It would be interesting to know what sets of numbers do not follow Benford's law.
Check Knuth's discussion of it in "The Art of Computer Programming, section 4.2.4 where he talks about the distribution of floating point numbers. Benford's research took numbers from 20299 different sources. Additionally, the phenomenon is bolstered by noticing, in the pre-calculator days, that the front pages of logarithm books tended to be more worn than the back pages.
The whole discussion covers about four pages, and contains what I think of adequate mathematics demonstrating the point.
Check Knuth's discussion of it in "The Art of Computer Programming, section 4.2.4 where he talks about the distribution of floating point numbers. Benford's research took numbers from 20299 different sources. Additionally, the phenomenon is bolstered by noticing, in the pre-calculator days, that the front pages of logarithm books tended to be more worn than the back pages.
The whole discussion covers about four pages, and contains what I think of adequate mathematics demonstrating the point.