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Is there any hidden rule for using the words "clearly", "obviously" or similar ones in a technical paper? It can be offensive to the readers in many cases (especially in mathematical proofs), since the reader may not find it "clear" or "obvious". But does that mean that we should completely avoid the use of these words?

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  • 22
    these words usually preface a lie. its a tell.
    – nathan hayfield
    Jun 27, 2013 at 17:55
  • 16
    "proof by intimidation"
    – Nick
    Jun 28, 2013 at 5:14
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    Clearly, the answer to your question is obvious.
    – JRN
    Jun 28, 2013 at 13:49
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    smbc-comics.com/index.php?db=comics&id=2991#comic
    – Josh
    Jun 28, 2013 at 23:14
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    Besides providing a popular alternative to actually proving your claims, those words are also useful when something really is "easy to see" (but is nevertheless useful) and you wish to point out that you're aware of that. Referees sometimes seem to feel like they're talked down to when something is "too easy", so that can serve as a way of avoiding their wrath. If something is not too difficult but does not deserve a proof because it's well-known at least by the community I'm aiming at, I usually provide at least a reference (see Exercise x in Smith et al. [y], page p).
    – Anthony Labarre
    Jun 29, 2013 at 8:19

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Seconding posdef's appraisal, but being a little more blunt: if one is in a position to get away with bullying or intimidating people by implying that it's their problem if one has not explained well enough ... well, I'd say it's still a jerk-y thing to do. If one is in a lower-status position, such words will often be red flags.

Or, coming to functionality versus rhetoric versus "formal proof": at best these words are functionless filler. That is, saying something is clear is not what makes it clear: if it is clear after these words, it was clear before. Conceivably a thing is clear _once_noted_, and thus deserves "Observe that...". But this, too, can be abused if used outside situations where one is noting that something is "a-fortiori" true, that is, is weaker than what the argument has already demonstrated... but presumably suffices for the issues at hand.

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    But even "Observe that" is redundant. You don't need to announce that you're about to say something. Just say it.
    – JeffE
    Jun 28, 2013 at 3:45
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    Meh, it is redundant, but I agree with his idea that it is a better way of 'underlining' a point (and is OK to use occasionally) - Similar to VS's (below) 'it follows'.
    – hunter2
    Jun 28, 2013 at 3:51
  • I prefer "We emphasize that..." to indicate emphasis. Sparingly, of course.
    – JeffE
    Jun 28, 2013 at 16:19
  • @JeffE I propose it's circumlocution
    – Tobias Kienzler
    Jun 29, 2013 at 6:56
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    I think saying something is obvious (if it actually is) can be useful though, it helps the reader do a sanity check and make sure they're following all your arguments correctly.
    – user541686
    Feb 17, 2015 at 7:46
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I don't think there is a very clear rule for using such words. One possible reason for my claim is that some authors don't even use words "clearly" or "obviously", but they simply say "it follows ...". In mathematics the level of details of a mathematical proof mostly depends on the writer's kindness to her/his readers. I have encountered with many not-so-obvious claims in papers written by experts, where needed several pages of explanations and perhaps some proofs, and several years later, I have found the proofs of those claims in newer papers written by other authors.

Unfortunately, there is an adage which says "brevity is a sign of genius" and it seems some people strongly believe in this adage and try to impress others by leaving not-so-obvious gaps in their works.

Personally I apply the following rules for using these words:

  1. If the claim follows from previously mentioned materials by applying well known techniques in 5 minutes or so.

  2. If it can be obtained by a few lines of computations again by applying well known techniques. Then I use the word "straightforward".

  3. If it easily follows from a well known type of mathematical proofs, like induction, Zorn's lemma.

  4. The proof is similar to a previous proof in the paper or in the literature. In this case I mention the resource.

  5. I expect a PhD student in the field can prove it easily.

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    +1 for "it follows that ...". Instead of saying "obvious" or "clear," I just say "it can be seen that ..." or "thus, ..."
    – JRN
    Jun 28, 2013 at 0:13
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    I thought it was "Brevity is the soul of wit".
    – hunter2
    Jun 28, 2013 at 3:54
  • @hunter2: I think what I mentioned is a Russian adage.
    – user4511
    Jun 28, 2013 at 4:23
  • Ah, neat. We do have similar, eg "Still water runs deep."
    – hunter2
    Jun 28, 2013 at 4:33
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    This reminds me of Daniel Oppenheimer's paper “Consequences of Erudite Vernacular Utilized Irrespective of Necessity: Problems with Using Long Words Needlessly” which won the 2006 Ig Nobel Prize for Literature. His one-line acceptance speech: “Conciseness is interpreted as intelligence, so thank you.”
    – JRN
    Jun 28, 2013 at 13:44
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I don't think there is a clear consensus on how to use these words.

As mentioned in some other answers, some people find them annoying or obnoxious. Others think they are a perfectly acceptable way to mention a fact for which you believe a detailed explanation is not necessary. Certainly they are quite common in published writing.

I think it is a choice that you make as part of developing your own personal writing style, and your feelings may change over time.

My only advice is: when you write that something is "obvious", make absolutely sure it is true! I've been embarrassed this way before.

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More broadly then in regards to mathematical proofs, a mark of good writing is to avoid the superfluous. Whether something is clear or obvious comes from the content, not the writer labelling it as such. Trimming unneeded adjectives and adverbs like those you describe should be a regular step in a proof-reading stage. See Strunk and White's Elements of Style for a more detailed treatment.

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We touched this particular subject in a "Technical Writing" course; the simple answer is that it's a power-stance. In other words, if you are a big-name professor in your field, you can use it without offending someone. Alternatively if you are a petty PhD candidate, then you are better off avoiding not only these two words but also other forms of bold statements when you are drawing conclusions.

As I said this is rather the short answer, I am sure those who are more into linguistics etc might have more insight into the matter.

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  • I would add that if it is clear or obvious, explain how it is clear: "X is clearly the case, as shown by Y." (In other words, the words "clearly" or "obvious" are unnecessary fillers and can be omitted.) If it is being used as a power-stance, I would not accept it even from a top-level expert — or my boss.
    – Paddy Landau
    Jun 27, 2013 at 17:18
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    if you are a big-name professor in your field, you can use it without offending someone — [citation needed]
    – JeffE
    Jun 28, 2013 at 3:46
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    @JeffE it was the lecturer in the course I mentioned, who is a professor in linguistics I believe. So it's not something I made up myself :)
    – posdef
    Jun 28, 2013 at 6:20
  • @JeffE: I remember that we were studying once in school a text written by "Ibn Khaldoun", an Arabic scholar in the 1300's. We noticed the use of many statements that would be be considered nowadays as "arrogant". The teacher, I remember, said that the author (i.e. Ibn Khaldoun) is allowed to do that given that he is a big-name scholar. I remember the teacher said this technique was followed by other big name scholars of that time. But this could be a cultural matter more than anything.
    – AJed
    Jun 28, 2013 at 13:29
  • @AJed I would suspect that the field in which the article in question is written in, has a role to play. Many here are from maths or CS-related fields, where the articles are written inductively instead of deductively, which is the case for chemistry, biology and medicine... The difference being that findings need to be interpreted in deductive research, which leaves the door open for clumsy expressions such as "... clearly indicates that ..." (Note that I do not approve these expressions, nor do I try to justify them)
    – posdef
    Jun 28, 2013 at 13:42
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I was always taught that if you had something to say that was "clear" or "obvious" to your intended readership, then it wasn't really worth saying at all. Made a lot of sense to me, and I've never used those words in any of my technical or academic writing since.

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By reading the comments and answers here, the conclusion is, that it is usually not a good idea to use these terms. Keep in mind that it might not always be the case that something is obvious to your reader. That being said, the reason you want to use such words is probably because you want to point out/conclude/summarize your findings to the reader.

The bottom line is not to tell your readers what (you find) is obvious, but to tell them what the obvious thing is (conclude/summarize). This way they will either:

A. Confirm their own observation
or
B. Let them know they haven't fully understood yet (they might re-read your article now)

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I propose never using these words unless your goal is to trick the reader into thoroughly checking your claim, or in an exam's trick question where you set a false premise (though these words are give-aways if not overused). If something is obvious there wouldn't be a need to even state it. And if you need to state something, it is not obvious.

If you think some non-trivial1 steps should be omitted so your 5 page paper doesn't bloat up to a 30 pager, then please have the decency to either briefly state the trickiest tool involved (be that induction or some specific part of Wile's proof of Fermat's Last Theorem) or - even better - put the detail which you should have done anyway into the appendix / online supplement and refer to it.

1Trivial is also one of these words.

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I might go against most of the answers here and say why not?.
I am going to this right now. I am writing a paper proposing a solution for problem X by adopting well known mathematical model Y. Now Y has clear axioms and definitions (for instance, the set of considered elements has to form a commutative semigroup under combination). I defined X then defined the combination operator. Should I go further and proof it is commutative semigroup? I believe it is clear that X form a commutative semigroup within my framework. Yes It is obvious..

Now whether the author of these words is a student or professor, I believe it doesn't make difference. At the end, there is minimum knowledge required to understand any given paper, if its clear then it's clear and you better utilize the paper limited space in something not clear enough.

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  • There's nothing wrong in stating that Y being a commutative semigroup implies X being one too (due to none of the possible exceptions occurring, of course). But there's no need to state that this is obvious, just state the fact and instead of "it is obvious" write "because Y is". Also three words, but much more helpful IMHO
    – Tobias Kienzler
    Jul 1, 2013 at 10:23

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