Are they considered to have Artes Liberales as their Theory skill? After all, they use it to boost their Lab Totals. But can it be used for other Theory purposes, or would they need a new Ability entirely (and still get to add Artes Liberales to their lab totals)?
Interesting Question. Based on a passage in Typical Learned Magician Abilities, I'm lead to believe that Mathematici use Latin as their MT for Verbal Charms & Artes Liberales for Amulets and Chartae, but this is completely unofficial. It works well enough in practice though...
EDIT: Check the final paragraph of the Magic section of the Cunning-Folk alternate tradition... It doesn't exactly explain what to do, but seems to suggest LA being treated as MT...
In various instances I would use AL as substitute for MT, especially in order to have an upper limit for Form & Material Boni in the lab. But given the description of learned magic as a rather unorganized tradition, I would say it still lacks a magic theory of its own, meaning that no learned magician can really make any other breakthroughs or improve his lab unless he develops such a theoretical framework first. I am not sure how I would handle lab totals afterwards, probably I'd go for including both abilities (giving the tradition a minor boost in power) or for giving the character a choice, which abilitiy to use, unless it is a breakthrough research project or something in that style.
This would fit nicely with the impression I got of learned magic: Among the hedge traditions presented it seems to be the youngest tradition, even so it is based on older lore, and it has the potential to become the most challenging alternative to hermetic theory. The later still has the advantage of centuries of research and refinement and (for political reasons) the nearly exclusive access to the Parma Magica, but the academics might stand a chance to close the gap, especially as they live and work in a structure that allows for cooperation and exchange of research and also breeds people who are likely to undertake such an endeavour.
But all this is just my interpretation, as far as I know there is no definite canon answer, and even my own learned Magician character might have to live with a different ruling, as I am not the SG in the saga.
Alexios ex Miscellanea
Actually, that reminds me strongly of Integrating Aristotelian/Platonic thought into Magic Theory, which permits Artes LIberales to act as a Lab Total boost for Hermetic Magi, so that actually works perfectly.
I agree completely with Alexios's summary. I thought this was expressed explicitly in the text, but it's been a while since I read it. The Mathematici are a young tradition, relatively speaking, and the in-period, real-life texts on this type of amulet/charm magic was devoid of analysis similar to what one would expect from a Magic Theory equivalent. It was not until later in history that meta-magic was discussed by practitioners of this of this type of magic in historical Europe. The texts that did exist are very functional in nature and are little more than lists of spells.