I've seen in a lot of questions about "which textbook to use for intro analysis", and inevitably Rudin's Principles of Mathematical Analysis comes up, with the (almost cliche) rejoinder that "today's incoming US freshmen cannot handle Rudin." [emphasis mine].
As a product of the crumbling edifice of pre-college US mathematics education, I can attest that I was not well versed in methods of proof, and I found geometry, which was proof based, quite awful when I took it (I'm referring to the experience, not the subject matter). My experience certainly did not endear me to proofs.
My question is...was there a generation of high school students in the US who could jump right into Rudin without "a bloodbath" (to quote an MAA review of Rudin's PMA)? If so, was it the "new math" era in the 1960's that put the first cracks in our math system?
Is it the case that the more widespread use of math in our society led to a need to "democratize" it, pulling it out of its rigorous, ivory tower to a level that is more focused on applications, of which there were becoming many. Was this "industrialization" of math perhaps the real issue?
Conjectures on my part, but I keep hearing about how "un-prepared" my generation is, so I'd like to know the genesis of this statement (besides the usual "..in my days we walked to school with newspaper on our feet.." sentiments).