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I came across this question on Academia.SE and I noticed its first comment. The question points to an article in the New Yorker magazine written by Sylvia Nasar and David Gruber, both of whom seem to be native English speakers. The comment says:

I really dislike how the authors of that article keep writing "the Poincaré" for "the Poincaré conjecture".

The comment has gained some upvotes, but I really don't get it. What exactly is wrong with that phrase? Is it the inappropriate use of "the"? I am not a native English speaker, but from what I have read/heard so far, I think we should use "the" in such cases and it wouldn't sound so annoying.

I hope this question is on topic for this site, because I thought it was about English language usage, and I appreciate any feedback.

  • so your beef is: abbreviating 'the Poincare conjecture' to the Poincare or even just Poincare? – lbf Mar 25 '18 at 13:08
  • and that in doing so it demeans the man, the field of study? – lbf Mar 25 '18 at 13:37
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    Was the downvote really necessary? – polfosol ఠ_ఠ Mar 25 '18 at 14:02
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    The title and body do not match. The title asks whether a certain subset within the phrase "the Poincaré conjecture" is correct, while the title asks whether substituting the subset in place of the entire phrase is correct. Is this a typo or a symptom of your confusion? – jwodder Mar 25 '18 at 21:28
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    It's a symptom of my confusion apparently @jwodder – polfosol ఠ_ఠ Mar 26 '18 at 0:53
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Using the surname of a mathematician as a metonym for his famous conjecture seems as counterintuitive as saying Christian fundamentalists don't believe in the Darwin or that some new discovery in astronomical physics substantiates the Einstein.

No one seems to object, however, if someone admires “the Dior she wore to the Golden Globes” or wonders how many Rembrandts might have been destroyed in World War II. A proper name as a metonym for something created by that person, then, is not in itself unusual, but seems so in this context.

In mathematics jargon — which I assume these authors are employing to imply their membership in this discourse community — the name Poincaré, with or without the accent aigu, is being used by some writers as a technical term for Poincaré’s conjecture and associated terms such as map, plot, or surface, as Peter Shor has so kindly pointed out. Once the writer establishes which particular one is meant, as the New Yorker article does with conjecture several times, then it becomes the Poincaré just like the Dior at the Golden Globes.

A simple Google search for “the Poincaré is” yielded so many hits for a variety of omitted nouns I didn’t bother to count them or search using another verb. Such a search cannot, of course, determine how many mathematicians use such a construction as opposed to those who don't or who object to it. All we can know from the posted question is two writers for the New Yorker and some dude grousing about it on the internet.

Ultimately, this is a prescriptive-descriptive conflict to be decided by the discourse community that uses the construction.

A few samples show both the variety of contexts and the almost pronomial use of Poincaré:

The Poincare is a central question in topology, the study of the geometrical properties of objects that do not change when they are stretched, distorted or shrunk. [Poincaré conjecture] —BBC news report.

Although the Poincaré is useful visual pattern for HRV, it has limitations. [Poincaré plot] — International Journal of Medical, Health, Biomedical, Bioengineering and Pharmaceutical Engineering Vol:9, No:9, 2015.

If the Poincaré is a finite set of points, then the corresponding system motion is periodic motion state. [Poincaré map] — Kehui Sun, Chaotic Secure Communication, DeGruyter 2015.

The Poincare is just what he said: the group of symmetries of flat spacetime. [Poincaré group] —Physics Forum post to question “What is a Poincaré group?”

In the proof of (ii) we use the Poincaré map and degree theory. The following lemma guarantees that the Poincaré is well defined. [Poincaré map] — Journal of Mathematical Analysis and Applications 185(1994), 480.

But the implication generally does not go the other way, and since the Poincaré is true there was no special number. [Poincaré conjecture] — "Gödel’s Lost Letter and P=NP,” Blog by Prof. Dick Lipton (Georgia Tech) and Prof. Ken Regan (SUNY Buffalo).

In this paper we discuss the natural candidate for the one dimensional free Poincaré inequality... As in the classical case the Poincaré is implied by the others. — Trans. Amer. Math. Soc. 365 (2013), 4811-4849.

From peer-reviewed journals and monographs to blogs and forum posts, some writers, having specified unambiguously which Poincaré x is under discussion, then employ the Poincaré for subsequent mentions. While this metonymic usage may be the mathematician’s version of the split infinitive or sentence adverb, the variety of genre and the status of the authors within the discourse group — seriously, are you going to tell a tenured professor at Georgia Tech how to write? — suggest that, regardless of one's personal opinion, the usage will not likely disappear any time soon.

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    A minor nitpick: in mathematics and dynamical systems, we also have the Poincaré surface or Poincaré map, which is sometimes simply referred to as the Poincaré. – polfosol ఠ_ఠ Mar 25 '18 at 13:56
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    In fact, only your first and sixth citation refer to the Poincaré conjecture. Others refer to the Poincaré map, the Poincaré plot, the Poincaré group. And looking in Google, "the Poincaré" can also mean the Poincaré inequality, the Poincaré algebra, and probably also the Poincaré equation. – Peter Shor Mar 25 '18 at 14:24
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    @KarlG: first, I think it is probably relatively uncommon for a mathematician to say "the Poincaré" rather than "the Poincaré conjecture" (although it's clear that sometimes they do). Second, with only a little searching, I found "the Euler" used for "the Euler path", "the Euler constant", "the Euler angle", and "the Euler scheme". All of these documents seem to use the full term the first time they use it, and only use "the Poincaré" or "the Euler" afterwards. – Peter Shor Mar 25 '18 at 14:47
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    One more nitpick: the Poincaré group, the Poincaré inequality, etc., have nothing to do with the Poincaré conjecture (other than both having been introduced by Henri Poincaré). – Peter Shor Mar 25 '18 at 18:28
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    This answer is a good example of confusion caused by the sloppy language. It's not, in my opinion, a good answer. – anatolyg Mar 26 '18 at 13:14
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I think the point is not that Nasar and Gruber are native speakers of English. Instead the point is that they are not mathematicians, and that mathematicians would usually not call the Poincaré conjecture merely "the Poincaré".

Now an art lover might indeed call the Guggenheim museum simply "the Guggenheim". So this question is not about English language and usage so much as about customary ways of speaking.

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    Is understanding of the English language driven by theoretical (academic) precision, vernacular (customary) usage or both? – DJohnson Mar 25 '18 at 16:42
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    @GEdgar What is the difference between "usage" and "customary ways of speaking"? – iconoclast Mar 25 '18 at 23:56
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    As a mathematician (who also commented on the post in question), this is the correct answer to me. As comments on Karl's answer establish, Poincare's name is attached to a lot of substantial or ubiquitous concepts in mathematics, as are many of the great mathematicians of old (and a few living ones). There is no particular one to unambiguously refer to. "The Guggenheim" is relatively clear, as there is really only one thing in the world that could be the Guggenheim (contrast with "a Guggenheim"). But there are many important things that could be "the" Poincare. – zibadawa timmy Mar 26 '18 at 7:58
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    @zibadawatimmy Indeed this is a better answer. I seem to remember a question in Math SE a while ago asking about all the different things named after Gauss. I can't find it right now, but imagine referring to "that Gauss thing". – uhoh Mar 26 '18 at 18:39
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What does the Poincaré mean? It's a conjecture, so call it a conjecture. The comment is not about the use of the but about leaving out the head noun in a compound. You don't refers to the toy store as the toy, because it would make it completely unclear what you're talking about.

The lazy assumption that readers will assume that the Poincaré refers to a conjecture, instead of, say, a nice restaurant down the street, seems to have caused the dislike in the comment.

  • agree with your answer. another: Magna Carta Libertatum (Medieval Latin for "the Great Charter of the Liberties") > Magna Charta > Magna Carta > Great Charter – lbf Mar 25 '18 at 13:41
  • Oops. Looks like a naive misunderstanding by me. Thanks – polfosol ఠ_ఠ Mar 25 '18 at 13:41
  • I guess "there goes THE king" will never be "there goes da dude with the crown'? – lbf Mar 25 '18 at 13:45
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This is an interesting post! Besides habits and customs within a certain social sphere, I think that there are at least two specific aspects that come into play here:

(1) Ambiguity vs. clarity: Poincare, Einstein, etc., have made so many contributions that the meaning of "the Poincare" or "the Einstein" simply is not clear. (This point has been made above already).

(2) Concrete thing or physical object vs. abstract idea or concept: Calling the paintings of Rembrandt, which are all unique and concrete physical objects, "Rembrandts", seems to work better than calling Mozart's music pieces (which are not tied to a certain physical representation or concrete object) "Mozarts".

In the case of "the Guggenheim" (museum), both conditions are fulfilled, and seem to foster the perhaps unusual use of the term as a metonym: Firstly, the expression is unambiguous, since there is only one Guggenheim museum in town, i.e., per social sphere of the (imagined) speaker. Secondly, "the Guggenheim" also refers to a unique physical object, namely the building itself.

On the other hand, calling the Guggenheim foundation, say, "the Guggenheim" does not seem to work as well, at least not as long as we try to refer to the abstract entity which the foundation constitutes. It only seems more common when we refer to the physical building in which the foundation is located. This presumably would also support our above observation (2) on physical objects vs. abstract concepts.

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