My Mathematical Lineage


I am one of 54 siblings descended from Peter Lax. I am a Kleinian through Hilbert. Going back further, one can argue with somewhat less certainty that I am a Lagrangian through Klein. Tracing backwards, my lineage is Remarkably, Felix Klein seems to have been the sole habilitation student of each of his two advisors: The practice of having two advisors seems to have been fairly common in the 19th century. Plucker seems to have been the advisor while Lipschitz seems to have been the chief examiner. However Lipschitz seems to have taken on a larger role for Klein because Plucker died shortly thereafter.

In the early nineteenth century the notion of what constitutes proper academic credentials was in a formative stage. The record becomes spotty and even contradictory. Indeed, I could find no record of who was Plucker's advisor. The lineage of Lipschitz traces back through

Dirichlet has a complicated story. While Dirichlet was trained in Paris, in order to obtain a position in Germany he needed an habilitation. Although Dirichlet could easily submit an habilitation thesis, this was not allowed because he did not hold a doctorate, nor could he speak Latin, a requirement at the time. The problem was solved when the University of Cologne gave Dirichlet an honorary doctorate, thereby allowing him to submit his habilitation thesis to a special examining committee. Needless to say, this made his appointment quite controversial at the time. Moreover, it clouds his connection to Poisson and Fourier.

One of Poisson's students was Dirichlet, who had only three habilitation students: Eisenstein (1845), Kronecker (1845), and Lipschitz. Eisenstein seems to have had no students, while Kronecker had six students. Lipschitz only had one: Felix Klein, who had 52 students. One was Fredinand Lindemann, who had only five habilitation students. However, one of them was David Hilbert, who had 70 students! The most notable among them include Richard Courant, Hermann Weyl, Hugo Steinhaus, Erhard Schmidt, and Erich Hecke. The lines of Courant (through all of his 29 students ), Weyl (through Saunders MacLane), and Steinhaus (through most of the descendants of his five students ) lead to the United States.

Poisson's only other student was Michel Chasles (1814), who went to Yale where he advised only H.A. (Hubert Anson) Newton (1850). Newton had only two students (both in 1885 at Yale): Charles Little, who had no students, and E.H. (Eliakim Hastings) Moore, who became the first Mathematics Department chairman at the University of Chicago where he had 21 students. One of Moore's students was Oswald Veblen (1903). Jointly with Veblen, E.H. Moore also advised R.L. (Robert Lee) Moore (1905), who had 51 students. Another student of E.H. Moore was G.D. (George David) Birkhoff (1907), who had 46 students plus one well-known son (Garrett Birkhoff).

So the Lagrangian line seems for the most part to pass through Felix Klein and E.H. Moore. (Kronecker is the only other route.) The Kleinian and Moorian (?) lines were prolific. It seems that through these two routes, many American-trained mathematicians are Lagrangians!

Lagrange only had three students: Fourier, Poisson, and Giovanni Plana. In fact, Plana was also Fourier's only other student. Plana seems to have had no students. So the entire Lagrangian line seems to pass through Poisson. Poisson had only two students. However these students and their descendents played major roles in the development of mathematics in Germany and the United States. Lagrange was a student of

  • Leonhard Euler , 1707-1783

    who was a student of

  • Johann Bernoulii , 1667-1748

    who was a student of

  • Jacob Bernoulii , 1654-1705

    who was a student of

  • Gottfried Wilhelm Leibniz , 1646-1716

    I had fun putting this page together with the help of Dave Levermore, the websites at the Mathematics Genealogy Project (Minnesota State University, Mankato) at "http://mathgenealogy.mnsu.edu" and the MacTutor History of Mathematics Archive (University of Saint Andrews, Scotland) at "http://www-groups.dcs.st-and.ac.uk/~history". I welcome any comments or corrections.