So I'm coming around to believing that if I ever really want to understand the crazy modern parts of physics like quantum and GR, and for some reason I feel like I'm a Bad Person if I don't get around to this at some point in my life, it really would be a good idea to understand in my guts the modern point of view on how to do classical physics, which is all this lagrangian and hamiltonian stuff I last tried to take a stab at about a year ago. The lagrangian is finally feeling like second nature, but the hamiltonian formulation is still weird to me.
I went off on a bit of a Wikpedia tangent starting at this page and looking at the Poisson bracket a bit. Then I was like, wait a minute! Poisson was the guy who had as a student Michel Chasles, who taught Hubert A. Newton at Yale, who went on to advise E. H. Moore at the same institution, who moved to Chicago, ran the AMS for a while, and advised Oswald Veblen, first to give a correct proof of the Jordan Curve Theorem, who oversaw the ENIAC project, went to Princeton, and had a student name of Alonzo Church, who invented the lambda calculus, speculated that people aren't fundamentally more awesome than computers, and had a ridiculous number of famous (at least immediately recognizable if you're a logician or computer scientist) students, like Leon Henkin (of Henkin Sentence fame), Stephen Kleene (of Kleene Closure fame), John McCarthy (LISP), Michael Rabin, Hartley Rogers (wrote an excellent book on recursion theory), Dana Scott (invented domain theory), Raymond Smullyan (wrote several awesome books), and Alan Turing (of Turing machine fame).
Oh, and also Church advised Peter Andrews. Who supervised a PhD thesis at CMU, titled "Proof Transformations in Higher-Order Logic". By Frank Pfenning, my advisor. History is crazy!