Chokhmei Umoth HaOlam are [[Hagarim]] who have ''not'' taken the [[Oath Brith]] [[Tevilah]] even if they send offerings as Augustus Caesar did for example.
The terms indicate non-Jews who have taken upon themselves the observance of [[Noahide Law]] for their own rational reasons. Maimonides seems to imply that ''Chochmei Umos HaOlam'' do not have a portion in the world to come, although he doesn't actual actually say that. The implication therefore is that they will be judged according to their merits.
Compare this with [[Tzadikei Umos HaOlam]] and [[Chasidei Umos HaOlam]] who observe the [[seven laws]] because they were revealed through [[Moshe Rabbenu]] as explained by Jewish tradition.
