For example, one of the articles in volume 183 issue 1 (January 2016) of Annals of Mathematics is titled "On the fibration method for zero-cycles and rational points". Why not just call it "The fibration method for zero-cycles and rational points"? Is there any difference in meaning? Conversely, there's an article in the same issue titled "Defining ℤ in ℚ", which could be titled "On defining ℤ in ℚ" with no apparent change in meaning.

My perception is that the leading "on" used to be more common (e.g., the very long complete title of Darwin's Origin of Species actually begins "On the Origin of Species"; but even here, the 1859 title page prints the "on" in relatively small letters, suggesting a certain disposability).

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    I'll bet that the real reason is because all the medieval scholarly texts had titles in Latin that began "De ...." to mean "about" or "regarding" or "on the matter of". – tchrist Jul 24 '17 at 17:34
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    And it goes back much further than that. Cicero wrote De officiis and Lucretius wrote De rerum natura in the downward counting years @tchrist – Unrelated Jul 24 '17 at 19:01
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    One of the more celebrated instances of the use of "on" in this way was the 1859 publication On Liberty, by John Stuart Mill. In that and other examples, I believe the "on" is important, as an abbreviation for "(A dissertation) on (the subject of ) liberty". It would have been out of order and presumptuous to call it simply "Liberty". The title, as it stands, recognises that it is a considered statement about the matter. Similarly with Darwin's "(A treatise/observations) on the origin of species". – WS2 Jul 24 '17 at 20:13
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    A title without the "on" implies that it is a comprehensive treatment of the title's subject matter. "On" implies that it is discussion related to the subject. Perhaps it's a matter of managing expectations. – fixer1234 Jul 24 '17 at 22:36
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    Echo @fixer1234. "The Origin of Species" carries the danger of being perceived as the definitive word about how species came to be -- the whole subject, with absolute certainty. On the other hand, "On the Origin of Species" would only claim to be part of the discourse on the subject, and allows that some parts may be speculative. – TripeHound Jul 25 '17 at 6:52
up vote 69 down vote accepted

This naming convention extends back to ancient times.

  • Many of Aristotle's (384–322 BC) works are titled On ---
  • Lucretius (99 - 55 BC) wrote De rerum natura or On the Nature of Things
  • In 44 BC Cicero wrote De officiis, or On Obligation

I am not certain whether these writers titled their own works. I'm vaguely remembering that these titles are simply how subsequent scholars referred to the works, but I haven't been able to verify this.

Scholars carried this convention forward. Montaigne, the Renaissance writer and father of the essay, titled many of his essays in this way.

When an author (or whoever is naming the article) uses On in their titles today they are joining this academic lineage, whether consciously or unconsciously. It may be an attempt to seem scholarly.

As for a difference in meaning,

I personally read a difference if the preposition is present or missing, though not enough to cause any real confusion. The On indicates that the writer is commenting on a known concept; the lack indicates they will be announcing a new one.

  • "On the fibration method for zero-cycles and rational points" would mean that we already know about these fibration methods; the writer is adding to the discourse.
  • "The fibration method for zero-cycles and rational points" would mean that the writer is announcing the discovery of these methods.
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    @Wildcard While you may choose which form of title to use, I do agree with Unrelated in that the two have different meanings. You can choose a title that implies you are adding to discourse about an existing topic, or choose a title implying that you have a new idea/discovery. – Doc Jul 25 '17 at 0:50
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    @Wildcard (and Doc) I think there's also an undercurrent of humility in choosing the "on ..." titles; such authors are self-deprecating their new ideas as mere additions to existing discourse, and acknowledging that the reader may have known of these ideas from elsewhere. – muru Jul 25 '17 at 2:39
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    @muru, exactly; that's actually what I was trying to say. :) In other words, nearly every paper adds some new idea in order to be worth publishing in the first place, but it hardly speaks of scholarly humility to charge in and name your new techniques after yourself. It's hard to imagine Turing naming Turing Machines, or him being taken seriously if he did. At least in the world of academia. – Wildcard Jul 25 '17 at 3:08
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    @Wildcard I think we are in agreement. I don't believe that the lack or presence of a preposition is any indicator of how significant, seminal or groundbreaking the text is, but I do think it expresses the role of the document differently – Unrelated Jul 25 '17 at 6:01
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    Regarding your last paragraph, I'm reminded of a book I read a few years ago called "Denying Science", which got me a lot of weird looks while I was reading it. It was actually a book discussing the denial of science. I always thought "On Denying Science" would have been a more accurate title. – Carcigenicate Jul 25 '17 at 14:46

The phenomenon appears to be a result of translation that dates back to early Greek writings. Early works by Greek writers would introduce a topic with Περὶ, meaning about, which Latin scholars translated to De, and were then translated to English as On. The trend of starting essays with On then stuck with English writers, who adopted it in their own titling.

Observation suggests that Περὶ was used to introduce an examination of a subject, such as medicine, grammar, sleep, dreams, etc. Titles by Aristotle that lack this introductory word tend to be those focused on more original concepts, such as Metaphysics (Greek: τὰ μετὰ τὰ φυσικά).

On who titled the works

It's not clear to me whether Aristotle provided titles for his own works, or if they were cataloged by other Greek scholars, particularly the scholars at the Library of Alexandria, where treatises were collected. Several sources, including Encyclopedia Britannica, seem to indicate that the titles were added by Alexandrian scholars, and as such the original titles would have been in Greek, even if they weren't named by Aristotle himself.*

This article from Standford indicates that much of the editorial work related to Aristotle's writings might have been done by Andronicus of Rhodes. Credit to Matt from History.SE for that finding.

Notably, translators used their discretion in applying the original naming to their well-known English names. For example, Aristotle's Poetics is seldom translated in English as On Poetics, though the original Greek is still Περὶ ποιητικῆς, and the Latin is De Poetica.

Another classic example from Aristotle:

  • Greek: Περὶ οὐρανοῦ, 350 BC // Latin: De Caelo // English: On the Heavens (Aristotle)

Aristotle was not the first Greek writer to use this style. Writings by Hippocrates have similar titles in Greek.

  • Greek: Περὶ Ἀρχαίας Ἰατρικῆς ?450-400BC // English: On Ancient Medicine (Hippocrates)

An example of an English writer adopting the style:

  • On Liberty, 1859, John Stewart Mill [credit to WS2 in the comments for pointing to this example]

Additional examples from the Aristotle canon:

  • Greek: Περὶ Ψυχῆς // Latin: De Anima // English: On the soul

  • Greek: Περὶ αἰσθήσεως καὶ αἰσθητῶν // Latin: De sensu et sensibilibus // English: On Sense and the Sensible

  • Greek: Περὶ μνήμης καὶ ἀναμνήσεως // Latin: De memoria et reminiscentia // English: On Memory

*Seeking some added clarity on the origin of the titles of the works, I've posted a question on the History Stack Exchange: Who titled the works of Aristotle?

  • Do you happen to know what the presence or absence of "Περὶ" signified for the ancient writers? – Kodiologist Jul 24 '17 at 22:16
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    @Kodiologist Based on observation, it seems like a common introduction to an examination of a well-established subject, as opposed to introducing a new concept (I added a small edit to my answer on this). In that sense, the end-note on Unrelated's post seems accurate to me. – RaceYouAnytime Jul 24 '17 at 22:32
  • I know next to nothing about Latin: Why would Latin 'de' be translated to English 'on', instead of to 'of' (as in 'discussion/explanation/investigation of') - or indeed to 'about'? – Jeremy Jul 26 '17 at 12:37
  • @Jeremy Latin de is one of many prepositions that is a variation on from, in this case, down from or away from with verbs that involve some form of taking. Since when we have something “about” a topic, you “take away” new knowledge on that topic, de was often used to mean on, about, concerning, and similar (in fact, it has these meanings more often than its from meanings). I cannot tell you about the early translations of various Latin writings titled with de and why on was chosen and standardized as the translation, however, so this is only half an answer. – KRyan Jul 26 '17 at 13:07
  • Side note, renders terribly (accent way above and to the right of the downstroke) on my machine in the answer, but not in comments. – KRyan Jul 26 '17 at 13:09

While all the other answers are very well thought out, let me point out a case where "On" keeps a title from being misleading.

The paper

On large subsets of 𝔽qn with no three-term arithmetic progression,

gives an upper bound on how large such subsets can be. In other words, it shows that no extremely large subsets exist. If this paper had been titled Large subsets ..., it would be misleading, as it might give the impression that it actually constructs large subsets with no three-term arithmetic progression.

  • Great example ! – Georges Elencwajg Jul 25 '17 at 21:15
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    It seems to me that a better title would have been An upper bound on subsets of F… – 200_success Jul 27 '17 at 9:05
  • @200_success: It would actually have had to be titled An upper bound on the size of subsets ...; While I don't want to make a judgment on which title is better, On ... is more succinct. – Peter Shor Jul 27 '17 at 13:39

Contra some previous posters I would submit that there is a semantic distinction in using the prepostion 'on' in the title, and that it concerns not the subject of said text, so much as what kind of treatment of the subject, the prospective reader may expect.

Suppose the title was ' The fibration method for zero-cycles and rational points'. And suppose that was all we knew about the text. What could one reasonably expect? An introduction to said method; terms will be properly introduced and defined; there are likely to be exercises, and so on. Also, introductory texts may exist at various levels; from a high school textbook to a compendium for professionals specializing in other fields; but as novice readers at whatever level of proficiency, we may reasonably expect that the authors aim to faithfully represent the field, including all sides of what controversies may reside in it, and that the work therefore aims to be thorough and authoritative at its intended level.

But if the title is 'On the fibration method...'; the reasonable expectation is that this is part of an ongoing inquiry, submitted into an ongoing discourse on said topic. Prior knowledge or at least some familiarity with the subject is going to be presupposed, and the authors may, for all we know, have some strong opinions on the subject, or the direction the field is taking, that, depending on one's own view, may inform or bias their approach. But by that little 'on', they are also telling us that they neither claim any exhaustive treatment of the subject, nor any authority of the text itself, beyond that which the community may eventually give it.

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    +1. You've nicely further developed the conjecture at the end of my own answer. I must admit I am curious, though, how you came to this site and decided that this was the question that made you make an account. Welcome to EL&U! Glad to have you – Unrelated Jul 26 '17 at 16:11
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    Why, thanks! I was looking for something totally unrelated when I saw this, and figured, 'hey, I know that!' – JValgreen Jul 27 '17 at 16:58

It appears to be due to the stylistic preference of the author.

When you see a title like that, you can think of it as meaning "On the subject of ...."

So using your example, you could think of it as:

On the subject of fibration method for zero-cycle and rational points.

Also, you are correct, you could omit the "on" and the subject of the paper would still be clear to the reader.

Alternatively, you could be verbose and expand the title to something ridiculous like "This paper is on the subject of fibration method for zero-cycle and rational points."

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    I agree with what you say, but you doesn't seem to answer the question, except perhaps to suggest that there is no difference in meaning and the choice is made purely arbitrarily. – Kodiologist Jul 24 '17 at 18:57
  • You are correct. I was trying to explain that it is a style preference because the meanings are the same. I would say its based on the preferred style of the author, as opposed to purely arbitrary. – Devil07 Jul 24 '17 at 19:00

I always thought it was to eliminate repetition.

Let's say all books were titled as (for example) 'A Book on Quantum Mathematics', or 'a Book on The Politics of Ancient Rome'. Books were not originally written for enjoyable fiction with fun titles to catch your eye, they were notes, records, documents for learning (text books) on topics of government and history.

Would you really keep calling books 'A Book on XXX'? It is obviously a book, so wouldn't society eventually just call it 'on TOPIC'? It seems to me that they even kept the 'on' in lower case, so it was not an important part of the title of that there would be an implied precursor to the 'on' which everyone knew so it was left off to save space and repetition.

In my mind this fits well with the OP comment of:

My perception is that the leading "on" used to be more common (e.g., the very long complete title of Darwin's Origin of Species actually begins "On the Origin of Species"; but even here, the 1859 title page prints the "on" in relatively small letters, suggesting a certain disposability).

A paper, article, essay, book, etc. so titled is the author's exposition on its subject. Beginning a title with "On", i.e. "On this particular subject", implies the title is an abbreviation of a phrase such as "This is the author's point of view/breadth of knowledge on this particular subject." It's actually a personal and even humble touch, a reminder that the paper is written by its human author(s) and therefore subject to the error of their limitations.

Looking at it another way, consider an interview where a single question covering multiple subjects is asked. The interviewee might respond by addressing one subject at a time, as such: "On the subject of [subject A], here's what I think: ..."

In short this is just a style of presenting the subject of the titled work as if it was being presented verbally or even as if it was being discussed in conversation as a person's point of view.

To me it is a means to not claim that this the definitive work on a subject. To be a definitive work requires peer acceptance and time to stand the rigours of analysis.

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    Unfortunately a text usually doesn't have that status when it is named – Unrelated Jul 25 '17 at 16:03
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    So you think (say) Isaac Newton was overly presumptuous in naming one of his books Opticks, and he should have called it On Opticks, and waited for a committee of scholars to rename it Opticks 100 years later? – Peter Shor Jul 25 '17 at 16:48
  • @PeterShor I think you're drawing an illogical conclusion from this answer: that all works not named "On [subject]" claim to be the definitive work on their subject. This answer only suggests that adding the word "On" clarifies that the work is not intended to be definitive. A work not intended to be definitive could just as easily not be named "On [subject]" and this answer would still stand. Also a work named "On [subject]" could happen to become definitive, and this answer would still stand. – talrnu Jul 26 '17 at 20:11
  • I think "comprehensive" would be a better word than "definitive" here. The title "On X" means "this paper adds something to the total human knowledge about X," not "this paper contains everything that humans know about X". But the additional knowledge may be "definitive" even if it is a small part of the total. – alephzero Jul 26 '17 at 23:44

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