> there are two types of mathematics: cutting-edge stuff like this ,and then the stuff that fills textbooks, random arxiv pre-prints, etc that is more mundane

> there are two types of mathematics: cutting-edge stuff like this ,and then the stuff that fills textbooks, random arxiv pre-prints, etc that is more mundane I somewhat disagree. First: obviously, if you want to read really cutting edge stuff, in nearly all cases you have to read papers or preprints. On the other hand, there do exist various kinds of math books: in rough decreasing order of topicality and increasing order of understandability for "ordinary" mathematicians (i.e. not specialists in the respective field): - collections of recent research papers - research monographs - survey monographs/survey collections about some active research topic - textbooks for postdoctoral researchers - textbooks for gradudate students