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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 colloquial. My secondary question is what the alternatives are if it is too colloquial.

For example, right now I have a sentence "Given a point $P\in X$ we have the residue map ${\text {res}}_P \colon \Omega_{K(X)} \rightarrow k$, as defined in ...". I don't feel saying "there exists the" is quite right. Even if it is grammatically correct, I don't think this conveys the implication that it will be almost certainly familiar to the expected audience.

I have seen this question but I feel this is slightly different. If not then my apologies.

Community
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Joe Tait
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    When one wants to avoid "we have", there is always "one has". – Marc van Leeuwen Feb 08 '14 at 20:19
  • This might be a good, possibly a better fit for the English SE. I personally think that using "we" rather than "I" automatically disqualifies it as being colloquial. – Jack M Feb 08 '14 at 20:37
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    "We have" is fine. "One has" is also fine, if you are at least 50 years old. – TonyK Feb 08 '14 at 23:00
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    @MarcvanLeeuwen "We have 'one has'" – user Feb 09 '14 at 01:45
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    I think 'one has' would be better, 'we' does imply that most readers will know what you are talking about and thus it has the potential to make readers who don't know about it feel alienated or stupid. Also it might possibly sound patronising, like a teacher to a 5-year old: "Now Timothy, we don't eat the crayons now, do we?". – Pharap Feb 09 '14 at 05:19
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    Is such question on-topic on academia.SE? – Vi0 Feb 09 '14 at 12:30
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    "Now Timothy, one doesn't eat the crayons now, does one?" – JRN Feb 09 '14 at 15:20
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    Though I agree that "we have" is fine, there is an alternative: "To each point $P \in X$ corresponds a residue map $\operatorname{res}P:\Omega{K(X)}\to k$, as defined in . . ." – Nick Strehlke Feb 09 '14 at 17:40
  • Perhaps this is relevant here. – Shaun Feb 09 '14 at 18:06
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    "We have" is also perfectly acceptable when the author of the paper is a king or queen. – Emily Feb 09 '14 at 19:07
  • This "we" includes the reader, so you should make sure that this is actually appropriate. In addition, if "we have" sounds strange, it is most likely due to the fact that it could be replaced with a more precise phrase, not due to the "we". – Phira Feb 10 '14 at 01:13
  • "Given a point P∈X, the residue map resP:ΩK(X)→k is defined by ...." or "Given a point P∈X, XYZ defines the residue map resP:ΩK(X)→k" – Ben Voigt Feb 10 '14 at 01:47
  • @TonyK, What's with the 50 y/o? – Pacerier Sep 19 '15 at 14:17
  • @Pacerier: "one has" sounds old-fashioned to me (even though I'm over 50). – TonyK Sep 19 '15 at 14:40

12 Answers12

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In my opinion it is even good style. You are involving the reader somehow to the discussion, if you write phrases like "we have", "we consider", "we may assume", "one can see that" etc.

By the way, it is common in other languages as well and you can read similar phrases in papers of famous mathematicans all over the world.

Some examples:

Noi sappiamo (...) $\tag{Fubini, 1903}$ (we know that, ... Ref, p.6 )

or

(..) nehmen wir an, dass (..) $\tag{Minkowski, 1900}$ (We assume that ... Ref)

or

However in the reducible case (..) we have to consider (..) $\tag{Wiles, 1999}$ (Ref, p.4)

Furthermore I found a guide by MIT in which is said

Be forthright: write in an unhesitating, straightforward, and friendly style, ridding your language of needless and bewildering formality. Be wary of awkward and inefficient passive constructions. Often the passive voice is used simply to avo id the first person. However, the pronoun “we” is now generally considered acceptable in contexts where it means the author and reader together, or less often, the author with the reader looking on.

user127.0.0.1
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    OK, how some examples that aren't more than a hundred years old? ;-) – vonbrand Feb 08 '14 at 22:06
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    @vonbrand you could take almost every actual paper and find this kind of phrases. With my examples I was about to point out that this is even well-established all around the world and for decades now – user127.0.0.1 Feb 08 '14 at 22:12
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    @vonbrand however, I added a newer reference by A.Wiles, who proved i.a. Fermat Last Theorem – user127.0.0.1 Feb 08 '14 at 22:36
  • The writer of the MIT guide appears not to know what the "passive voice" is, nor that "we" is the first person. – hobbs Feb 09 '14 at 09:51
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    @hobbs How do you figure that? It makes perfect sense if reading it as "Often, the passive voice is used to simply avoid "we". However, there is no need to avoid "we"." – hvd Feb 09 '14 at 11:42
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    I have a huge objection with using 'we have'. The reason is something you seem to take for granted. To me it is not clear if 'we' means all of the authors and the reader or just the authors. Clearly you assume it is the first case, but I see no reason to suppose it is so and due to this ambiguity I avoid using it. – Git Gud Feb 09 '14 at 21:25
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    @GitGud If that would be a problem, then it is because of other problems in the paper. Fix the underlying problem, and it no longer feel bad. Most usually, from what I have read, the problem is that the 'tell what you found' and 'teach readers about it' parts of the paper get mixed up. I have read papers that do it each way, and papers in which 'we' would be ambiguous are usually already confusing anyway. (Although this might have less applicability to maths, as what I was reading was mostly CS stuff.) – AJMansfield Feb 09 '14 at 22:58
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    I agree with Git Gud. In fact every time I see "we have" I take it to mean "my co-authors and I have". You at least be aware of the different ways your reader might interpret it. – R R Feb 10 '14 at 00:26
  • @user127.0.0.1, actually Minkowski should be translated as "Let us assume that". Source: I'm a native speaker. – Alan Plum Feb 11 '14 at 15:58
  • I do understand that it was mainly meant to be entertaining, but of course there is no reason to assume that great mathematicians also have to be great prose stylists. –  Jul 12 '18 at 01:43
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It is not too colloquial -- it is used all over the place in papers. In your example, "we have" is preferable (IMO) to "there exists the," which is verbose and a bit ugly.

student
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    Okay, thank you. I think I am at least a bit paranoid due to general bad writing and a pedantic supervisor (as all are). – Joe Tait Feb 08 '14 at 17:48
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    But it does not mean "Most readers know this and I am about to use it" (as suggested in the question). – Michael Hardy Feb 09 '14 at 04:39
  • @MichaelHardy I meant that it implies this (perhaps quite subtly), not that it says precisely this. – Joe Tait Feb 09 '14 at 11:07
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(EDIT:) The basic difference is that 'we' suggests two minds, specifically a teacher/student paradigm.

This is perfect for any teaching context.

But academic peers exchanging information will go to absurd lengths to avoid insulting their colleagues by insinuating such a relationship.

The object of maths is understanding.

The object of mathematical writing is communicating that understanding with the utmost clarity.

And at the heart of communication is dialogue. It is one person explaining to another person.

Look at the Greek dialogues (e.g. http://www.sacred-texts.com/cla/plato/laches.htm), and observe how easy it is to understand the material when both parties are voiced, even if the student's part is little more than a device.

This duality is critical; question and answer complement one another; the question creates a space into which the answer may manifest, the answer provokes further questions, and so on. This creates an interconnected web of understanding.

And if the 'we' is lost, then the dialogue is also lost.

Look at Einstein's famous papers (e.g. http://milesmathis.com/five.html) and notice how you feel he is looking over your shoulder and explaining something to you.

It is unfortunate that academic papers feel the need to be absolutely impersonal, because it makes them dry. I have to read through a lot of them, and the conventional style is a hindrance; you should break every rule in the pursuit of clarity.

Interestingly, as YouTube videos are gaining popularity over written text as teaching resources, we are seeing a resurgence of the Socratic Dialogue paradigm! As a video is typically made in real-time, the presenter doesn't have the luxury of formalising the presentation. This is a good thing!

P i
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    I am more and more aware that the point is to communicate, and with this I am more and more aware of the fact that I often do not do this well. I guess that if you stare at anything long enough it doesn't look right... – Joe Tait Feb 09 '14 at 16:09
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"We have" is just an expression that is meant to involve the reader. It's a little less dry than "there exists"; it's a bit of a colloquialism, and a little friendlier than the passive voice or third person. I think it's a good stylistic choice.

Here's an example to illustrate the point, from a different field entirely:

"Looking at the top-right corner of Van Gogh's Starry Night, there is a bright-yellow moon, a great contrast that draws one's attention."

vs.

"Looking at the top-right corner of Van Gogh's Starry Night, we can see a bright-yellow moon, a great contrast that draws our attention."

I think the latter sounds more pleasant than the former, because it is less stilted and less distant. The case for wanting to use "we can see that" or "we have that", etc. in mathematical writing is similar.

For reasons similar to the above, I sometimes even use expressions like "then our sequence converges" instead of "then the sequence converges", which is perhaps a little more controversial.

Newb
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    A nice example, thank you :) – Joe Tait Feb 08 '14 at 18:01
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    First person plural does seem a little bit chummy; for the first, how about "...a bright yellow moon draws viewers' attention with its contrast"? – supercat Feb 08 '14 at 20:54
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    Passive voice is generally considered a no-no in writing. – vonbrand Feb 08 '14 at 22:07
  • @vonbrand: Where is this "passive voice" that you speak of? The only passive voice I see, in this answer and all of its comments, is "is meant". – TonyK Feb 08 '14 at 22:50
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    @vonbrand: Apart, of course, from your "is generally considered". If that was deliberate on your part, then you are too subtle for the internet :-) – TonyK Feb 08 '14 at 22:54
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    @TonyK, guilty as charged. – vonbrand Feb 09 '14 at 01:00
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    The first version, "Looking at ..., there is ...", suffers from a dangling participle. The second version provides a proper subject "we" for "Looking". – Andreas Blass Feb 10 '14 at 02:58
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Aside from its effectiveness as a rhetorical tool, as discussed in all the other answers, and argued in the Knuth paper in the question you cite (point 6), there is a much deeper — and to me more compelling — reason for using "we".

Mathematics, like all the sciences (and arguably all human endeavors, when done right), is a collective enterprise: we advance and appreciate and critique its contents together, over centuries. No individual owns it, and no authority controls it.

Given "$P\in X$" we — truly, all of us together — have "the residue map...". No one is excluded from this statement; each of us can confirm it, and has the potential to refute it; many, stretching back to ancient times, have contributed to establishing it; and all of us together will contribute to the elaboration of its implications, for as far as math is true and "we" have descendants.

orome
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6

Another characterization of the use of "we" can be found in the introduction to William Bloch's The Unimaginable Mathematics of Borges' Library of Babel:

This should not be construed as a “royal we.” It has been a construct of the community of mathematicians for centuries and it traditionally signifies two ideas: that “we” are all in consultation with each other through space and time, making use of each other’s insights and ideas to advance the ongoing human project of mathematics, and that “we”—the author and reader—are together following the sequences of logical ideas that lead to inexorable, and sometimes poetic, conclusions.

orome
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"We have" not only sounds reader friendly and nice, it also seems much more appropriate to me than "there exists", because "existence" is a complicated thing when dealing with theoretical entities. We sure have numbers. But do numbers "exist"?

But I must confess, I'm a philosopher, no mathematician.

Goodsquirrel
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  • We don't have numbers. Numbers have us. 8^) – Zane Feb 11 '14 at 11:17
  • I can't help but feel the most common understanding of 'existence of mathematical entities', at least for the mathematicians for whom the paper is written, will be in the sense that axioms have implied the existence of the object, as opposed to whatever wishy washy definition that philosophers choose to attribute to the term. – Dan Rust Feb 11 '14 at 19:06
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I would replace " we have" by ", then" or just ", "

user127362
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    +1. Why say "given $P \in X$, we have the residue map, as defined in ..." when you could just say "given $P\in X$, the residue map is defined as..."? – sjy Feb 10 '14 at 05:38
  • Well, if I think that anyone reading the paper should already know something then I am not going to "is defined as...". Obviously it would be nice to explain everything, but this is unrealistic if you want to have a paper that is of a readable length. – Joe Tait Feb 10 '14 at 08:58
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interesting meta at "An impersonal and precise way of writing is important if we want to seem rigorous." [italics mine] Either the author is unaware or fiendishly clever!

I think "we have" and so on is already an established, rigorous math norm. Also, check out the Russian "imejem" which is the "have" of "we have", without "we". What is the Greek word?

PA6OTA
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It's a matter of standard practices. Euclid didn't say "we have" in making a conclusion, but he did say "I say that" to declare a claim just before proving it.

Personally, I'd like to see technical papers written in a less formal style. We dropped the subjunctive and future tense some time ago. We no longer write "If $x$ be a real number, then $x^2$ will be nonnegative." Language marches on, and it makes sense to keep with the times.

David Joyce
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In all disciplines, there are rules. I think there's an unwritten rule about precision:
An impersonal and precise way of writing is important if we want to seem rigorous.

Unless you are communicating in a casual context, divulging informally, I would always use an impersonal speech and writing style. But that's only my opinion.

"I have" or "we have" should be replaced by "there is" or "there exists" in a formal mathematical context.

Ellie Kesselman
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Stella
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    "Impersonal and precise" is the realm of automated proofs (yes, there are journals publishing such; some 10 times longer than human-oriented proofs and totally unreadable for non-initiated). When you write mathematics, you want the reader to understand, and that (if you want it or not) has a large non-rigurous, psychological component. We like to consider ourselves "rational animals," when the thruth is that we aren't. – vonbrand Feb 09 '14 at 14:48
  • We're not only rational animals, of course. In fact there's been a lot of research about intuition and the beneficies you can get from taking decisions, not only after a long process of rational thinking. But that wasn't my point in this answer. I was just trying to explain that if you want to publish in a rigorous journal , for example, you have to be precise, but if you are trying to reach are wider spectrum of people, to make divulgation, then you have to do it the way you say, adapting the content to the audiance. That's what education is about, of course, but I wasn't talking about that. – Stella Feb 09 '14 at 15:06
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    *Most style guides recommend the active voice over the passive voice, and most readers prefer it. But in some academic fields, especially the sciences, authors use a stilted and awkward style that replaces clear concise sentences like, "We performed the experiment," with circumlocutions like "The experiment was performed."

    Asked why they write like that, many scientists admit that they don't like it, but they are under the impression that journals require it.

    They are wrong. Of the journals that have style guides, the vast majority explictly ask authors to write in the ACTIVE VOICE.*

     – Sjoerd C. de Vries Feb 09 '14 at 16:02
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    From: The Passive Voice is a Hoax! by Allen Downey. – Sjoerd C. de Vries Feb 09 '14 at 16:03
  • I'd like to add that not only journal style guides advocate a more personal style of writing, but that a long list of academic style guides (like the Chicago manual of style) do the same. Still, the misunderstanding that scientific writing should be impersonal and dry persists. – Sjoerd C. de Vries Feb 09 '14 at 16:09
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    Maybe I should have a look at new academic style guides. Is the Chicago manual of style the one you most recommend? What about european publications? – Stella Feb 09 '14 at 16:14
  • Actually, this advice is far from new. When I started to write my first article almost 25 years ago I consulted quite a few guides and found them to be unanimous there. Since then, I have been mostly using the APA publication manual, as that was the most appropriate for my research area. I have no real experience with European style guides, though I recall thumbing through the Oxford style guide. – Sjoerd C. de Vries Feb 09 '14 at 21:11
  • Thank you. I'll get the Oxford style guide. – Stella Feb 10 '14 at 08:17
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    This is irony, right? You are using the construction yourself "if we want to seem rigorous" – Zane Feb 11 '14 at 11:19
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Agree with all others about the value of friendliness in math education when it doesn't reduce precision. But in this particular case you could write a little more directly:

"Given a point P∈X we can define a residue map resP:ΩK(X)→k as..."

Still has the "we" concept, just ditch the verb "to have" and go straight to "define".

Dee Dub
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    I was assuming the definition, and just referencing where someone can look it up in case. However, there certainly are ways that I could restructure the whole thing to varying degrees. Indeed, I was once told that if you have to change a sentence, you should start the entire paragraph again, and that would certainly lead to different phrasing – Joe Tait Feb 09 '14 at 17:46
  • Ah, I didn't quite grasp the larger context. To be honest, I grew up hearing teachers use the "we have" preface to a lot of facts and coming at it from the 'less is more' ethic is a bit of a rebellion on my part – Dee Dub Feb 09 '14 at 21:23