My advisor's name is Nilotpal Chakravarti. He worked under Michael John Best. Best's advisor was Robert Thomas Glassey, whose advisor was Walter Alexander Strauss, whose advisor was Irving Ezra Segal, who in turn had C. Einar Hille as his advisor. Thomas Saaty also worked under Hille's supervision. Hille's advisor was Marcel Riesz, who in turn had Leopold Fejér as his advisor. John von Neumann was another of Fejér's students. Fejér's advisor was the famous Hermann Amandus Schwarz. Schwarz had two advisors, Ernst Eduard Kummer and Karl Theodor Wilhelm Weierstrass, the father of modern analysis. (Georg Cantor also studied under Kummer.)
Kummer was guided by Heinrich Ferdinand Scherk, who was guided by Friedrich Wilhelm Bessel. (Remember Bessel functions?) Weierstrass had Christoph Gudermann as his advisor.
Carl Friedrich Gauss (who among other things lent his name to the Gaussian distribution) guided both Bessel and Gudermann. He also guided Georg Riemann. Gauss studied under Johann Freidrich Pfaff, who in turn was guided by Abraham Gotthelf Kaestner. Kaestner worked under Christian August Hausen, who was guided by Johann Christoph Wichmannshausen. Wichmannshausen's advisor was Otto Mencke, who along with Leibniz started the first German scientific journal Acta Eruditorum. Mencke was a professor of Morals and Politics in the Philosophy department of the university at Leipzig.
I have not been able to find out who Mencke studied under.