Academic writing is difficult to do. Good academic writing (just “good writing”) is even more difficult to do. There are lots of contradictory styles, and different things sound right to different people. What's worse, something that sounds right to you when you read it may not sound right to you when you write it. Sorting out your own style, ensuring it's a good one, and then sticking to it is hard.

I've been writing academically since I started university in 2001, but I only started thinking about how I was writing late in 2007. Here are my collected thoughts so far. As my position changes over time I'll edit and update this essay, rather than write sequels to it. It is oriented towards writing for computer science and the other mathematical subjects, but style is almost completely independent of subject.

There are three references I would especially recommend as introductions to the subject:

• Mathematical Writing, by Knuth et al. is an edited and synthesised transcript of lectures on good writing style for mathematics. It covers the full gamut, from tense and grammar to the clearest way to use inline equations. I don't agree with all of the ideas, but that's just my style versus his and your opinion could be different again.
• This is handy.
• Strunk & White (Elements of Style) is crucial.

In fact, there's one passage in Strunk & White that needs to be quoted: “Vigourous writing is concise. A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all sentences short or avoid all detail and treat subjects only in outline, but that every word tell.”

There's also Fowler's Modern English Usage. This is just another style, but it is encyclopaedic in its coverage and consistent too. Even if you don't agree with it you should use it as a common, fixed reference point that you personally deviate from in specific and limited ways.

What is the point of good academic writing? Clear communication. It has no other point. If it makes the writing confusing, dense or ambiguous it is bad writing. However, clear communication is not necessarily easy to read. If the ideas are especially complex the reader might proceed at the rate of only one page per hour. When this is the case it is wrong inflate the readers page speed by adding padding. Such padding distracts the reader and will only increase the total length of time it will take them to read the document.

The grammatical aspects of good writing come smoothly from the goal of clarity. Tense, careful use of the passive and person are the three most important aspects of grammar. When you have several grammatical options you should judge which is clearest and use that. If several are equally clear then use the one that jars the reader's line of thought least.

First and foremost, good grammar means consistency. Consider person. Don't switch from “I” to “you” or from “their” to “your” part way through a paragraph for no reason. Each person conveys a slightly different sense. The first person is very personal and can be jarring. It can be effectively used in a piece like this when making recommendations or suggestions which aren't objective, but it should be used rarely even then. In other, more expository, work its use should be even rarer.

The second person is similar to the first person. Even in an instructive piece of work it may come across as patronising or aggressive. It should only be used when a particularly strong recommendation needs to be made, or when not using it will leave the text wooden and passive. In other documents there is almost never any reason to use it.

The third person is difficult. Most of the time it does not fit, other times it fits very well and no other pronoun seems natural. When it does fit like this it usually turns a passive verb into an active one. As we will discuss in the next subsection, this transformation is good.

Generally, the first person plural “we” is best. It is normally interpreted as referring to “the reader and the author(s)” rather than the “authors” and its use is much friendlier than “you”. In certain cases though, like “you”, it can also sound patronising. It seems that “we” is often patronising where “you” is not and vice versa. To try and decide which to use in a particular case say both alternatives out loud or imagine hearing them said by someone else. Even say them to someone else and get their feedback. If this doesn't make it clear which is better it may be the case that either will work.

“We” can also be used in a psychologically inclusive way. If you're trying to persuade people of a point it can assist you, but in this case it should be used with a light touch, else it will come across as manipulative. The first person singular “I” may be more appropriate. If the reader starts to think that they're being manipulated they will be jarred out of whatever line of thought you had created and the content of your writing will no longer be the first thing on their mind.

Passive sentences are sentences where the object comes before a (possibly implicit) subject. This means that they place greater emphasis on the object of the sentence. This is their only advantage; passives sentences are usually longer and clumsier than active sentences. Passive sentences can be avoided by using pronouns or the third person. They can also be avoided by turning a passive phrase into a noun. For example, “Predicting the stock market well is hard” can be changed to “Good stock market prediction is hard”. The latter reads more smoothly and the meaning of the sentence is clearer.

Passive sentences can also be (mis)used to make the writing sound more authoritative, intimidating and formal than it actually is. Contrast “It can be seen…”, with “We can see…”. One common, noisome example is “It is obvious that…”. Who is it obvious to? Should it be obvious to me? If it isn't did I misunderstand something? Am I stupid? Or is the writer just trying to cover up their own literary and academic weaknesses by pushing the blame onto the reader?

Tense is more complex, because the verb tense that you use also says something about the subject and object of the sentence. This web page has a very good summary of which tense you should use when the object of the sentence is not the paper itself.

You have two choices when the paper is the subject of the sentence. The paper will be the subject of the sentence whenever you are describing the structure of the document, and we will discuss the use of such sentences in the next subsection. Whichever tense you choose for references, you should use it consistently to avoid jarring the reader.

You can either use the simple present tense throughout the paper (“Section 17 describes…”), or you can use the past tense for references to earlier in the document (back-references, e.g. “Section 2 described…”) and the future tense for references to later parts of the document (forward-references, e.g. “Section 46 will show…”). In all cases you should use the present tense for references to the current section of the document: “This section describes…”. Sometimes the future tense works well, but it quickly becomes clunky if it is used too much. This is not necessarily a disadvantage though, as it can act like a “canary in a coal mine” and warn the author that he is using too many forward-references.

There are two kinds of intra-document reference. Back-references refer to an earlier part of the document. Forward-references refer to a later part. You should minimise the number of forward-references, and the number of back-references will (should) depend on the complexity of the ideas. Try to make forward-references as explicit and as well described as possible, so that the reader knows exactly what to expect from them. Thus, writing “Section 6.3.2 proves that this condition is sufficient” is OK, as is “Section 4 describes linear genetic programming”. Just writing “This is proven in section 5.4.2” commits the sins of ambiguity and passivity. What “this” is could be ambiguous. Even worse is to wave all of the details away: “This will be discussed later on,” (but we're not going to tell you what or where).

Just as your references should be explicit and well described, you should signpost the structure of your document, so that readers can more easily keep track of what you have done, are just about to do, and will do much later on. In longer documents this normally means adding a paragraph to the introduction which summarises what each section will do and adding a more detailed paragraph at the beginning of each section as well. It is also useful to insert comments in the text which place immediate results in a wider context. For example, “This concludes our proof of blah, which shows that blech. We will use this result to analyse blabble.” and “This general proof is incomplete in three ways: foo, bar and baz. However the next three subsections show that foo, bar and baz are not relevant to the wibble-problem.”

Rather than writing “We show in section 5…”, we think it is clearer, more direct and more powerful to write “Section 5 shows…”. As a general rule, words should be cut whenever possible.

This bias towards eliminating words extends to adjectives as well. It might seem that using adjectives will emphasise important points. However this is only the case if they are almost never used. Emphasis (italics) works similarly. It should only be used to highlight new technical terms. Many phrases used to link and introduce only make the document longer, they should also be cut. Contrast: “Importantly, note that one very important result is what is known as X. We can see that X has very wide applications in almost all areas of Computer Science such as P and Q, etc. It shows the total irrelevancy of Y to Z, and thus it essentially leads to A. In addition, A simply implies that B is false.”

And: “X has applications in P and Q, and it shows Y to be irrelevant to Z. This leads to A, which implies that B is false.”

This example also illustrates why catch all terms like “computer science” or “artificial intelligence” are a bad idea. What is a catch all term and what is not will depend on the situation. Adjectives also lose their impact very quickly. Even when infrequently used they can distract the reader, which makes the document harder to read.

Certain phrases are unnecessary. They can be used to give readers a breathing space, but should be used sparingly. Such phrases include:

• “Note that…”, “Importantly, …”, and “Importantly, note that, …”. Of course it's important and of course it should be noted. If it isn't then cut it and the prefix too. “It is quite obvious that…” and ”…, indeed, …” fall into the same basket, and they also patronise the reader.
• Dashes (”—”) are a sign of laziness. Separate your ideas into complete sentences and resist the urge to transcribe a “stream of consciousness”.
• “Essentially, X…”, “As can be seen, X…”, and “What is known as X…” should be deleted. Just say “X…”.
• Be suspicious of “Thus”, “Therefore” and “However”. Always make sure that what follows “However” is in contrast to what precedes it, and most “Thus”'s and “Therefore”'s can be deleted unless the reader needs a breathing space.
• Don't use exclamation marks! Like adjectives they lose their impact very quickly!!
• “In addition, …” and “Similarly, …” are unnecessary, the link between the sentence and its predecessor should be obvious to the reader.
• Never use “etc”, it's worse than a catch all term. If you use a catch all term like “artificial intelligence' you have at least drawn boundaries. When you use “etc” all you have done is implied that there is more. If there is and its important then say it. If it's not then don't say anything at all. Using “etc” makes it sound like you don't know what you're writing about.
• Don't say “some”, say how many, e.g. “four”.

This concludes most of our stylistic analysis, the fact that there is a grab bag of minor suggestions which we haven't covered elsewhere indicates an incomplete and imperfect document structure. This section enumerates them.

• Make the section title descriptive. Prefer “Bayesian Networks compared to Other Representations” to “Other Representations”, even if the relevant entry is a subsection inside the “Bayesian Networks” section. Except where they are common and non-technical or stand for a very long phrase, don't use abbreviations in section titles.
• Possibly, use full sentences which summarise the contents of the section as the section title. Done well, the contents will almost be an abstract. It is important to do this consistently if you do it at all though. With such section titles it may be necessary to use abbreviations in them due to the overall length of the title.
• Define abbreviations (and emphasise the abbreviated term) when you first use them.
• Adding whitespace, either illustrative figures or blank space, makes the document seem much lighter. It increases the page speed without adding words.
• Repeat yourself, especially if defining or proving something mathematically. One approach is to show it mathematically, sum it up colloquially and then to give a concrete example. This gives readers a second (third) perspective and a second (third) chance at understanding it.
• Keep most of your paragraphs short, usually about 4-6 lines in a single column document. I'm bad at this.
• Make the start of each long caption the same as the entire short caption. This means that readers will be able to easily match what they saw in the contents with what they see in the document.
• Ask someone else to read what you've written. It's better if they understand the material, but they can still point out bad writing even if they don't.
• Rewrite it multiple times.
• Structure it (sections, sub sections, a sentence describing what each will do) before you start writing anything more than notes.
• Minimise your use of jargon and technical terms. If you can explain it concisely and accurately without them then do.

Modern spell checkers are very good. Use one. Nothing will jar a reader more than a misspelt word and it is so easy to avoid. Bad spelling, even just one word, immediately flags a paper as an amateur effort.