So, I'm planning to introduce this group, the Mystic Fraternity of Samos (see Mysteries Revised) in my campaign, but I have a question. It's a generel question, really, but it comes up here.
To become the first degree in this mystery, the character need to have Artes Liberales (Mathematics) on 3. The next degree requires, among other things, Artes Liberales (Geometry) of 4. But how does this work with the specializations? One can't have two specializations, right? How should I handle this?

Artes Liberales (Mathematics) 3 would either mean you have a score of 2 and a Mathematics specialty, or a score of 3 and some other specialty. Artes Liberales (Geometry) 4 would either be a score of 3 and a Geometry specialty or a score of 4 and some other specialty.

That really is wierd. Well in any instance you could just have them change the speciality as the reach the next score level passing from 3 to 4 (or 2 to 3 if you count the Spec in the final score as Fruny noted).

Yes, I was thinking about adding my own house rule (I usually dislike house rules) which says that whenever you raise your ability one level, you can also change your speciality.