I am thinking of ways,how one(who is not a mathematician, but wants to know what's going on in the field of mathematics) can properly read Princeton companion to mathematics to make sense of it. I think first one should read part 3(which has mathematical concepts,which are briefly discussed in part 1 and 2),then part 2 and part 1 and then part 5(which has theorems and problems which are discussed briefly in part 4) and then part 4 and then parts 7,8 and 9 cover to cover. I think that's the right way to read this book.
Any suggestions?(I may be completely wrong)