In Germany they have the concept of a Doktorvater (or Doktormutter obviously). It translates to “doctor-father” or “doctor-mother” and refers to your Ph.D. thesis advisor. It is quite common for someone to mention that so-and-so was their Doktorvater. In my case, I have two Doktorväter
Of course, the analogy of family can be taken further, if two people share a Doctorvater, then they would be Doctorgeschwestern (doctor-siblings). In fact, you could create an entire doctor-geneology based on who are the descendants of whom.
In the case of mathematics, it’s already been done. You can browse the Mathematics Genealogy Project and see which mathematicians were advisors to which students and who their advisors were and so on.
For a couple of extreme cases, we can see C.-C. Jay Kuo and Manuel Bryennios. C.-C. Jay Kuo has the most students of any advisor in the database, 125 at current count. Manuel Bryennios has the most descendants in the database, with 120,596 but only one registered student from 1315.
As you can see, I’ve got a somewhat sordid family history, where one of my Doktorväter is also my Doktorbruder, but we can skip over that.