Q. A friend of John or a friend of John’s? I’ve heard that both are correct. A friend tossed the famous ambiguity at me this way: “A student of Einstein.” Unless it’s Einstein’s, then it might be taken to mean a student who is working on Einstein.
A. It is best, and, what is more, perfectly idiomatic, to use the double genitive when “one of So-and-so’s” is what you have in mind:
a student of his (that is, one of his students)
a student of Einstein’s (that is, one of Einstein’s students)
Then you have the liberty of writing “a student of Einstein” to mean by contrast either someone who is working on the great theoretical physicist as a scholarly subject or, more broadly, someone who is a close observer of Einstein and his work.
Fowler’s notes in its third edition that such phrases as “a student of his” are illogical—one of the “freaks of idiom” (pp. 542–43). In any case, your friend’s “student of Einstein” example is an excellent refutation of those who would avoid the apostrophe s at all costs.