[ll55tt]

It is interesting to see this analysis about the progress a student sees throughout their career since the situation is fairly analogous in mathematics. Although I make the more audacious claim that a "standard" pure mathematics educations (at least in the U.S.) is not even geared toward preparing students adequately for graduate school and this is somewhat intentional. Throughout the hundreds of conversations I've had with professors in my department they have routinely espoused the opinion that all of their students are lazy, stupid, and do not deserve anything resembling a quality lecture. Many of the classes taught are simply a regurgitation of proofs in some textbook on the board with absolutely no intuition, examples, etc. given. If someone asks a question in an attempt to clarify a point, or even ask for basic help, I've found extraordinary pushback from faculty members. Typically this is done through moralizing the value of hard work, but what they end up actually saying is "get the hell off of my lawn!".

What's even more sad is many of the students hold the blind belief that the school will provide them with a quality education, but in reality the professors look to cut corners at every possible step. The students who then go on to accelerate their own education are generally looked down upon as well, unless of course they act as propaganda pieces as well and make sure not to go too far so that the professors don't look bad.

It's a depressing situation which will only be remedied by figuring out how to democratize mathematics education completely. Unfortunately, I've only seen such efforts at extraordinarily high levels so that only beginning researchers who have been lucky enough to get advisors as a top 10 university will be able to readily access these materials.