I see the bolded phrases every day, multiple times a day on this site. It may be in the title of the question or in the body of the question. Sometimes, it's even in the comments. I feel it is my duty to give a friendly reminder to the community about something that should not be taken lightly in mathematics: Writing.

The following are incorrect:

"How to prove $x$?"

"How to prove $y$?"

If you want to be correct, use the phrase: "How do I prove $x$?" or "How does one prove $y$?"

The forest from the trees:

I remember being in a linear algebra class when a student made a remark to the professor implying that mathematicians don't really need to know how to write, they just need to know how to do math. The professor told him bluntly that he was wrong and lectured us about the importance of writing in mathematics.

In my experience, mathematicians in general are some of the most eloquent people on this planet and their eloquence was not achieved by ignoring the writing process.


I think the best way to tackle this issue is to edit a post that makes this grammatical mistake, and maybe leave a constructive comment. This will sieve out the mistakes over time. I think in the end users will be grateful for this process. I know I'd want to be corrected if I was making a mistake in a language I was trying to learn.


I would like to add, that I am a user that improves and perseveres. My first question on meta got negative eight votes and this one got negative six, but I think I can do even better next time. In general, my progress might be slow. It might take me twice as long, but I will continue to improve.


closed as unclear what you're asking by Noah Schweber, TheSimpliFire, YuiTo Cheng, Joel Reyes Noche, Shailesh May 26 at 0:06

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ So what exactly is your question here? (Also, "mathematicians in general are some of the most eloquent people on this planet" has not been my experience - although just like in every profession, some mathematicians are amazing writers and speakers.) $\endgroup$ – Noah Schweber May 24 at 9:35
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    $\begingroup$ If the official language of science is Broken English, I see a problem with using the correct form of the statement! :P $\endgroup$ – Asaf Karagila May 24 at 13:02
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    $\begingroup$ I'm a bit saddened by the voting on this question - 6 down to my 1 up at the time of this comment. While I agree with postmortes' response that we should understand that many users here are not native speakers, that doesn't mean that we should not correct poor grammar when we see it. On the contrary, writing mathematics is an extremely important skill. As a college professor, I would certainly correct the type of mistake pointed out here if I found it on an assignment. $\endgroup$ – Mark McClure May 24 at 13:08
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    $\begingroup$ @MarkMcClure From where I sit, I think that the downvotes have more to ddo with the fact that there is neither a question nor a policy proposal in the original post. As such, this topic reads like a rant, rather than something appropriate for SE. Perhaps if the question were edited to include an actual question or policy proposal, the downvoters would be mollified? $\endgroup$ – Xander Henderson May 24 at 17:03
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    $\begingroup$ @MarkMcClure or the OP or anyone, could you explain what exactly is the issue? Is it the construct "how to [infinitive]" generally? I'd not know what else is meant. But that seems ubiquitous to me, at least for titles/headlines, but that seems a common use case. $\endgroup$ – quid May 24 at 19:24
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    $\begingroup$ @quid e.g. 'How to' vs. 'How do I' $\endgroup$ – Bill Dubuque May 24 at 20:17
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    $\begingroup$ @BillDubuque thanks. Yet I am still given to understand that "How to [infinitive]?" is arguably alright as a heading (as in, e.g., "How to solve it"), which is how it is often also used on this site. Thus, the post here might need some clarification to make explicit that only some usages are incorrect. Except if OP wishes to main otherwise, yet then this might be less clear cut. $\endgroup$ – quid May 24 at 20:24
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    $\begingroup$ @quid To clarify, that was only for reference. My opinion is also that it is fine in this context. In fact I support the much stronger position that one should not let any other languages (be they human or machine) obstruct mathematical language. So I don't mind abusing such extra-mathematical entities when it helps to clarify mathematical exposition (e.g. TeX purists sometimes complain about my "abuse" of TeX/MathJax, but such code is meant to be read by machines - not humans). $\endgroup$ – Bill Dubuque May 24 at 20:32
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    $\begingroup$ Unfortunately the great mathematician George Polya who wrote the book How to Solve It passed away a long time ago without the benefit of this discussion. $\endgroup$ – RRL May 25 at 4:07
  • $\begingroup$ @MarkMcClure Xander Henderson is right: until there's an actual question here, my downvote remains. $\endgroup$ – Noah Schweber May 25 at 8:08
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    $\begingroup$ @RRL, "How to Solve It" is correct; it is a phrase and doesn't end with a punctuation mark. "How to Solve It?" is incorrect as a sentence (it doesn't have a verb or a predicate). $\endgroup$ – Joel Reyes Noche May 25 at 11:26
  • $\begingroup$ With limited space to write , not everything can be phrased "correctly". Similarly, in LaTeX , if you want rotation allowed, technically you should use the rotate, turn, or other rotati9n package, but you can inneffect make it work, or look to work via other means. $\endgroup$ – Roddy MacPhee Jun 8 at 14:36

There's a biblical quote about removing the beam from one's own eye before attempting to cast out the mote from someone else's that seems appropriate here :)

Not everyone on the site has English as a first language, or even as a language they're especially fluent in. Not everyone asking a question on the site intends to go on and produce mathematical (or other) works in English. While I see little harm in editing someone's post to correct English that is ambiguous, wrong, or confusing (since these all improve the post), or providing a helpful comment to someone on how they might improve it themselves, some people will take offense or feel criticized. You will have to expect that some of your comments will fall on deaf or angry ears and be able to handle that without retaliating.

Writing is important in mathematics as means of communication. English is flexible: native speakers can pretty much pick out the intent of a garbled sentence and often ignore small mistakes in conversation because correcting them isn't necessary. The same here: "How to prove $x$?" isn't Shakespeare, but I have no trouble understanding what's being asked for. (It might interest you that I would choose neither of your rephrasings, but would prefer "How can $x$ be proven?"). If the question communicates its intent clearly, then I would be slow to criticise it.


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