prepositions - Why do the titles of scholarly works sometimes begin with the word "on"?


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).



Answer



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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