This is just one anecdote here: I am a physics graduate of a state school. I thought my physics program was excellent. I have since studied some additional m

This is just one anecdote here: I am a physics graduate of a state school. I thought my physics program was excellent. I have since studied some additional math from MIT's OpenCourseWare and some machine-learning classes from Coursera. In my opinion, the quality of the classes are roughly the same. But what I have noticed is that a lot more of the original research comes from the big-name universities. (I suppose that professors compete to go where the most funding is, and also where they can get access to the best grad students.) If I wanted to get a PhD in machine-learning, I'd most want to go to U.Toronto or UCL (University College London). Because that's where the action is. As a graduate student, if I'm studying the xyz algorithm, I might be learning it from the guy who invented the xyz algorithm. (As well as surrounded by grad students and post-docs who are studying the next version of the xyz algorithm.) I suppose that, in the STEM fields, there's a trickle-down effect to the undergrads. Surely there's more energy in studying something right where it's being invented.