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).