Are there non-trivial theorems about all finitely generated groups?

Abstract

We discuss several interpretations and potential counterexamples to the meta-mathematical question in the title of the paper, focussing on geometric group theory and probability on groups.

I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description, and perhaps I could never succeed in intelligibly doing so. But I know it when I see it, and the motion picture involved in this case is not that.
Jacobellis v. Ohio, 378 U.S., p. 197 (Stewart, J., concurring)