This is certainly a matter of taste. I saw many prominent people everywhere praising TAOCP, but I was disappointed when I finally read the first three books some 10+ years ago. So much disappointed that I regret taking all the time to read it - not because they're bad books, but because I think that time would have been better spent learning things a different way.
What bothered me most is MIX. I think using a very low-level language to teach algorithms is a pretty bad choice. Algorithms are high-level concepts, and using an assembly-like language just distracts from those concepts; it requires you to solve so many micro-problems orthogonal to the real problem, and forces you to repeat yourself over and over. I prefer to implement abstract ideas in abstract code. Using MIX just causes suffering for no point.
I learned a lot about math from TAOCP (but I've never needed it for anything).
When the books were written, the target audience would all be writing programs in (very different) machine languages, so the “mix” he created of existing computer architectures was a good one (https://retrocomputing.stackexchange.com/a/18176). The specific MIX language is no longer similar to present-day machines (self-modifying code is out of style, for instance), which is why he came up with "MMIX" and there's a book (“The MMIX supplement” by Martin Ruckert, but carefully proofread by Knuth) with the MMIX equivalents of all the MIX programs.
But in any case the algorithms are taught in English not MIX; the MIX programs are only a very tiny part of the books (https://news.ycombinator.com/item?id=14520230 — the 3000+ pages of Vols 1–4A have only 90 assembly programs), used only when the low-level details are actually relevant. So they can be skipped if one is not interested in them.
For my argument, MMIX is not an improvement because it's still a low-level assembly language. True, you can simply skip over the MIX/MMIX source code, but that doesn't help me to like TAOCP. For me, (abstract) source code is the primary source of understanding a concept, and English text is just an accompanying explanation, not the other way round.
Your comments put TAOCP in a historical context. Yes, for the time, TAOCP was a huge achievement and it is a magnificient work. History is interesting, but the question here is about today, and I don't think it's the best way to learn the stuff today. (Again, just my opinion, there's no right and no wrong here.)
Yeah as you say it's just opinion/preference, but re:
> source code is the primary source of understanding a concept, and English text is just an accompanying explanation, not the other way round
note that most algorithms in TAOCP are only described in English (pseudocode), no (MIX) source code. (So if you want source code as primary you simply won't find it… but then again, a typical algorithm textbook like CLRS also would have only pseudocode).
The TAOCP pseudocode is also in a unique style that's not similar to modern programming languages — e.g. here's a note that Knuth wrote just earlier this year: https://cs.stanford.edu/~knuth/papers/cvm-note.pdf explaining (and generalizing/correcting) in his own style, the algorithm from a recent paper (https://arxiv.org/pdf/2301.10191v1.pdf): compare how the algorithm is described in Knuth (first page) vs the paper (second page): Knuth is simultaneously more high-level and more low-level (and also uses “goto” rather than “structured programming” for-loops, about which heretical preference of his I can write a long essay some other time :D).
It is possible to have different opinions about which one is the best way to learn the stuff today, but clearly Knuth rewrote it in his style because he thought it was better. ;)
