J. Michael Steele is teaching Statistics 530 (first-semester graduate measure-theoretic probability) at Penn this semester. (I’ve taken classes from him, and I took this class, but he wasn’t teaching it.) Embedded in his course web page is an interesting aside on how mathematics gets done:
GRaVy: This stands for “Generalizations”, “Refinements” and “Variations” and this one word represents the way that 80% of day-to-day mathematics (and mathematical science, including statistics and computer science) gets created. The paradigm needs no modification in mathematical statistics, and the story for applied statistics requires only small modification.
This also includes an implicit list of “genres” of mathematical papers (which is incompletely written; I assume that this picks up on something said in class): the “Generalizations”, “Refinements” and “Variations” above, “Greenfield Projects”, “P+Q=R”, “synthesis” or “survey”, and the “Pollution Piece” (which pollutes the literature). What other genres are there?
Also from Steele: videos of ten lectures on “Probability Theory and Combinatorial Optimization” – I haven’t watched but I assume these are related to his little book of the same title, and I can’t resist linking to Steele’s random rants.