The Mathematics Genealogy Project allows you to track a mathematician’s students, their students, and so on. For example, I am listed with 75 descendants, and Isaac Newton has 21507.
But unlike me, Newton nearly died out! If the Project’s data are correct, he was followed by eight generations consisting each of one man having just one student, for 150 years (from Smith through Sedgwick, to be exact):
Isaac Newton, Cambridge 1668
Roger Cotes, Cambridge 1706
Robert Smith, Cambridge 1715
Walter Taylor, Cambridge 1723
Stephen Whisson, Cambridge 1742
Thomas Postlethwaite, Cambridge 1756
Thomas Jones, Cambridge 1782
Adam Sedgwick, Cambridge 1811
William Hopkins, Cambridge 1830
And then suddenly, we get the Cambrian explosion. As British science flourished in the Victorian era, William Hopkins had students Cayley, Galton, Maxwell, Routh, Stokes, Thomson, and Todhunter, all famous names still and all with hundreds or thousands of descendants of their own. It is to these that Newton owes his 20,000 or so descendants alive today.
If any link in the chain had been missing, Newton would have had no descendants in the present. Of course his actual impact would have been undiminished, so this is a reminder that there are more forms of inheritance than genetic.
[8 August 2021]
trefethendotnet 
I think this is a quirk of the math genealogy website. In modern times, they list Ph.D. students, but the information on the site goes back way before the Ph.D. degree even existed, and some countries (like the UK) adopted the degree later than others. In particular, just about all the pre-1900 information for UK math genealogies has nothing to do with doctoral degrees. Instead, it’s a random collection of information about who was whose mentor or protege. This is neither well defined nor well documented in general, so the records end up rather sparse. Basically, biographies of famous people will mention a few key mentors or students, but there’s pretty much no record for those less famous. This means whatever ends up in the site will be rather sparse and centered around famous people, maybe with a few less famous people filling in the gaps.
I’m guessing that the path from Newton to the Victorians is largely artificial. Some Victorian scientist was curious about their connection to Newton, and researched a plausible path connecting them. They mentioned it in a memoir, and this information eventually made it to the math genealogy website. I imagine the path is real in the sense that the people in each link genuinely knew each other and had the level of seniority the path represents. However, I’m skeptical about how meaningful it is. I doubt that each person on the path would name the person above them as their primary or most important teacher or mentor, and there’s no way they’d all identify the person below them as their only student.