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.
God plays dice 
Do you know the origin of the name “Greenfield Project”? It wouldn’t happen to be this Greenfield by any chance? http://www.math.rutgers.edu/~greenfie/ My recollection is that he did have a bit of a habit of doing this (I think I have three problems that are open and that he gave me because “You’re an algebraist. It has polynomials. Go algebra it!” or the like.
Can you write a post where you elaborate more on these? What makes a pollution piece a pollution piece? What the heck is a Greenfield Project, I’ve never heard of it. What do you mean by P+Q=R? Can you really sleep with yourself at night after casually brushing aside so many papers as “synthesis” (throughout history, many of the greatest works of science would arguably fall into that broad genre)?
Charlie: I think it’s “Greenfield” like the two words “green field”. Note that Steele spells it with a lowercase “g” when it’s not at the beginning of a sentence. Anonymous: essentially I’d be rewriting what Steele’s written, so go take a look there.
Ahh, ok. I was curious because said professor at Rutgers had a habit of handing out problems to people that came out of nowhere.
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