For example, one of the articles in [volume 183 issue 1 (January 2016) of *Annals of Mathematics*](http://annals.math.princeton.edu/2016/183-1) 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](https://en.wikipedia.org/wiki/File:Origin_of_Species_title_page.jpg) prints the "on" in relatively small letters, suggesting a certain disposability).