The best way to view Knuth's project with these volumes is that takes in all published computer science on a particular topic, digests it, and outputs into the books some sort of "summary" of the field, or whatever he considers the most important bits, but still organized as readable/learnable textbook material, and in the way he thinks makes for best exposition. (In other words: he's doing his best to explain, and his best is very good indeed. Often Knuth's writing is clearer than the original papers, and a lot more fun.)
I read the volumes roughly 30mins a day, and try most of the exercises. Like the above linked blog post I at least attempt to just understand the question on the M[40]+ exercises which still can teach you something by merely understanding why it's a difficult problem.
Edit: sorry, misread your comment, thought you were wondering what was Knuth's opinion. Still, I'll leave the link here, since it's a great read nonetheless
> Donald Knuth: (Retired from Stanford) It will be solved by either 2048 or 4096. I am currently somewhat pessimistic. The outcome will be the truly worst case scenario: namely that someone will prove “P=NP because there are only finitely many obstructions to the opposite hypothesis”; hence there will exists a polynomial time solution to SAT but we will never know its complexity!
