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The Old Lineage, often simply referred to as "the Lineage", is a term used to describe the continuation from pre-Mathic times of a theoric tradition descending from Metekoranes through Thelenes and Protas that sought a deeper understanding of the Hylaean Theoric World. Having an origin prior to Cartas and her Discipline, the theors of the Lineage persisted through the Old Mathic Age, Rebirth, Praxic Age and Reconstitution in an unbroken chain of mentor and fid, through Halikaarn, Evenedric, Erasmas and Uthentine (founders of Complex Protism) and down to the present time in which the novel Anathem is set.

Associated with the Old Lineage is the non-trivial tiling problem known as the Teglon which, it was believed, could not be solved by reason alone, but by upsight into the Hylaean Theoric World. As the HTW is seen by followers of the Sphenic tradition as superstition verging on Deolatry, the Lineage and theors associated with it are viewed mistrustfully by some avout. Among them persists a rumor that the Old Lineage conspires to diguise its religious aims as valid theorical discourse while violating the Cartasian Discipline in pursuit of its shadowy aims.

The Old Lineage has acquired custodianship of the Old Mathic complex at Elkhazg where the Teglon problem was pursued after the fall of Baz, as well as the island of Ecba where, at the Millenial Convox of 3000 AR the Edharian Order established an archeological effort to excavate the Temple of Orithena where Metekoranes taught and where the Teglon problem was first propounded. Existing as it does partially outside the strictly supervised Mathic Society, the Orithena site offered a refuge to Orolo after he was Thrown back, and was the location of the initial attempt of contact between the Fulcrum and Arbre at the Visitation of Orithena.

During the treaty proceedings on the Daban Urnud, Magnath Foral, the Heritor of Elkhazg speaks of himself as aligned with the Lineage, implying the involvement of his relative Ignetha Foral as well, confirming that the Lineage maintains ties and exerts its efforts both within and without Mathic society.