@Charles Rezk A related question -- who first realized that K(G,n) could be characterized by its homotopy groups? After a quick look (probably overly-quick) at Eilenberg-MacLane's original papers, I'm not sure they knew the homotopy of K(G,n)!

Sorry if this is off-topic, but I noticed today that on Wikipedia, "homotopy theory" redirects to "homotopy," which is about homotopies between functions and doesn't have much to say about homotopy theory. This seems a little weird to me

(for comparison, Riemannian geometry, symplectic geometry, and complex geometry all have their own articles, distinct from Riemannian manifolds, symplectic manifolds, and complex manifolds, respectively)

@ArunDebray i think this isn't such a terrible oversight -- they're just leaving it as an exercise to the reader to deduce all of the existing literature on homotopy theory from that one definition