This is really a tough one. My opinion is no - the sweat is the learning. Skipping the problems would just lead to knowing a lot about math, without actually knowing any math.

On the other hand, it's tempting - and in the Real World (tm), people do just plug their giant, buck-nasty equations into Mathematica and avoid doing all the book-keeping.

I guess the question is: should pilots all just train on auto-pilot, while having only a conceptual understanding of what piloting is about? Or should they learn to pilot manually first, and then use the auto-pilot judiciously? There are legitimate points going both ways - but I vote for the 2nd.

Cohesion is a problem with xeroxed articles. Not to say it isn't with most textbooks, but it can be one of their primary goals, whereas the primary goal of an article is to disseminate a set of ideas in as efficient a way as possible, with some assumptions about prior knowledge of the reader.

I remember sweating through problem after problem in calculus so I could do problem after problem on the tests.

So did I. Part of internalizing the fundamentals of a subject is working through exercises that depend on those fundamentals. You don't get that when something else is doing the work for you. Learning isn't easy, and we need to get over the desire to want to make it so.