Since I last looked at it, the Mathematics Genealogy Project has added a fair amount of interesting information. I had not been aware, for instance, that Norbert Wiener is my great-great academic grandfather - his student's student was my advisor's advisor. Wiener's doctoral work was in philosophy, so through him my work is related to a long line of continental thought. The link to Kant himself is a little forced - not all the contributions in the site follow the highest standards of academic precision - and in any case the connection does not get me excited about continental philosophers. The imaginative reader may try to imagine a Freudian interpretation of my efforts to put some sense into non-stochastic estimation in non-Euclidean spaces.
More interesting is the link to a long line of scholars down to the Italian Renaissance and earlier, which appears to be shared by an overwhelming majority of contemporary scientists. The earliest person on the database was Georgios Gemistos Plethon, and without attempting to check all the intermediate links, I managed to add one more generation by finding about his late Byzantine Empire "advisers" in the book "Byzantine philosophy and its ancient sources," by Katerina Ierodiakonou (Oxford; New York: Clarendon Press, 2002).
The relevant part about Plethon's advisor Elissaeus, sometimes also called Judaeus, is in the chapter by Polymnia Athanassiadi, pages 248 to 250. George Gemistos (Plethon) had as tutor Demetrios Kydones, a pupil of Nicholas Kabasilas (thinking carefully, I would not use the word adviser to characterize their relationship - teacher would be better). As a young man Gemistos traveled to Adrianople (Turkish Edirne) to study with Elissaeus Judaeus, a mysterious figure who may or may not have been a Jew despite the epithet, but apparently managed to get himself burned at the stake anyhow. Gemistos studied with Elissaeus as a live-in pupil, in a relationship that I judge can be appropriately called advisor-advisee. Much later in his life he wrote Nomoi ("Book of Laws"), but it is clear that this work was based on his studies of Zoroastrianism with Elissaeus. I judge that it can properly be called his thesis advised by Elissaeus. As such it was considered by Gennadios Scholarios, the first Ottoman Patriarch of Constantinople, who burned most of the book after Plethon's death. I find it hard to give a date for the thesis, though the advisor-advisee relationship probably happened in the 1380s.
Though we would not recognize his line of work as that of a mathematician, Plethon did some astronomical calculations besides his now better-known philosophical work. He was highly regarded in Florentine Renaissance for his knowledge of Plato and ancient Greek philosophy, and as such occupies a rightful place in our mathematical genealogy. It would be interesting to extend the genealogical investigation down to the original Greeks, but I suspect that the Byzantine early Dark Ages will prove unsurmountable.