Matthias sees Persington as a father figure. He's keenly aware of this void in his life because he never had a father and for a long time has been a father figure for his younger brothers and nephews, so he's often, consciously intentionally seeking a father.
Matthias wants to make him proud.
Persington sees potential and comes to see him as a son. Persington never had a family and is sort of a strange loner, open and friendly to everyone but attaching to no one. his attachment to Matthias is no more emotional than any of his attachments, he has no personal feelings for him, but more like a professional interest. it does not hurt him if Matthias hurts, but he's pleased when the boy does well, and supportive when he does not.
He's willing to take chances for him and invest his own time money resources reputation, but equally willing to kick him out if he screws up. Persington's love ad respect is more earned than a free gift, but Matthias merits it most of the time.
Persington also values him as a student hoping he can dream and expand he dream studies department, which he sees a soon to fail with Jonathan dying and Jason getting restless and not wanting to mentor students individually