Talk:Mathematical jargon

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Articles for deletion This article was nominated for deletion on 23/2/2006. The result of the discussion was keep.

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[edit] Iff

Should "iff" be on this list? Isn't it a rigorous term, rather than jargon? And how is it pronounced in a lecture, anyway: I've only heard "if-and-only-if" spoken. - DavidWBrooks 20:30, 5 Oct 2004 (UTC)

Jargon does not necessarily imply that a term is less than rigorous. It's terminology that is used specifically within one field and would probably not be understood by those outside that field. "If and only if" does have a specialized meaning in mathematics. [[User:Aranel|Aranel ("Sarah")]] 23:46, 20 Oct 2004 (UTC)
Iff has two uses, imho. One is used in logic (and related fields, I suppose) to mean a binary function from a theory to a truth-value set
iff : Th x Th → {T,F}
and the other is used in arguments in any math paper or lecture. The meanings are the same, I think, but the uses are different. I think that Iff should be edited to reflect these two uses; right now it blends them. (Actually, I think Iff should only refer to the logical iff, with the other one being merged into Mathematical jargon, but that's part of another argument, which I'll make under a separate heading, below.) As for pronunciation, I, too, have only heard iff pronounced as if and only if is. —msh210 17:03, 9 Nov 2004 (UTC)
David Lewis (philosopher) used to pronounce it iffffffff (or so I've heard or read somewhere).
--dbtfztalk 19:59, 24 February 2006 (UTC)
I think i recall either professors or undergrad peers pronouncing it in a way that i would render as either "if-if" or "IFFif".
--Jerzy•t 17:49, 25 December 2006 (UTC)

[edit] Merging

It seems to me that most of the articles linked to from Mathematical jargon are very short. Not short enough to be stubs, perhaps, but short enough to be merged into here. Why not do that?

(An exception is Iff, but, as I wrote above, I think iff has two uses; the one can be merged into here, and Iff can be about the other.) —msh210 17:07, 9 Nov 2004 (UTC)

Necessary and sufficient is also a large-ish article in its own right. And some of these articles have many links from other articles which will be followed by readers who are unfamiliar with a particular jargon phrase. Redirecting these links to a general jargon article will make it more difficult to find the specific meaning of handwaving, for example. My vote is leave it as it is. Gandalf61 11:46, Nov 10, 2004 (UTC)
I agree - leave it as it is. In its current form it serves a valuable purpose for the casually curious reader, who hadn't even realized that mathematics *has* jargon. It gives them a very quick overview of the sort of ideas that fit into this category. I think it's a perfect example of a wikipedia "introduction article", presenting a concept that is rarely encountered in the outside world without bogging you down with detail. Readers who want more insight can easily follow the links - which will, I bet, expand over time. - DavidWBrooks 14:24, 10 Nov 2004 (UTC)

If we leave it as is, then why are we considering it a stub? It's a complete article, isn't it? —msh210 19:36, 15 Nov 2004 (UTC)

Stub notice? I don't see any stub notice!!! - DavidWBrooks


[edit] Obtain

Mathematicians use obtain for two things:

  • Getting a simplified expression from a complicated one:
    • By adding three and five we obtain eight.
    • By summing this expression over N, we obtain one-half.
  • Proving a theorem:
    • Applying Lemma 3, we obtain our result.

So I was going to add obtain to this list. But then it struck me: is this actually mathematical jargon, or is this just the usual meaning of obtain? That is, are these two uses of obtain just small variations on the dictionary definition of obtain, understandable to "outsiders", or are they real jargon? I'm not sure, so am not adding obtain to the list. What do y'all think? —msh210 17:21, 11 Nov 2004 (UTC)

I would say no. I think this entry should be for terms that are only used by mathematicians, or that are used by mathematicians in ways radically different than by normal human beings - er, I mean, than by the rest of us. I don't think "obtain" meets those criteria. - DavidWBrooks 21:39, 11 Nov 2004 (UTC)

What about meet, miss, and avoid (which mean, respectively, "intersect", "intersect in the empty set", and "intersect in the empty set")? Are these jargon? —msh210 00:44, 17 Nov 2004 (UTC)

Whoof ... that's the trouble with making rules; things always get complicated near the boundaries! You've got the same definitions for "miss" and "avoid" - is that correct? As you have written them, my personal opinion was that they do not rise to the level of "jargon," per se - they are more like tweaked versions of terminology found in the wild. But they're pretty close ... - DavidWBrooks 03:22, 17 Nov 2004 (UTC)
Hm. I've already added we to Mathematical jargon. Would you (DWB) say it doesn't belong either? (I think it does, unless the same use of we is found in most academic fields.) —msh210 19:14, 17 Nov 2004 (UTC)
Um, er, ah, I guess no, I don't think it is sufficient different from other fields - that is, using "we" to mean "one" in the non-specific-person sense - and therefore shouldn't be here. - DavidWBrooks 20:51, 17 Nov 2004 (UTC)
So we is used in other fields, you're saying? (I just don't know: I'm in math.) Or are you merely saying that, if it is, then it shouldn't be here?
If the former, then someone should remove we from this list, and also edit We#mathematics to be about academic fields in general, not just math(s). —msh210 18:25, 18 Nov 2004 (UTC)
It's an alternate to passive constructions. ("This result is obtained" vs. "we obtained this result".) I know that this is done in scientific contexts. I use it in non-scientific papers all the time, but I don't know if that is just because of my science training or because it is actually used in non-science fields. I would guess that's a general academic writing technique. -[[User:Aranel|Aranel ("Sarah")]] 19:55, 18 Nov 2004 (UTC)
"We obtained this result"? That's not what I referred to at We#mathematics. That's actually the first-person (unless I'm misunderstanding): the author(s) obtained the result in question. The "we" I mean is a real third-person, and is used primarily in the present tense (though sometimes in the future, the present perfect, the subjunctive, and perhaps others): "by adding three and five we obtain eight", "if we were to mod out by the action of G, we would of course have a simply connected space". —msh210 20:44, 18 Nov 2004 (UTC)
Excuse me. I was thinking of the wrong variation. What it is really comparable to is the use of the indefinite pronoun "one", which is, indeed, a sort of generic third person. Your example could as easily be written "by adding three and five, one obtains eight". I don't know about standard practice, but I use it all the time in non-mathematical writing. "If we examine the facts, we find that..." -[[User:Aranel|Aranel ("Sarah")]] 23:11, 18 Nov 2004 (UTC)
Do we (  :-)  ) have a consensus? Do you all agree with Aranel? —msh210 14:40, 21 Nov 2004 (UTC)
Yes, I agree. I have certainly encountered it in this usage in both technical and semi-popular scientific (even soft-science like psychology) works , so it's not mathematical enough (so to speak) for this article. - DavidWBrooks 19:16, 24 Nov 2004 (UTC)
Fine, I've removed 'we' here and edited We accordingly. —msh210 21:02, 24 Nov 2004 (UTC)

Someone just added smooth; is this jargon? It's just a word found in math, like plus or group. No? —msh210 14:18, 17 Mar 2005 (UTC)

[edit] In general

I'm not sure I agree with all that is said. But in any case it might warrant an article. Charles Matthews 12:02, 11 Apr 2005 (UTC)

An "In general" article would have no potential for becoming anything more than a dictionary definition.As such, it'll be tagged (rightfully imho) with {{move to Wiktionary}} and then {{vfd}}, merged back into here, and deleted or replaced with a redirect link. So don't bother. —msh210 03:39, 26 Apr 2005 (UTC)

[edit] wrt

this is not really specifically mathematical, is it? — MFH: Talk 08:27, 13 May 2005 (UTC)

I don't believe so. See WRT and Wikipedia:Votes for deletion/WRT. —msh210 18:19, 13 May 2005 (UTC)
well, currently this (math jargon) page says :
         *  wrt, with respect to
while wrt says:
         *  In mathematics, "With Respect To" ; see mathematical jargon.
and that's all (not very mathematical, neither useful, imho). But see my vote (at the end) of the voting list, with constructive suggestions. — MFH: Talk 18:58, 13 May 2005 (UTC)

[edit] Structural revision

I've given a new face to this page, since I found the old version to be sprawling, arbitrary, and rather ugly. I've simply divided the terms into categories and given a broad overview of each category. My next move will be to regularize the presentation of the page and add simple descriptions to each term. Finally, a few terms landed in "Miscellaneous" for a few reasons: LHS/RHS is seemingly none of the above categories, "transport of structure" is a term I've never heard and has no page to describe it, and "wrt" is hardly specific to mathematics. I think that the latter two ought to go, and if anyone could argue whether LHS/RHS belongs under Proof or Qualitative, or even Philosophical, it would be nice. Ryan Reich 00:29, 24 February 2006 (UTC)

Okay, well, I've given descriptions to everything but "Miscellaneous". Perhaps some of the dead links should be filled in, or removed if my description is thorough enough, and some unlinked terms may want their own pages. Conversely, I've tried to be as concise but authoritative as possible, so maybe a better route is to excise some of the specific pages. Pedantry is endless, and even if one can write a whole paragraph on the term, a single sentence might suffice. Ryan Reich 01:11, 24 February 2006 (UTC)

Wikipedia frowns on major edits to an article when there's an AFD discussion going on, since it confuses things, but your changes are so excellent that I don't think anybody will object. - DavidWBrooks 14:07, 24 February 2006 (UTC)
Not that almost anyone is objecting to the article at large, anyway. Thanks. Ryan Reich 14:17, 24 February 2006 (UTC)
Not sure what general opinion would be, but if you go by Wikipedia:Guide to deletion, then it positively encourages editing an article during an AfD discussion, simply recommending that significant edits should be noted on the article's talk page (it does prohibit blanking, renaming or redirecting and strongly discourages merging during AfD). But we can certainly agree on the excellent quality of Ryan's edits - keep up the good work ! Gandalf61 14:44, 24 February 2006 (UTC)
That's the trouble with having been on wikipedia too long - I learn things, then they go and get updated! I got yelled at for editing a then-VFD article ... but then again, that was 2003. - DavidWBrooks 16:05, 24 February 2006 (UTC)

[edit] In general

Yesterday I made a few changes to the page, one of which was to split up "in general" so that, rather than appearing as a single, large entry in one category, it is now three entries in three categories. Depending on your perspective on this page this is either obviously right or obviously wrong. It makes it harder to come in looking for a specific phrase and learn everything about it in one place; on the other hand, my opinion is that people will come here having seen a phrase in a particular context and go straight to the correct place. They have to do that to find any of the terms, anyway, in the new layout.

I feel that splitting up this term is reasonable on those grounds, then. I also think that it's reasonable on the grounds that the nature of mathematical jargon is to overload common words, in this case "general", rather to make up new ones, so that the context is particularly important; thus, the same phrase should appear multiple times if it's used in multiple contexts. It also keeps the entries short; if it's not already clear from the way I did things at the beginning, I favor definitions which are as consise as possible: every term either has its own page or isn't worth having its own page because it's so simple. Finally, there are probably only one or two terms that have their hands in every pot like this, so it won't happen much.

Obviously I can do whatever I want and if people don't like it they can revert the changes; however, since this is a reasonably blatant change and also a little odd, I thought I'd explain it and ask for opinions. Ryan Reich 00:19, 4 March 2006 (UTC)

I added an introductory phrase to warn of such multiple uses. Its application is less than clear on my screen, where it is separated from the actual sections by a wide area of white space. One obvious solution to this is to move the TOC up so that the italicized warning falls immediately above the first section.
I prefer my edit to Scaife's, but either is preferable to the default. Septentrionalis 16:55, 5 March 2006 (UTC)
Ha! Wikipedia has a code to place the TOC directly, which is sort of hidden in the style guide. I've put it where, I think, everyone really wanted it to be. Ryan Reich 17:21, 5 March 2006 (UTC)

[edit] some more

Somewhat related to the non-techniques, there are the invalid techniques, such as

  • Proof by intimidation (As any idiot can see,...)
  • Proof by lack of imagination
  • Proof by example
  • Proof by picture

Googling such terms reveals many others. Btyner 17:24, 5 September 2006 (UTC)

These all remind me of a joke poster I saw up around school a year or two ago, which had a whole list of these together with suggested methods. They're also self-explanatory and not specific to mathematics, really. Some of them (especially "lack of imagination") could have a case made for being put in logical fallacies, though. Actually, that one already is. Ryan Reich 22:25, 6 September 2006 (UTC)

[edit] frontier question

How about frontier question?—msh210℠ 16:58, 7 December 2006 (UTC)

How about it? I don't know the term but others might. Ryan Reich 18:49, 7 December 2006 (UTC)

[edit] Proof non-techniques

I'm sorry, I don't see why this is more accurate. Can you even explain what this term (i.e. non-technique) means? The phrase furthermore strikes me as being excessively cute. .--CSTAR 18:56, 7 December 2006 (UTC)

I also don't see why logical fallacies need to be mentioned here. --CSTAR 19:06, 7 December 2006 (UTC)
As for the fallacies, since someone thought it worth mentioning incorrectly it is at least worth mentioning correctly. And now that I think about it, there is a point to be made that these terms are not logical fallacies, but simply bad form. As for the terminology, I was first of all trying to write concise, efficient headings and this is the best I could do to convey that these terms: a) appear in proofs; b) purport to contribute to the proof; and c) in fact detract from it, or at least fail to constitute proper technique. Hence, they are non-techniques. Writing "Non proof techniques" is ugly, "Non-proof techniques" is just wrong since it suggests that they are techniques to do this imaginary "non-proof" thing, and omitting the term "technique" fails to make the connection with the previous section, which I think is important. Your suggestion, "Other phrases appearing in proofs", is far too general since it doesn't mention that these are phrases (or strategies) that do not belong in proofs. And yes, I wanted it to be sort of cute. Ryan Reich 18:32, 8 December 2006 (UTC)
They do not belong in proofs? The fact is they are in proofs appearing in papers, books as well as in the lecture hall. To say they do not belong in proofs seems like a normative judgement about what constitutes a proof, which does not belong here, in my opinion. We are here, I believe not talking about proofs developed within some formal system. --CSTAR 19:35, 8 December 2006 (UTC)
Yes, they don't belong in formal proofs, but I chose the titles to reflect the reason I think underlies this, not the fact itself. The question is still about technique: what differentiates these terms from the ones in "Proof techniques" is that those are methods of rigorous, albeit shorthanded argument, and these are at best guidelines to such an argument. "WLOG" is to "clearly" as a model ship is to the box of parts with a picture on the cover. That's the only distinction I'm trying to make: even someone who puts "clearly" in a proof knows he is being terribly informal, however accepted the proof might be as a result of the fact that people are not, after all, machines, and have the imagination to build the ship. I'm not trying to make a judgement about what a proof is with my title; I'm just separating terms which are prescriptive from those which are descriptive. However, while I was writing this I thought of a solution. Let's call "Proofs and proof techniques" instead "Proofs and rigorous proof techniques", and the current "Proof non-techniques" instead "Informal proof technqiues". We might want to call "Informalities" something like "Descriptive informalities" to distinguish it from informalities of argument, in this case. Ryan Reich 14:49, 9 December 2006 (UTC)
Though I think your suggestion is an improvement, I think there is still a problem here which results from the following: a mathematical proof (in a lecture, or paper or book) isn't necessarily a sequence of inferences (say in a sequent calculus) or even an approximation to such an object, but is itself a higher order object -- in part, a recipe for constructing such a proof object or even more abstractly an argument why such a proof object exists (which could legimately include appeals to other principles, assumptions about the interlocutor's experience, even pictures). That is why there is all this jargon. The view of proof that is suggested here is too narrow in my opinion and does not adequately convey the flavor of mathematical communication.--CSTAR 15:23, 9 December 2006 (UTC)
Going by what you describe, it would seem there is no problem with calling them "informal proof techniques", since they are indeed tools for the informal proof-like communication that you mention. Or are you saying that we should just put all the proof-related jargon into a single subsection? Ryan Reich 15:58, 9 December 2006 (UTC)
No I'm satisfied with the distinction you make. I'm just pointing out that an informal proof should not be thought of as a bad proof.--CSTAR 16:02, 9 December 2006 (UTC)
Oh, okay. I'll make the changes, then. Ryan Reich 16:28, 9 December 2006 (UTC)

[edit] as desired

I've seen "as desired" used in place of QED in some papers recently - though, more informally. Anyone else, or does anyone think it's common enough to include? Tparameter (talk) 03:57, 14 December 2007 (UTC)

But is it jargon? Ryan Reich (talk) 06:14, 14 December 2007 (UTC)
Seems to me that it is. It means, QED - but, that isn't what it means in regular use. It really only means QED in the context of a mathematical paper. Tparameter (talk) 15:11, 14 December 2007 (UTC)
Several examples can be found in proofs in Wikipedia articles. In some cases you can only reconstruct that the proof author set out to demonstrate the truth of a proposition by their use of "as desired", as for the conclusion ν0 = 0 in the proof of the Radon–Nikodym theorem for finite measures. This use of "as desired" appears (according to my own, very original, research) to be an outgrowth of a more normal use in proofs of, specifically, the existence of some object having some property. If the proof proceeds by constructing an object that is to bear witness to the claimed existence, the proof will culminate in a demonstration that the constructed object indeed has the desired property – the raison d'être for its construction –, which then can be phrased as "..., and so OBJECT has PROPERTY, as desired". Other uses, like the one noticed above for ν0 = 0, appear to mimic the words without comprehension and are in some cases (see, e.g., Proof of Szemerédi–Trotter theorem (second formulation)) indistinguishable in meaning from Q.E.D. I tend to agree that this is jargon, as I can't think of (nor find by Googling) any analogous use of this phrase outside the context of proofs.  --Lambiam 15:41, 14 December 2007 (UTC)
But I think it is used with its natural meaning here. My impression of "as desired" is that people use it when they are trying to write a chattier sort of proof, and this phrase, unlike the opaque Latin QED, blends with the ambient text. The form is:
Theorem: 2 - 1 = 1
Proof: By the associative law, 2 - 1 = (1 + 1) - 1 = 1 + (1 - 1) = 1 + 0 = 1, as desired.
(obviously this depends on your definitions, etc. etc.) If I may generalize, it looks like "as desired" means "this expression is exactly the logical statement claimed in the theorem". However, I have previously been wrong-by-consensus about just this point, so perhaps I'm just a mathematician rationalizing, in the name of more "accessible" writing, his profession's increasingly jargonistic use of a "natural" phrase to mean something that is actually quite specialized. Ryan Reich (talk) 19:27, 14 December 2007 (UTC)
I only asked in the first place because it seems exactly like, "clearly", or "can easily be shown", which are used to mean, "clearly" and "can easily be shown", respectively. They're used to mean exactly what they say, but sort of in a mathematical context. This seems to be the case with "as desired". I'd say they're analogous. This one, "as desired", is like the little box - it's kind of there to say, "I'm finished." Tparameter (talk) 21:57, 14 December 2007 (UTC)

[edit] quality of the text

I am not sure if that kind of comment is regarded as bad wikipedia-style (if so please feel free to delete it) but i just wanted to mention that for me the article was very insightful and valuable. It is not easy to find that kind of information in a standard introductionary text book about mathmatics although I think it would definitely belong there. Just wanted to thank the editors of this page for their work, highly appreciated. —Preceding unsigned comment added by 130.88.179.123 (talk) 23:28, 3 June 2008 (UTC)

Saying "thank you" is never bad style ! Glad you found the page useful. Gandalf61 (talk) 08:41, 4 June 2008 (UTC)