What is combinatorics?

Igor Pak collected opinions from many experts. Some of these are very interesting, and in HW 5 I ask you to react to them. Feel free to discuss them here if you’d like. They are at: http://tinyurl.com/c8nvcfq 

Today in class I read part of Gian-Carlo Rota’s text — not because it is my favorite (though I like it!), but because it is timely for us right now, as we transition from “balls-into-boxes” questions into more “structural” combinatorics:

“Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven’t. You get the feeling that the result you have discovered is forever, because it’s concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing: you don’t get a feeling of having done an honest day’s work. Don’t get the wrong idea—combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.”


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