I was looking at The Mathematics Genealogy Project today. It's a project that kind of sounds like what it is - for (many) math professors, it lists their advisor and students, so you can trace up and down. And it's kind of astonishing.
I did a search on one of my professors, and this is what I found as I went up the chain of advisors (leaving out some initial steps for anonymity):
1. my Professor - no known students (makes sense; my school doesn't have graduate programs)
2. his advisor
3. the advisor's advisor, PhD from Indiana University, 1960.
4. Tracy Yerkes Thomas, Princeton, 1923. I knew I was getting into the past because the dissertation title was "The Geometry of Paths," which is just way too basic and short to be modern.
5. Oswald Veblen, U of Chicago, 1903.
6. E.H. Moore, Yale, 1885.
7. H.A. Newton, Yale, 1850.
8. Michel Chasles, École Polytechnique, 1814.
9. Simeon Denis Poisson, École Polytechnique, 1800.
10. Poisson had two advisors - Joseph Lagrange, and Pierre-Simon Laplace.
11. Lagrange's advisor was Euler, and Laplace's was d'Alembert.
12. Euler's advisor was Bernoulli.
Anyway...it's kind of amazing how few steps it takes to get from anyone to someone famous (even famous to me).
Another of my previous professors led me upward to Darboux (of Darboux sums fame, presumably) within a few clicks.
I got from one of Sally's professors to Isaac Newton! (It did take a few clicks, though.)