit "that" when it helps the reader to parse the sentence. Bad: Assume $A$ is a group. Good: Assume ...
17
votes
8answers
918 views

Undergraduate Research Thesis

1. General background information ★ At my university [whose name I will omit] the following practices are customary: ● During their third year of study, students have approximately $4$ ...
16
votes
14answers
3k views

What are better words to use in an article than “obvious”?

I've heard often than it is ill-form to use the word "obvious" in a research paper. I was hoping to gather a list of less offensive words that mean generally the same thing. For example, one that I ...
16
votes
3answers
842 views

Starting sentences with mathematical symbols.

I apologise if this is a duplicate in any way or is too opinion-based. To what extent is it best not to start a sentence with a mathematical symbol? I find that when trying to solve a problem or ...
16
votes
3answers
283 views

Good examples of mathematical writing (structural organization, style, typesetting, and so on)

A very famous question on MathOveflow asks for examples of good mathematical writing. Here, I'd like to narrow down the topic and ask: $\color{#c00}{\text{Question:}}$ Could you point ...
13
votes
8answers
296 views

Mathematicians' manual of style

I know that there are many styles to write citations and footnotes and that they are all equally good (as long as the reference is complete), but I would like to know if mathematicians follow some ...
12
votes
4answers
217 views

Checking that a $3$-D diagram is commutative

When proving certain results I need to use commutative diagrams, some of which quite complicated. My question is: Do we need to check every small square all the time to make sure that they are all ...
12
votes
0answers
357 views

Papers with unorthodox writing style

I'm not sure if this is the right forum for this question, in any case probably CW is appropriate? I've been looking around the mathblogosphere for the past few weeks and ran into mathgen. It's ...
11
votes
4answers
689 views

Short forms like “haven't”, “don't”, “let's” [closed]

Is it true that short forms like "haven't", "don't", "let's" should not be used in serious mathematical texts?
11
votes
8answers
978 views

Book about technical and academic writing

I'm in the process of writing my Master's Thesis on automata theory. The writing must be in English which isn't my mother tongue. So the question is, given that this is my first time long (hundred ...
8
votes
6answers
1k views

What is an adjective for “weaker than weak”?

I defined a notion (say, some kind of equivalence) in three forms, the first implies the second, which in turn implies the third. I would like to use "strong", (nothing), and "weak" to describe them. ...
8
votes
3answers
436 views

Instructive examples of elegant, clear, rigorous, terse, but “non-dull” mathematical prose

On the "About" page of the Mathgen project one can read: "More seriously, I think this project says something about the very small and stylized subset of English used in mathematical writing. ...
8
votes
1answer
56 views

Is there a standard name for this “continuous induction” principle?

I am working on a paper, and I want to prove that some statement $P(x)$ holds for every value of a parameter $x \in [0,\infty)$. I plan to proceed as follows: Show that $P(0)$; Show that if $P(x)$ ...
7
votes
1answer
696 views

What is “observation”?

Often in mathematical writing one encounters texts like ''..we observe that this-and-that..''. Also one may find a review report basically saying ''..the paper is just a chain of observations...''. ...
7
votes
3answers
70 views

Formal writing in math: equations

What is the formally correct way to solve a bunch of equations in math? Is it \begin{align} 42x = 4324 \\ x = 4324/42 \end{align} or \begin{align} 42x = 4324 \\ \Rightarrow x = 4324/42 \end{align} or ...
6
votes
4answers
360 views

Should I include obvious steps in mathematical paper?

I am writing a formal school paper (by formal I mean, with an abstract, a bibliography and 20 pages in length) on mathematics (it is called 'Extended Essay,' for those having knowledge of the ...
6
votes
4answers
601 views

Are there rules in the useage of prepositions in Math?

It is often to use prepositions in various expressions. E.g. $2$ is in the set of natural numbers $\mathbb N$ The symmetric group on 3 letters $S_3$ is the group consisting of all possible ...
6
votes
1answer
149 views

How to properly mention names and surnames when writing introductions

I am writing a historical introduction to my master's thesis. Therefore I am mentioning a lot of people and I don't want to write their full name and surname each time. However, I cannot write their ...
6
votes
0answers
105 views

Use of “I” in mathematics papers

Some people consider the use of "I" in a paper to be a great evil. Others, however, consider the use of the passive voice to be an even greater evil. I will be presenting a paper at a competition, ...
5
votes
2answers
311 views

Writing computer code in a mathematics paper.

I have some computer computations (using GAP) in my research which I would like to write in the paper. How should I go about it? Should I include the full working code or just the major algorithms? ...
5
votes
1answer
6k views

How could I type “not exist” by Latex? [closed]

How could I type "not exist" by Latex? (I can type ``$\exists$''.) Thanks for your help.
5
votes
4answers
196 views

Why does nobody use the deduction symbols $A \Rightarrow B \Rightarrow C \Rightarrow D$ in their thesis/dissertation?

I am studying for a Master's degree of mathematics. There are some deduction in my thesis is written as the following form. $A $ $\Rightarrow B $ $ \Rightarrow C $ $ \Rightarrow D $ But my ...
5
votes
2answers
78 views

Nuances of the word “proposition” (versus “theorem”) in mathematical writing

In mathematical writing, the word "Proposition" is often used to label lesser theorems. However, I tend to feel that there's a further difference in the way the words "Proposition" and "Theorem" are ...
5
votes
2answers
268 views

Basic guidance to write a mathematical article.

I'm trying to put together a mathematical article on how to obtain certain infinite series for some well known functions by a method of integrals (I like to call it "The Integral Method" - thank you), ...
5
votes
1answer
104 views

What word means “the property of being holomorphic”?

As in the title, I am looking for a single word meaning "the property of being holomorphic". The obvious candidates are "holomorphy" and "holomorphicity" but both look wrong to my eye. ...
5
votes
1answer
88 views

Referencing Lemma before introducing it

I am always confused about this: When I am writing a paper I would like to first provide the big picture and then address some detail issues. On the other hand, I think it's common knowledge that ...
5
votes
0answers
133 views

Writing an abstract for a conference [closed]

For the first time, I'm preparing a 2-page abstract, jointly with a faculty member, to submit to a conference in mathematical logic so that the committee can decide if they allow me to present the ...
4
votes
2answers
577 views

Smart Pen For Math Writing

Next month I will begin to learn in the university, and I am not sure if to buy smart pen such as Livescribe or Logitech IO 1/2 to write math with.(handwriting is not an option) The problem is that I ...
4
votes
1answer
58 views

How to denote sum over partitions?

How does one denote a sum of partitions of an integer when writing an article? For example, I have a formula regarding an integer-valued variable (say q=5), and I need to write an expression of the ...
3
votes
2answers
218 views

When writing a mathematical model for non-mathematical audiences, how do you begin a sentence defining a variables and parameters? [closed]

Say you are writing a mathematical modeling paper in a science journal. How do you write your variable and parameter definitions in paragraph form so that you keep active voice but do not sound ...
3
votes
2answers
234 views

Can mathematical definitions of the form “P if Q” be interpreted as “P if and only if Q”? [duplicate]

Possible Duplicate: Alternative ways to say “if and only if”? So when I come across mathematical definitions like "A function is continuous if...."A space is compact ...
3
votes
3answers
171 views

Shorthand for $0<i<1$ , $0<j<1$, $0<k<1$

Is it good style to write $0<i<1$, $0<j<1$, $0<k<1$ as $0<i,j,k<1$? The following does not seem so clear: $0<i,j<1$ as it may be interpreted as: $0<i $ and $ ...
3
votes
1answer
240 views

Commas separating adjectives to describe mathematical objects.

Is there a convention which rules that in mathematics an object with some properties should be referred to as a "property 1 property 2 property 3 ...object" rather than a "property 1, property 2, ...
3
votes
2answers
223 views

When to begin a new paragraph? [closed]

When writing a mathematical article, when should someone begin a new paragraph? Is there some specific rule or convention? And more generally, what rules are there about articles-writing?
3
votes
1answer
67 views

On the usage of words instead of numbers to denote numbers

[To the best of my knowledge, I did not find any previous question that deals with this issue. I hope it is not a duplicate.] I have a problem with the way in which mathematicians sometime use ...
3
votes
1answer
68 views

writing papers: definition in word or formula?

If we write papers, is it or is it not desirable to write definitions in formulas AND words. So if I want to define the following set: $$S:=\{ x \in \mathbb{N} : P(x) \}$$ where $P$ is some predicate ...
3
votes
1answer
45 views

Is there a name for this curve? Or, how should I describe the behavior of this graph (in words)?

I simulated some results that look like this: but I don't want to include the plot (my advisor is keeping me to a strict limit on figures and these are minor intermediate results). Is there a name ...
3
votes
1answer
83 views

Commas between adjectives [duplicate]

Is it correct to use these expressions without commas (as written below)? A finite simple group. A finitely generated abelian group. A finitely generated torsion-free abelian group. A ...
3
votes
1answer
286 views

Writing small numbers in Articles [closed]

In primary school I learned that numbers less than 13 should be spelled out in writing. I am suddenly not sure anymore, how I should handle this situation when it comes to article writing in ...
3
votes
0answers
44 views

In a math paper, what is a remark?

I sometimes see paragraphs labeled 'Remark.' However, papers that include remarks also include unlabeled explanatory paragraphs (i.e. all the other writing in the article) that seem to be remarks. ...
3
votes
0answers
42 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
2
votes
2answers
200 views

Using Comma in if…then Conditional Sentences

Many English grammar books state that in an "if ... then" conditional sentence, the word then should be preceded by a comma. However, in mathematical writing I often see that this rule is ignored. ...
2
votes
4answers
136 views

Use of the word “shall” in mathematical writing [closed]

Sometimes I really want to use the word "shall" in my writing. But I get unnerved because I got a feeling it's pretentious or outdated. Any opinions? Is it a nice variation on "will"? Other ...
2
votes
3answers
187 views

Publishing an article after a book?

If I first publish an article, afterward I may publish a book containing materials from the article. What's about the reverse: If I first publish a book does it make sense to publish its fragment as ...